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Physics Reports 422 (2005) 65–117www.elsevier.com/locate/physrep

Exchange bias in nanostructures

J. Noguésa,∗, J. Sorta, V. Langlaisb, V. Skumryeva, S. Suriñachb, J.S. Muñozb, M.D. Barób

aInstitució Catalana de Recerca i Estudis Avançats (ICREA) and Departament de Física, Universitat Autònoma de Barcelona,08193 Bellaterra, Spain

bDepartament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain

Accepted 18 August 2005

editor: G.E.W. Bauer

Abstract

The phenomenology of exchange bias and related effects in nanostructures is reviewed. The types of systems discussed include:lithographically fabricated ferromagnetic (FM)—antiferromagnetic (AFM) nanostructures, chemically surface modified FM par-ticles, FM particles embedded in an AFM matrix, controlled core–shell particles, nanoparticles with surface effects and coupledAFM–AFM systems. The main applications of exchange biased nanostructures are summarized. Finally, the implications of thenanometer dimensions on some of the existing exchange bias theories are briefly discussed.© 2005 Published by Elsevier B.V.

PACS: 75.75.+a; 75.70.Cn; 75.50.Ee; 75.60.Cn

Keywords: Exchange bias; Magnetic nanostructures; Antiferromagnetic materials; Magnetic domains

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662. Basic phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673. Nanostructured systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.1. Lithographically fabricated nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.1.1. Patterned wires, dots, rings, etc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.1.2. Ion irradiated structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793.1.3. Pseudo-ordered structures—“Networks” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.2. Surface chemically modified nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.3. FM nanoparticles embedded in AFM matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.3.1. Co-evaporation of FM–AFM materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.3.2. Mechanical milling of FM–AFM materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.3.3. Incomplete reactive evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863.3.4. Segregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.3.5. Partial reduction or overoxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.3.6. Coupled ferri–AFM nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.4. Controlled core–shell nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

∗ Corresponding author. Tel.: +34 93 5813851; fax: + 34 93 5811350.E-mail address: [email protected] (J. Nogués).

0370-1573/$ - see front matter © 2005 Published by Elsevier B.V.doi:10.1016/j.physrep.2005.08.004

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66 J. Nogués et al. / Physics Reports 422 (2005) 65 –117

3.5. Surface effects (AFM, Ferri, FM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.6. Coupled AFM–AFM systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4. Applications of exchange biased nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925. Theoretical implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.1. General exchange bias models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.1.1. Macroscopic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.1.2. Mesoscopic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 965.1.3. Microscopic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.2. Characteristic length scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985.3. Consequences of lateral size reduction on standard models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005.4. Models specific for exchange biased nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

1. Introduction

Fine particles were the first type of system where exchange bias was reported. Meiklejohn and Bean observed thatfield cooled, partially oxidized, Co particles exhibited hysteresis loops displaced along the magnetic field axis [1].They attributed this phenomenon to the exchange interaction at the interface between the ferromagnetic (FM) Cocore and the antiferromagnetic (AFM) CoO shell [2,3]. Although there has been some research in exchange bias innanoparticles in the last decades, the bulk of exchange bias research has focused mainly on thin film systems [4–14].This was initially due to: (i) the possibility of an increased number of FM–AFM combinations in thin films. Note thatin fine particles, traditionally, one could only carry out a chemical treatment of the surface (e.g., oxidation, nitration orsulfation) in order to create reacted shells that would be AFM (e.g., CoO, NiO, CoN or FeS); (ii) the greater controlof the FM–AFM interface that thin films allow, in which the microstructure of both the AFM and FM layers (e.g.,grain size, orientation, crystalline quality) and, to some extent, the interface (e.g., roughness, spin structure or interfacelayers) can be controlled; and finally, (iii) the fundamental role of exchange bias in spin valve and tunneling devices[12–46], which has triggered the explosive increase of research in FM–AFM thin film systems. Nevertheless, the recentadvances in magnetic fine particle production [47–62] and the fabrication of magnetic nanostructures by lithographicmethods[63–78] have propelled a renewed interest in nanostructures in general and exchange biased ones in particular.Moreover, the industrial demand to systematically reduce the size of spin valve and other exchange bias based devicesis also fueling new research in lithographically fabricated exchange biased nanostructures. From the more basic pointof view, it is well known that a range of novel properties arise, in both FM and AFM materials, as the size is reduced(e.g., increased importance of surface effects, changes in the magnetization reversal modes or superparamagnetism)[47–78], hence it is appealing to investigate how does size reduction affect FM–AFM coupled systems.Additionally, theinterest in proximity effects, which have been shown to be enhanced in nanostructured systems, because an appreciablefraction of the electronic wave function resides outside the physical extension of the nanostructure, are also generatingan increased interest in FM–AFM nanostructures [63,79].

The study of FM–AFM exchange interactions in fine particle systems has recently found interesting applicationsto improve the performance of permanent magnetic materials (by means of an enhancement of the coercivity whichtypically accompanies the hysteresis loop shift) [80,81] or to combat the superparamagnetic limit in magnetic recordingmedia [82,83]. Hence, in fine particle systems exchange bias studies may be particularly interesting not only for theloop shift itself, but also for other exchange bias related phenomena.

It is noteworthy that throughout this review we will use the term “nanostructured” rather loosely, referring to structureswith at least one of their lateral dimensions in the range from a few nm to hundreds of nm (up to 1 �m).

In this review, after the introduction (Section 1) we summarize the basic phenomenology of exchange bias, mainlyfocusing on nanostructures (Section 2). Subsequently, we discuss different kinds of nanostructured systems whereexchange bias has been studied, including artificial nanostructures (e.g., lithographically fabricated nanostructures)(Section 3.1), chemical surface modification (e.g., oxidation, nitration or sulfation) (Section 3.2), FM nanoparti-cles embedded in an AFM matrix (Section 3.3), controlled core–shell nanoparticles (Section 3.4), surface effects(e.g., ferromagnetic, ferrimagnetic or antiferromagnetic particles with magnetically disordered surfaces) (Section 3.5)

J. Nogués et al. / Physics Reports 422 (2005) 65 –117 67

and coupled AFM–AFM systems (Section 3.6). We finish with the applications of exchange biased nano-structures (Section 4) and the implications of the nanometer dimensions on some of the existing exchange biastheories (Section 5).

2. Basic phenomenology

The phenomenology of exchange bias has been extensively described in the different reviews published on the subject[3–14]. The main tell-tale indication of the existence of exchange bias is the shift of the hysteresis loop, HE, along thefield axis after field cooling from above the Néel temperature, TN, of the AFM (and below the Curie temperature, TC,of the FM) in materials composed of FM–AFM interfaces [Fig. 1(a)]. Accompanying the loop shift are other relatedproperties. Probably the most common in nanostructures is an increase of the coercivity, HC, below TN after a fieldcooling procedure [Fig. 1(b)].

Another closely related effect often studied in nanoparticles is the unidirectional anisotropy. Namely, exchange biasedstructures exhibit a new type of anisotropy with a Kud cos(�) angular dependence of the magnetic torque rather thanKua sin(2�), as the common uniaxial anisotropy (where � is the angle between the magnetization and the anisotropyaxis and Kud and Kua are the unidirectional and FM uniaxial anisotropy constants, respectively). Shown in Fig. 1(c)is the sketch of the torque magnetometry, �, expected for both kinds of anisotropies. As can be seen in the figure, thepresence of this new unidirectional anisotropy implies that the magnetization instead of having two stable positions(zero �, i.e., minimum energy), as in the case for uniaxial anisotropy, it has only one.

Fig. 1. Schematic representation of the main effects induced by the FM–AFM exchange coupling, i.e., (a) loop shift, (b) coercivity enhancement and(c) unidirectional anisotropy.


Fig. 2. Schematic diagram of the spin configurations of a FM–AFM couple before and after the field cooling procedure [4].

Other effects such as asymmetric reversal [84–92], high-order anisotropies [93–95], perpendicular coupling [96–98]or rotatable anisotropies [97–101] are often observed in thin film systems, although they have not been systematicallystudied in nanostructures.

The physical origin of exchange bias is rather generally accepted to be the exchange coupling between the AFM andFM components at the interface. The microscopic way this coupling translates into exchange bias is more controversialand many models have been proposed to explain it [6,7,12] (see Section 5 for more details). Yet, the intuitive view ofexchange bias is rather simple [4–14]. Indeed, the exchange bias phenomena can be described in terms of an alignmentof the AFM spins at the FM–AFM interface parallel to the FM spins occurring during the field cooling procedure.The coupling between the AFM and FM spins at the interface exerts an additional torque on the FM spins, whichthe external field has to overcome. Within this simple intuitive model, two different opposite limiting cases can bepredicted, depending on the strength of the AFM magnetic anisotropy. If the AFM anisotropy is large, one should onlyobserve a shift of the hysteresis loop, while for small AFM anisotropies, the only observed effect should be a coercivityenhancement (without any loop shift) (see Section 5 for more details). Nevertheless, in general, both effects can beobserved simultaneously, due to, for example, structural defects or grain size distribution, which bring about localvariations of the AFM anisotropy.

Shown in Fig. 2 are the schematic spin configurations in the FM and the AFM layers, before and after a field coolingprocess [4]. If a magnetic field is applied at a temperature T so that TN < T < TC and the field is large enough, all thespins in the FM will align parallel to H , i.e., the FM will be saturated. Meanwhile, the spins in the AFM will remainrandom, since T > TN. When the FM–AFM couple is cooled through TN, the magnetic order in the AFM is set up.During the cooling, it is likely that, at the FM–AFM interface, the spins of both components interact with each other. Ifso, the first layer of spins in the AFM will tend to align parallel to the spins in the FM (assuming FM interaction at theinterface), while the successive remaining layers in the AFM will orient antiparallel to each other, so as to give a zeronet magnetization in the AFM. Note that growing or synthesizing the AFM in the presence of a magnetic field can be,in some cases, considered as equivalent to a “field cooling” procedure, especially if the FM is already present duringthe growth [4–14], i.e., the net result is to align the AFM interface spins to the field direction and hence to the FMspins. Moreover, applying large fields, i.e., above the AFM critical fields [102], could, in principle, be used to induceexchange bias [103–105].

The intuitive spin configuration, for a FM–AFM couple, is shown schematically in Fig. 3 for different stages of ahysteresis loop [4]. After the field cooling process, the spins in both the FM and the AFM lie parallel to each otherat the interface [Fig. 3(a)]. When the magnetic field is reversed, the spins in the FM start to rotate. However, if theAFM anisotropy, KAFM, is large enough, as is often the case, the spins in the AFM will remain fixed. Consequently,due to the interface coupling, they will exert a microscopic torque to the spins in the FM, trying to keep them in their


Fig. 3. Schematic diagram of the spin configurations of an FM–AFM couple at the different stages of a shifted hysteresis loop for a system withlarge KAFM [4].

original position [Fig. 3(b)]. Thus, the magnetic field required to completely reverse the magnetization in the FM willbe higher than if the FM was not coupled to an AFM, i.e., an extra magnetic field will be required to overcome themicroscopic torque exerted by the spins in the AFM. As a result, the coercive field in the negative field branch increases[Fig. 3(c)]. Conversely, when the magnetic field is reversed back to positive values, the rotation of spins in the FM willbe easier than in an uncoupled FM, since the interaction with the spins in the AFM will now favor the magnetizationreversal, i.e., the AFM will exert a microscopic torque in the same direction as the applied magnetic field [Fig. 3(d)].Therefore, the coercive field in the positive field branch will be reduced. The net effect will be a shift of the hysteresisloop along the magnetic field axis, HE. Thus, the spins in the FM have only one stable configuration (i.e., unidirectionalanisotropy).

For the low AFM anisotropy case, the situation is different (see Fig. 4). As in the previous case, after the field cooling,the spins in both layers are aligned in the same direction [Fig. 4(a)]. In this case, when the magnetic field is reversedand the spins in the FM start to rotate, if the AFM anisotropy is exceedingly low, the spins in the AFM can be draggedby the spins in the FM [Fig. 4(b)]. In other words, it will be energetically more favorable that the spins in both the FMand the AFM rotate together. The extra energy associated with the creation of an irreversible twist in the AFM structuretranslates into an enhanced coercivity. An analogous behavior is observed after saturating in negative fields [Fig. 4(c)and (d)]. In this case, although no loop shift is observed, the magnetic field required to reverse magnetizations in bothpositive and negative branches becomes larger, i.e., the hysteresis loop becomes broader.

When the temperature approaches TN, the AFM anisotropy decreases, thus a system which belonged to the firstcategory (i.e., large AFM anisotropy) tends to transform into the second category (i.e., small AFM anisotropy) for atemperature range close to TN. This effect sometimes results in interesting phenomena, such as an enhancement of HCclose to TN [4,106].

Although this simple description gives a good basic view of the exchange bias phenomenology it should be takenwith caution. First, this model predicts a loop shift which is often several orders of magnitude larger than experimentallyobserved in most thin film systems [4–14], although in some cases better agreement is found [107–110]. Second, thisintuitive model neglects many parameters which have been shown to be important in exchange bias, such as AFMor FM domains, interface roughness or AFM spin structure, to mention a few. Third, it has also been experimentally


Fig. 4. Schematic diagram of the spin configurations of a FM–AFM bilayer, at the different stages for a system with small KAFM.

proven that many of the logical consequences of this model, e.g., HE = 0 for compensated AFM surfaces (i.e., zeronet AFM surface moment) [110–115], HE always negative [116–121] or monotonic dependence of HE with roughness[122–128] are not necessarily true. Finally, this approach is, strictly speaking, only valid for thin films since the spinstructure for certain kinds of nanostructures could be increasingly complex.

Note that, so far, we have mainly discussed exchange bias in terms of FM–AFM couples. On the other hand,ferrimagnetic (ferri-) or spin glass materials forming part of an exchange coupling system can also exhibit exchangebias effects. Moreover, due to their magnetic structure [129] both ferrimagnets and spin glasses can play the role of theantiferromagnet or ferromagnet in exchange biased systems.

In order to compare different types of exchange bias systems often rather than using the loop shift itself, a couplingenergy, E = HEMSVFM (where MS is the saturation magnetization and VFM is the volume of the ferromagnet), isevaluated instead. If this energy is normalized to the coupling area, A, we obtain EA = E/A = HEMSVFM/A. For abilayer system this energy is expressed as, EA = HEMStFM (where tFM is the thickness of the FM layer). Even though,for a spherical nanoparticle embedded inAFM matrix it becomes EA=HEMSdFM/6 [i.e., EA=HEMS(4�r3/3)/(4�r2)].Other microstructures have their own expression for the coupling energy per area. However, this simple formula appearsnot to be completely accurate, since it has been demonstrated in thin film systems that EA actually depends on MS[130–132]. Consequently, in this review loop shifts, HE, rather than EA will be used to denote exchange coupling.

As it has become evident in the preceding paragraphs the existence of exchange bias effects are closely linked to themagnetic order of the AFM. Hence, as the temperature is increased and the AFM Néel temperature, TN, is reached theexchange bias effects disappear. Conversely, it is often observed, especially in nanostructured systems, that exchangebias effects disappear at temperatures far below TN. The temperature at which the exchange bias field becomes zero,HE = 0, is usually denoted as blocking temperature, TB. Although the blocking temperature of exchange bias hasbeen correlated with finite size effects in the antiferromagnet [133–142] (i.e., the decrease of TN due to size reduction[143,144]), it has been recently demonstrated in thin films that this effect can be rather complex [145,146]. In highquality thin film systems with thick AFM layers TB ≈ TN is often observed, while other systems with very thin orpolycrystalline AFM layers tend to have TB>TN (e.g., a decrease of TB with smaller grain size has been reported forsome systems [147,148]). This effect can be especially important in nanoparticle systems (Sections 3.2 and 3.5) since


the shell is usually very thin (a few nm) and often polycrystalline. Nonetheless, the effect of the microstructure on TBcan be more effectively controlled in lithographically fabricated nanostructures (Section 3.1), which should basicallybehave as thin film systems from the TB point of view for a rather large range of sizes. Note that in some cases in thinfilms exchange bias effects have been reported at temperatures higher than TN [109,149–152].

Another effect that may have significant consequences in nanostructured systems is the dependence of HE and HCon tFM. From the above expression of the exchange bias energy the loop shift is inversely proportional to the thicknessof the FM layer, HE ∝ 1/tFM, as expected from an interface phenomenon [4–14]. This can have a profound effectin nanostructured systems, since the FM thicknesses (e.g., particle diameter) involved are rather small, hence largeloops shifts would be expected. The dependence of HC with the FM thickness is more complex, although a power-lawbehavior, HC ∝ 1/(tFM)n, has been observed and predicted theoretically, there are some discrepancies on the exponent,where both n = 1 and 1.5 have been obtained [106,153–156]. Independently of the exponent, it is clear that coercivityshould be larger for thinner (or smaller diameter) nanostructured systems [58,63].

Similarly, the dependence of HE and HC on the AFM thickness, tAFM, can also affect the properties of nanostructuredsystems. Actually, the HE and HC behavior on the AFM thickness can be rather complex [4–14]. According to theintuitive model presented above, exchange bias, HE, should be zero for tAFM for which KAFMtAFM < JFM–AFM (whereJFM–AFM is the FM–AFM coupling energy at the interface).Above a critical thickness given by tAFM=JFM–AFM/KAFM,it should become constant at HE = JFM–AFM/MFMtFM (where MFM is the FM magnetization) (see Section 5 for moredetails). On the other hand, HC should increase with tAFM until the critical thickness is reached, where it should drop tothe HC of the uncoupled FM. Experimentally, in exchange coupled thin films a similar behavior is usually encountered.Yet, due to the concomitant distributions of grain sizes, defects, and anisotropies, the described features are somewhatrounded. For example, rather steep raises of HE with increased AFM thickness are commonly reported in thin filmsystems. This onset of HE is often accompanied by a peak of HC close to critical AFM thickness. Moreover, theexistence of a critical thickness, which depends on the AFM anisotropy, KAFM, has been recently confirmed in thinfilm systems [145,157].

Another important property of exchange biased systems is the existence of a so-called training effect. This effectcomprises the reduction of HE and HC with consecutive hysteresis loops at a fixed temperature: HE(1st loop) >

HE(2nd loop) > · · · > HE(nth loop). It has been shown that there are two types of “training effect”, one between thefirst and second loop and another one involving subsequent higher number of loops [158]. The first type of trainingeffect has been proposed to arise from the AFM magnetic symmetry [159]. For the second type of training effect, ithas been demonstrated experimentally that, in thin film systems, the reduction of HE is proportional to the number ofloops HE ∝ (n)−1/2 (for n > 2), where n is the number of loops carried out [160]. Moreover, it is generally acceptedthat systems with thin AFM layers or small AFM grains exhibit much larger training effects [121,157,161–169].However, training has also been observed in some systems based on AFM single crystals with low AFM anisotropy(e.g., Co1−xMgxO, NiO and KCoF3) [163,167,170,171], suggesting that other factors apart from the microstructureplay a role in the training effect. This second type of training has been suggested to arise from the reconfiguration of theAFM moments or domains during the magnetization cycling [92,121,157–172]. Hence, similar to TB effects, trainingeffects may be enhanced in nanostructured systems.

Finally it is important to point out, that minor loops [173,174], i.e., hysteresis loops in which at least one of thebranches has been measured up to fields smaller than the saturation field (i.e., the field necessary to have all the FMspins parallel to the applied field), exhibit also different coercive fields for the increasing and decreasing fields branchesof the hysteresis loops, i.e., “loop shifts”. In fact, these shifts are an inherent effect to all magnetic materials whennot properly saturated and have consequently no direct relation to exchange bias effects. This effect can be especiallyimportant for small particles and hard magnetic systems, where the saturation field may be rather high and thus difficultto reach with conventional apparatus.

3. Nanostructured systems

3.1. Lithographically fabricated nanostructures

The development of advanced lithography tools (e.g., electron beam lithography, X-ray lithography, interferencelithography or nanoimprint lithography) to controllably fabricate magnetic structures at the submicron level has resulted


in an unprecedented growth of the studies on artificial magnetic nanostructures [63–78]. It is well known that themagnetic properties (e.g., coercivity or remanence) of submicron magnetic structures depend strongly on their size,aspect ratio or shape (i.e., elliptical, rectangular, triangular, etc.) [63–78]. Such effects could become even morecomplex in exchange biased nanostructures, since in this case the patterning would not only affect the FM part butalso the AFM part and/or the coupling between them. Despite the possible complex behavior and the paramountimportance of exchange biased lithographed nanostructures can have in magnetic recording, memories and sensorindustries (see Section 4), there exists very limited systematic research on the effects of size reduction to the 10 nmlevel in this kind of systems. Although there are many reports on submicron devices based on FM–AFM couples (e.g.,read heads [23,28,35,44], magnetic random access memories—MRAMs [23,25,28,31,34,35,37,38,40,42,43], or othertypes of devices such as sensors [28] (see Section 4 for more details), very few of them address in depth the effects ofminiaturization on the exchange bias properties of these devices.

Based on the intuitive view of exchange bias presented in the Introduction (Figs. 2–4), reducing the size of theFM–AFM system should not bring about any major changes in its behavior. Although, as pointed out, this intuitiveview is a simplification and when parameters such as FM or AFM domains, AFM or FM grain sizes start to becommensurate with the nanostructure dimensions important changes in the exchange bias behavior could take place.Certainly, one should expect novel effects setting in at some critical length scales. Hence, existing devices cannot bedownsized indefinitely without taking into account these effects.

In this section we summarize the existing results on different types of lithographed patterned exchange biased nanos-tructures (e.g., wires, rectangles, ellipses or rings) and other types of pseudo-ordered FM–non-magnetic nanostructures.Note, however, that systems composed of synthetic AFMs (i.e., having antiferromagnetically coupled multilayers play-ing the role of the AFM [107,175,176]) are not discussed. The main types of structures discussed in this sectionare shown in Fig. 5. It is important to emphasize that although Type Ia and Ib systems can be considered analo-gous, Types II and III should be taken as strictly different. Type IV structures are actually a special case of TypeIb, in spite of this, due to their formation process they can be thought of as a special type of structure with specificproperties.

3.1.1. Patterned wires, dots, rings, etcUnfortunately, due to the small number of studies, where most of them are on different FM and AFM systems,

different shapes or different types of structures, it is rather difficult to reach an overall understanding of the effects ofsize reduction in exchange bias. Here we will first compile the main results in the different studied systems and we willlater try to analyze them as a whole.

The first puzzling result is that while some authors report loop shift enhancements, with respect to continuous films, asthe lateral size of the system is reduced [177–196], other studies seem to point to the contrary [179,186,190,192,197–210].This can be ascribed, to a certain extent, to the differences between the investigated systems.

We discuss first FM–AFM wires (i.e., structures with a large in-plane aspect ratio). Wires with NiO as the AFM,seem to exhibit an increase in HE (as large as 135% increase) as the size is reduced from continuous films to submicrondimensions for Type I (see Fig. 5) structures when the unidirectional anisotropy (i.e., the anisotropy set by the fieldcooling procedure or the field applied during deposition) is along the long wire axis [180,181]. Moreover, a HE ∝ 1/w

dependence (where w is the width of the wire) has been reported for w in the range 200–400 nm [see Fig. 6(a)] [181].Conversely, other studies indicate a reduction of HE at room temperature [see Fig. 6(b)], while HE appears to beinsensitive to w at low temperatures [199] also for Type I structures. Similarly, CoO-based wires exhibit a decrease ofHE with the reduction of the dimensions for Type I structures [178]. In the case of IrMn, there exist also contradictingresults. For example, two studies agree that HE decreases, with respect to continuous films, for Type I structures withthe unidirectional anisotropy along the long wire axis [179,200]. However, while one study reports an exchange biasenhancement with size reduction when the unidirectional anisotropy is perpendicular to the wire long axis [179], theother study claims a reduction of HE [200]. Type I structures with a unidirectional anisotropy parallel to the long wireaxis for FeMn have also been shown to exhibit a decrease of loop shift as the size decreases [197], although, in othercases no reduction, for FeMn-based lines with widths down to 130 nm, has been observed [209]. Remarkably, thereduction effect observed in [197] disappears as the measuring field is applied away from the unidirectional axis. Thatis, when measuring perpendicularly to the unidirectional direction no change in HE is observed with size reduction[197]. A similar effect has been used in Type I FeNi–FeMn and Type II Fe (FM) wire structures on continuous FeF2(AFM) layers to actually tune the magnitude and sign of HE by having the measuring direction, the unidirectional axis


Fig. 5. Sketch and examples of the different types of lithographed nanostructures described in the text (a) Type Ia and Ib—patterned AFM–FMor FM–AFM nanostructures: (b) IrMn–CoFe dots [201] and Ni–NiO lines [199]; (c) Type II—patterned FM nanostructures on a continuous AFMlayer: (d) Fe dots on a continuous FeF2 film [204]; (e) Type III patterned AFM nanostructures on a continuous FM layer: (f) FeMn lines on a FeNicontinuous film [177] and (g) Type IV—surface oxidized (AFM) FM nanostructures: (h) Oxidized Co dots [218].

and the wire axis at different angles [196,209] (see Fig. 7). In the Fe–FeF2 system when all the axes are parallel alongthe wire axis there is also a small HE enhancement when compared to continuous films [196]. Another interesting effecthas been reported for FeMn-based Type III structures, where, if the etching of the AFM is only partial, i.e., the AFM


Fig. 6. Dependence of the loop shift, HE, at different temperatures on the wire width, W , for (a) Fe19Ni81–NiO [181] and (b) Ni–NiO [199], Type Istructures, evidencing the contradicting tendencies with W . Note the two different types of x-axis.

Fig. 7. Hysteresis loops at T = 35 K after field cooling in HFC = 1.5 kOe, for Type II Fe lines on FeF2, for three patterns with the lines +45◦ (a,d), 0◦ (b, e), and −45◦ (c, f) oriented with respect to the cooling field and the applied field during the hysteresis loop measurements. The appliedmagnetic field is parallel to the cooling field for (a)–(c), while it is perpendicular to it for (d)–(f). The directions of the applied field and cooling fieldwith respect to the lines are indicated to the right of each plot [196].

thickness is not uniform across the sample, rather complex loop shapes develop, as expected from the different couplingstrength between the FM and AFM layers in different locations [177]. On the other hand, in this FeMn-Type III system,when properly etched, a reduction of HE is observed compared to continuous films [177]. Interestingly, exchange biasperpendicular to the film plane, at room temperature (and above), has been observed in Type I [Co/Pt]n–FeMn wires[187]. In this case, there is a 40% reduction of HE in the 200 nm wide wires with respect to continuous films, althoughthe anisotropy remains out-of-plane [187]. Remarkably, this wire system exhibits a 10% decrease of the blocking


temperature, TB [187]. The decrease of HE for a patterned out-of-plane exchange bias structure has also been observedfor a system with CoO as the AFM. In this case, the HE reduction is so strong that the loop shift vanishes after patterninginto Type I lines [188].

It is important to stress that in most of the aforementioned systems a coercivity enhancement is reported whenmeasuring along the wire axis [177–180,196,197,199,209] or HC reduction when measuring perpendicular to it[179,196,197,209]. Nonetheless, these are well-known shape effects in FM wires [63], hence to separate exchangebias effects from the purely FM ones measurements above and below TB should be carried out.

Concerning submicron dots (i.e., structures with a small aspect ratio, such as rectangles, ellipses, etc.), the trendappears to be more consistent. Specifically, most of the systems exhibit a decrease of exchange bias with size re-duction independent of the range of sizes, the type of structure or the type of AFM (NiO, IrMn, FeMn, CoO, FeF2)[189,198,200–205]. Remarkably, for IrMn the HE reduction is more pronounced for a Type I structure than for a Type II[200]. However, it has been recently reported for sub-100 nm FeNi–IrMn square dots, that depending on the thicknessof the AFM layer the dots could either have larger or smaller HE than the respective continuous films. The authorsascribe this effect to the lateral size of the dots, which confines the AFM domains [190]. Another interesting case is theopposite trend observed for the Fe–FeF2 system, depending on the type of structure. For a Type I an increase of HE isobserved, while for a Type II (i.e., FM dots on a continuous AFM layer) a decrease HE has been found. The authorsrelate this behavior to the change in magnetization reversal mode in the FM in the two types of structures: coherentrotation for Type I and vortex formation for Type II [192]. Surprisingly, the enhanced HE observed in the Fe–FeF2Type I dots vanishes when the thickness of the FM layer is increased [193].

Other attractive features have been observed in exchange biased dots systems. Perhaps the most important is thechange in FM domain patterns when comparing exchange biased dots with purely FM ones. For example, many FMdots exhibit closure domain or vortex structures at remanence [63]. On the other hand, when exchange biased theyare often single domain [182,201,211–213], although in some cases closure domains or vortex are also observed evenin exchange biased circular dots or rings [191–193,195,214,215]. Moreover, in FeMn micron size dots it has beenreported that depending on the magnetic history the dots can exhibit either single domain or closure domain states[210]. Recently, exchange biased dots exhibiting vortex states have been systematically studied in FeNi–IrMn andFe–FeF2 [191,192]. It has been found that vortex states can actually be nucleated even in the presence of the AFM. Theconstricted hysteresis loops, typical of vortex states, are shifted along the field axis. Remarkably, for measuring fieldsaway from the cooling field, the loops no longer appear constricted, indicating that the magnetization reversal occursby coherent rotation rather than by vortex formation [191].

Another remarkable property reported for 60 nm Fe dots on a continuous FeF2 layer (Type II) is the increase of theremanent magnetization compared to the same dots deposited on non-AFM layers (see Fig. 8). In other words, theAFM provides an extra energy to the FM dots to stabilize their magnetization [204].

A technologically relevant feature observed in rather small (90 nm) Type I square dots based on IrMn is a reduction ofthe blocking temperature with respect to continuous films by more than 30 K [198]. Similar effects have been observedfor CoO-based nanostructures [205]. Note that in the case of IrMn-based dots, since the dots were deposited directlyon pre-patterned substrates (i.e., no annealing or etching processes took place) the observed effects should be intrinsicto the pattern, rather than an effect of the lithography process. This TB reduction can be a limiting factor for sometypes of devices, and should consequently be taken into account in device design. Another effect which might havetechnological relevance is the effect of interdot interactions, which in some cases has been reported to lead to complexmagnetization reversal [205].

Recently, an enhancement of HE has also been observed in IrMn-based Type I circular dots fabricated by nanosphereslithography [195], although the authors have ascribed this behavior to changes in the thickness of the layers due to thefabrication process.

Studies of submicron exchange biased rings show rather complex reversal mechanisms with asymmetric and kinkedhysteresis loops [208,215–217].

Ni and Co submicron dots are commonly studied uncoupled (i.e., without AFM) lithographed structures [63–78].Since NiO and CoO are AFM, when the surface of Ni- and Co-based nanostructures oxidizes, they become an exchangebiased nanostructure (Type IV, see Fig. 5). Hence, exchange bias properties, i.e., loops shifts and large coercivities,are observed below the blocking temperature [218–227]. Yet, the blocking temperatures in these systems have beenreported to be rather low (i.e., much lower than TN) [218,221,222,227]. There exist a few systematic studies of this typeof structure [223–227]. In oxidized Co dots a decrease of the loop shift after patterning has been observed simultaneously


Fig. 8. (a) Hysteresis loops of Type II Fe nanodot arrays (60 nm diameter, 15 nm thick) on MgO (unbiased, open symbols) and on a 90-nm-thickFeF2 film (exchange biased, solid symbols) at T = 10 K, after field cooling in 5 kOe from 300 K. Shown in (b) is a scanning electron microscopyimage of the structure of the sample [204].

Fig. 9. Schematic drawing of a system with (a) AFM antidots on a continuous FM layer, (b) FM antidots on a continuous AFM layer and (c) AFM–FMantidots.

with vertical shifts of the hysteresis loops [223] and asymmetric magnetization reversal [224–226]. The most novelproperty of this system is the effect of the dipolar coupling between dots, which brings about an asymmetrical reversalof the loops [220]. The lack of systematic studies of the different parameters in Type IV structures makes it difficult tocompare these systems with more controlled lithographed FM–AFM structures.

Another type of structure that has been investigated is “antidots” or arrays of holes rather than arrays of dots(Fig. 9). Two types of antidots patterns have been investigated: a continuous AFM layer—covered by a layer of FMantidots [79,194] or the other way around, i.e., continuous FM—AFM antidots [206,228]. Nonetheless, there are noreports of FM–AFM antidots. Interestingly, sizable increases of exchange bias have been reported in both types ofsystems with respect to continuous films [79,194,206], although a reduction of HE has also been observed in othercases [228]. Moreover, in the FM antidots case, strong asymmetries in the hysteresis loop and changes in magnetizationreversal have been observed [79,194].

Remarkably, larger patterned structures (several �m in size) exhibit a different trend. Very large exchange biasenhancements (up to 10 times increase in HE) have been reported for NiO and FeMn structures [183–186]. In thecase of NiO this large enhancement is only observed for single crystal AFM, while for polycrystalline NiO the effectdepends on the shape of the pattern, explicitly, enhancements are only reported for wire shape structures. Nevertheless,a slight reduction of HE after patterning in large IrMn structures has also been reported [207]. Similarly to smallerstructures, changes in the domain structure and magnetization reversal have also been observed in these larger patterns[183–186,229]. Finally, it is noteworthy that for FeNi–IrMn Type I 1 �m squares closure domains in the FM are found


at remanence. On the contrary, when the squares are 2 �m in size a more complex domain structure with a net momenttowards the unidirectional direction is found in zero field. This seems to indicate that in this system there is a crossoverfrom demagnetization-dominated behavior at 1 �m (leading to a closure domain, as observed for the same square dotswithout AFM), to a competition between demagnetization and exchange bias at 2 �m (leading to a more complexdomain structure, contrary to the same squares without AFM which show a closure domain state) [230].

Before analyzing the overall results of lithographed exchange biased nanostructures, it is useful to make a fewconsiderations on possible origins of the observed effects not directly related to size effects in exchange bias. The mainobvious concern would be, to what extent the observed effects arise merely from the patterning procedure itself? Forexample, many lithographic methods need different annealing steps or ion milling. These fabrication processes couldchange the microstructure of the bilayer (e.g., interdiffusion [231–233]), which, in turn, could lead to either an increaseor decrease of HE compared to the continuous FM–AFM bilayer itself. Although in many cases the reference films aresubjected to similar treatments as the patterned structures, in other cases the state of the reference film is not clearlyestablished in the experimental section. Occasionally, some effects from the patterning steps have been identified andmentioned in the text [194,204,234] or they have been tried to be addressed systematically [177,234]. Other patterningeffects such as shadowing or oxidation of the side walls should also be taken into account. Shadowing often occurswhen depositing in confined areas (i.e., patterned templates) and results in the thickness of the deposited layer beingdifferent (or inhomogeneous) with respect to the nominal one of thin films grown simultaneously. Since exchange biasproperties are very sensitive to the AFM and FM thickness, shadowing might result in spurious effects which could beidentified by a proper control of the dot thickness [195]. The oxidation of the edge or the side walls of the nanostructure[see Fig. 5(h)] both on the AFM or FM layers [25,235] (in systems where the AFM or the FM is sensitive to oxidation,e.g., FeMn) can play a non-negligible role, since the edge of a nanostructure can be a sizable part of it.

When analyzing the results of the different systems as a whole some simple conclusions can be drawn. The firstclear effect that can be inferred from the data is that the reported exchange bias properties are the result of thecompetition between magnetostatic (e.g., demagnetizing) and unidirectional anisotropy energies. Namely, as the sizeis reduced shape anisotropy starts to play a major role in the magnetic behavior of FM structures [63–78]. One ofthe consequences of decreasing the size of FM nanostructures is the reduced number of magnetic domains in thesystem and the concomitant change in magnetization reversal. This should have a substantial effect in exchange biasednanostructures. For instance, in small FM structures (without AFM) with small aspect ratio, the system tends to developstructures with zero net magnetization (i.e., closure domains and vortices [63]). In the case of an exchange biasednanostructure this type of magnetization pattern would be less stable since, while part of the spins would be parallel tothe unidirectional anisotropy direction, other spins would have to be at different angles, which should be energeticallyunfavorable. Therefore, this would induce a competition between the magnetostatic energy and the unidirectionalanisotropy energy, which, depending on the system (i.e., AFM material or type or shape of the structure), could resultin different types of behavior, as observed experimentally. This effect is especially clear in ring structures, since in thiscase the shape of the structure and the concomitant magnetization curling force the spins to be at different directionswith respect to the unidirectional anisotropy direction. This spin distribution results in complex magnetization reversals[216,236]. In the cases where the balance between the different energies is more critical, then effects such as differentmagnetization reversals in the magnetizing and demagnetizing branches of the loop could be observed [193,212]. Thiscompetition between shape anisotropy and unidirectional anisotropy is particularly obvious in FeNi–FeMn lines andFe lines on a continuous FeF2 film in which, by adjusting the angle between the shape anisotropy and the unidirectionalanisotropy, HE and HC can actually be tailored [196,209]. Consequently, in some systems, different behavior for thesame nanostructures (i.e., identical FM–AFM couple and the same type of structure) has been reported when changingthe shape anisotropy and the demagnetizing field of the structure (e.g., by changing the aspect ratio or the thicknessof the FM layer) [179,186,192,193,197,200]. To be precise, the balance between the different energies changes as theshape of the nanostructure is modified. Moreover, it has to be taken into account that induced anisotropies, resultingfrom the interaction between the FM and the AFM, may lead to changes in the critical magnetic length scales (e.g.,critical single domain radius [58,63]—see Section 5.2) compared to uncoupled systems.

Another effect related to the change in domain configuration between the continuous film and the nanostructuresis that in continuous films the magnetization reversal usually takes place through the nucleation and propagation ofdomain walls. In sufficiently small nanostructures, the possible magnetization reversal modes are more restricted andin the limit of single domain FM, the reversal can only take place by a few modes such as coherent rotation, curling orbuckling [63]. This change in reversal will result in a different interaction between the FM and AFM spins at reversal,


which could lead to modifications in the exchange bias behavior and could perhaps explain the reduction in HE observedin systems exhibiting vortex formation in the FM [191,192].

A second clear inference that arises from the published data is that the AFM system and its microstructure playan important role in the exchange bias properties of the nanostructured systems. For example, it has been shown thatthe behavior of identical nanostructures can be quite different if the AFM is polycrystalline or single crystal [186].Moreover, analogous structures grown from two different AFMs (e.g., NiO and IrMn) can exhibit opposite trends inexchange bias properties. AFM materials also exhibit domains, which in many cases are linked to magneto-elasticeffects (e.g., strains or defects) [237–253]. Consequently, the size reduction can certainly influence the behavior ofsuch AFM domains. Eventually, the size of the AFM domains can become of the same order of magnitude as thelateral size of the nanostructure decreases, which could lead to changes in their magnetic performance. For example,the edges of the pattern, with different magneto-elastic behavior from the bulk, could act as pinning sites and thusstabilize the AFM domains [254]. Moreover, with the reduced size, the number of AFM domains per pattern couldbe rather small. Hence, averaging effects, which result in continuous thin films due to the large number of domains,will consequently be readjusted. Note, however, that due to the absence of magnetostatic energy in AFMs the size andnumber of domains do not necessarily depend on the size of the structure. For example, domains in AFM single crystalshave been shown to reach several mm in size due to the small strain of the material [243,251,255,256]. If an AFM ispatterned while keeping the strain level low rather large single domain AFM structures could be obtained, although thiswould depend on each material and its microstructure. Thus, ultimately, when patterns reach the AFM single domainsize (which is more related to the microstructure than the size) the FM can interact with a single AFM domain, hencethe changes in exchange bias characteristics could be drastic. Explicitly, a single crystal AFM would become closerto a truly compensated or uncompensated spin structure, although interfacial roughness should still play a role. Thus,depending on the orientation of the AFM (with compensated or uncompensated AFM spin structure), the resultingexchange bias properties upon size reduction could be opposite. Similarly, nanostructures with sizes just above thecritical dimension for an AFM domain wall could result in partial domain walls (i.e., twists in the AFM spin structure),which could cause a modified FM–AFM coupling. Additionally, it has to be taken into account that the anisotropy ofthe AFM has a profound effect on the AFM domain wall width. Consequently, it would be somewhat expected that NiOwith domain wall width in the100 s of nm range exhibits a different behavior than FeF2 with a domain wall width in the1 nm range (see Table 4 in Section 5.2). Thus, larger AFM domain effects could then be expected for AFM with smalleranisotropies, where the AFM domain wall will be larger, �AFM = �(A/KAFM)1/2, (where A is the exchange stiffnessand the AFM anisotropy, KAFM, takes into account both magnetocrystalline and magnetoelastic contributions)—e.g.,�AFM(NiO)?�AFM(FeF2). Thus, similarly, the AFM domain behavior of polycrystalline materials with different grainsize or a single crystal should inevitably be dissimilar. All these effects should reflect in the exchange bias properties.

Similar to AFM domains, “uncompensated spins” (i.e., AFM spins which are not perfectly compensated due tolower coordination or defects) have been described to have a key role in exchange bias [4–14]. Some of the discussionpresented for AFM domains is also valid for uncompensated spins, i.e., patterning should alter the distribution ofthese spins. For example, in a single crystal AFM with a reduced number of uncompensated spins, patterning couldinduce uncompensation at the edges. In a polycrystalline AFM, as the number of grains or defects is reduced inside eachnanostructure, the amount of uncompensated spins should be lower. In spite of this, since the edge would act as a “defect”itself, the overall exchange bias performance will depend drastically on the exact system, type of pattern and so on.

Some recent studies argue that the exchange bias properties may be controlled, to some extent, by the FM anisotropy[257]. If this was the case, this could have a significant effect in lithographed nanostructures, since in this case theshape anisotropy would control the anisotropy of the FM (especially in FM with low magnetocrystalline anisotropy,e.g., permalloy). Consequently, each pattern with a different shape could result in different exchange bias properties.Unfortunately, no systematic research of this effect has been reported.

Another interesting effect of patterning could be to avoid “weak coupling” areas. It is usually claimed that magne-tization measurements probe only the weakest exchange bias path [258–264]. In continuous films, when a reverseddomain has been nucleated at this weak coupling point, it can easily propagate, hence the HE obtained by irreversiblemethods (i.e., methods that rely on the full rotation of the magnetization, e.g., magnetometry, in contrast to the onesthat only use small oscillations about a stable state) can be smaller than the average one (i.e., the one probed by re-versible methods, such as ferromagnetic resonance, FMR) [258–264]. In patterned systems, due to the reduced size,the probability to encounter the weakest exchange path is reduced. Consequently, from this point of view, one wouldexpect HE to increase in nanometric systems when measured using irreversible techniques.


Finally, a consequence of studying arrays in patterned systems, rather than individual nanostructures, is that oneusually measures the “average” behavior over many nanostructures. Hence, effects, such as small differences betweenindividual nanostructures can complicate the interpretation of the results, e.g., by inducing broader switching distri-butions. Moreover, another often-neglected effect in arrays of nanostructures is that dipolar interactions can play anon-negligible role, since the dipolar field for sufficiently close nanostructures may be of the same order of magnitudeas the exchange bias or the coercivity. This may bring about not only a change in the observed values of HE or HC, butit can also induce increasingly complex behavior (see e.g., [205,223]).

As a general conclusion, the performance of nanostructured exchange bias systems will strongly depend on manyfactors that can affect in different ways the diverse systems. Probably, the different parameters (e.g., AFM or FMdomains, AFM uncompensated spins or FM magnetization reversal) influencing exchange bias in nanostructures willhave different length scales for each specific system. For example, while the change in reversal mode can start at, forexample, 1 �m length scales, changes in the AFM domain structure (or uncompensated spins) should not take placeuntil the 10 nm range for many AFM (since the domain wall width will be of that order of magnitude). Thus the sametype of pattern could exhibit different effects at different length scales. Moreover, by changing the type of pattern, theFM or the AFM material could certainly alter these length scales. Therefore, two identical patterns with different FMor AFM materials could show opposite exchange bias behavior at the same length scale. This makes it complicated,indeed, to actually give a general description of the effects of patterning on exchange biased nanostructures.

3.1.2. Ion irradiated structuresAnother type of patterned exchange bias structure has been recently reported: ion irradiated structures [265–268]. It

is known that ion irradiation can be used to tune the loop shift and coercivity of FM–AFM bilayers [269–271]. Thus,if instead of irradiating the whole sample, some areas (hundreds of nm) are irradiated selectively (using a focusedbeam or a mask) patterned areas can be obtained [265–268]. Contrary to the conventional lithographed patterns, theseirradiated patterned areas are embedded in a continuous exchange biased film. In this case, a HE increase is observed inthe patterned areas, although this enhancement is not a size effect but rather the effect of irradiation in itself [265–268],since HE obtained by local irradiation is basically the same as for film irradiation. However, changes in the magnetizationstate of the irradiated area have been observed in submicron irradiated patterns, which are in agreement with the abovediscussion (i.e., arising from the competition between shape and unidirectional anisotropies).

3.1.3. Pseudo-ordered structures—“Networks”There are several types of structures that can be included in this section.We discuss three of them: (i) FM–AFM couples

deposited or grown on porous templates, (ii) FM–AFM bilayers deposited on Cu dots and (iii) FM layers depositedon naturally patterned (e.g., faceted or reconstructed) AFM layers. In the first case, three systems have been studied:FeNi–CoO and FeNi–FeMn bilayers deposited into porous alumina templates [272,273], and oxidized Co grown intothe pores of a three dimensional array of polymethylmetacrylate (PMMA) spheres [274]. In all cases the final systemconsists of a network of interconnected FM–AFM structures of different sizes (with the smallest dimensions in therange of a few tens of nm). FeNi–FeMn exhibits a large coercivity enhancement with a relatively low HE. Moreover,this system exhibits an unusual, non-monotonic, dependence of HE with the FM thickness [273]. Remarkably, two ofthe systems (FeNi–CoO and Co–CoO) exhibit rather large HE enhancements compared to continuous films [272,274].These results indicate that, in certain systems, if patterning can controllably reach the 10 nm range, large effects in theexchange bias properties could arise. In the second case, the effect of depositing CoFe–IrMn bilayers on a pseudo-ordered array of Cu dots was studied. Interestingly, although the effect of the patterned substrate was rather strong inthe coercivity, the exchange bias was largely unaffected [275]. This illustrates again that the effects of patterning onexchange bias are strongly dependent on the type of structure, i.e., its size, the AFM material or the microstructureamong many others.

Finally, as an example of the last case, Co–NiO bilayers deposited on MgO(1 1 0) and MgO(0 0 1) have been studied.NiO has the tendency to grow faceted when deposited on these surfaces in suitable conditions. This results in a pseudo-ordered pattern in the NiO layer. When the FM is deposited on these “patterns”, if it is not exceedingly thick, it grows aslong wires on top of theAFM, which leads to peculiar effects in the exchange coupled system. For example, exchange biasalways appears along certain directions independently of the cooling direction, leading to complex angular dependencesof HE [276–280]. This illustrates, once more, that the competition between shape and unidirectional anisotropies plays


Fig. 10. (a) Schematic drawing of a core–shell structure and (b) transmission electron microscopy (TEM) image of an oxidized Co particle.

a key role in the exchange bias of nanostructures, although in this case the AFM anisotropy may also play a role(as observed in certain thin film systems [281]).

3.2. Surface chemically modified nanoparticles

Many transition metal oxides are known to be AFM (e.g., CoO, NiO, FeO, and �-Fe2O3). Consequently, the firstapproach to obtain exchange bias in nanoparticles was by partially oxidizing transition metal magnetic particles (Co,Fe, Ni or alloys containing at least one of these metals). Some examples of this simple procedure are: Co–CoO, Co3O4[1–3,82,282–321], Ni–NiO [288,322–330], NiCo–NiCoO [309,327,331,332], FeCo–FeCoO [333–341], Fe–Fe3O4,�-Fe2O3, �-Fe2O3, FeO (note that Fe3O4 and �-Fe2O3 are ferrimagnetic) [286–289,321,324–326,342–374], FeAl–FeAl2O4 [375] or FeB–�-Fe2O3 [343,352,376].Alternatively, two oxides of the same transition metal with two differentoxidation states can also form a core–shell nanoparticle. For example, CrO2 core (FM)–Cr2O3 shell (AFM) [377–379]or Fe3O4 core (ferri)–FeO shell (AFM) [372] have been studied.

Moreover, it is well known that many other transition metal compounds are also AFM. Hence, different chemicalreactions have been used to obtain surface AFM layers on FM nanoparticles. For example, nitration, or sulphation havebeen used to obtain nitrides, e.g., Fe–Fe2N [355,356], Co–CoN [294] or sulfides, e.g., Fe–FeS [380,381]. The exposureof metallic nanoparticles to H2O environments can result in the formation of hydroxide shells, e.g., FM amorphousFeB nanoparticles have been observed to be covered by AFM �-FeOOH, which causes a coercivity enhancement belowTB = 40 K [382].

These chemical surface treatments of nanoparticles result in a so-called core–shell structure (Fig. 10), where thecore is a magnetic transition metal and the shell is the AFM (or ferri-) transition metal compound. The core diametercan be usually adjusted by the nanoparticles production techniques (e.g., chemical reduction, gas condensation, elec-trodeposition or microemulsion), usually within 3–100 nm. The shell thickness is somewhat more difficult to controlsince, although parameters such as the partial pressure of reactive gas or reaction time do influence the reacted layerthickness, in these systems core and shell cannot be controlled independently. That is, the AFM shell grows alwaysat the expense of the FM core. Moreover, in many of these systems the oxide shell produces a self-passivation effect,which makes further oxidation rather difficult [383–385].

These nanoparticles with a chemically modified surface, although they are simple to produce, have several drawbacks.The most important is probably the limited number of possible combinations of FM–AFM materials, since the AFMshell must come from a simple chemical modification of the core. Hence, the FM core and the AFM shell mustcontain the same transition metal, e.g., Co–CoO or Co–CoN. In other words, if the nanoparticle is made of a materialfrom which no simple AFM can be derived, a core–shell particle cannot be obtained by a simple surface reaction.Similarly, nanoparticles with core and shell of different transition metals cannot be obtained either (e.g., Co–NiO).Another drawback is that, due to the shape of the nanoparticles and their reduced size, the AFM shell usually growshighly disordered, making the control of its microstructure rather difficult [386–388]. Furthermore, if the particlesare overtreated (e.g., overoxidized), the core could be exceedingly small, becoming superparamagnetic [47,57,62].Consequently, the exchange bias properties could be lost.

One of the most important properties of surface treated nanoparticles is the increase of coercivity after field coolingfrom above TB, i.e., the same nanoparticles have a larger HC when field cooled (FC) than when zero field cooled (ZFC).


Fig. 11. Hysteresis loop of Co–CoO oxidized core–shell (dCore = 20 nm + tShell = 3 nm) nanoparticles at T = 6 K after zero field cooling (ZFC,open symbols) and after field cooling in HFC = 50 kOe (FC, solid symbols) [301].

For example in Co–CoO nanoparticles an increase of HC at 10 K, from HC(ZFC) = 39 kOe to HC(FC) = 59 kOe,has been observed [82]. In addition, it is noteworthy that, even when zero field cooled, the core–shell nanoparticleshave larger coercivity than the same particles without the AFM shell. This indicates that some degree of coupling isinduced, due to the presence of the AFM shell, even after zero field cooling [284,296,330]. However, since the cores arenot aligned to the field during cooling, the induced coupling would be local for each nanoparticle and hence random.Consequently, although locally the AFM shell will still pin the FM cores, it would do so in a different direction foreach nanoparticle. Thus, a coercivity enhancement rather than a loop shift would be expected after a zero field coolingprocedure. Note that exchange bias effects in zero field cooled systems have also been observed in thin films [389–391].Moreover, the main effect of exchange biasing, i.e., a loop shift, has been observed in many of the studied core–shellsystems [1–3,82,282–284,290–296,298–301,304–326,330,331,333,334,336,340,352–357,359,362,365,366,368–375,377–380]. In spite of this, only for a few systems, such as Co–CoO [1–3,82,282,284,290–294, 300,301,303,306–311,314–319], NiCo–CoNiO [332], Co–CoN [294], Fe3O4–FeO [371] and Fe–�-Fe2O3 [363,368,372] large loop shifts,expected from the small size of the cores (due to the 1/t dependence of HE), have been reported. Shown in Fig. 11 is ashifted hysteresis loop for Co–CoO particles, with a loop shift of 9.5 kOe [301]. The lack of large loop shifts for somesystems (e.g., in Ni–NiO HE ∼ 0.05–0.2 kOe, is often reported [322–326,330]), even far below TB can be, in part, due tothe low anisotropy of theAFM shells (e.g., NiO). In addition, another important factor for the reduced HE and HC valuesis the microstructure of the AFM shell, which in many systems is probably composed of very small crystallites or amor-phous, implying that its spin structure will be rather complex (e.g., spin canting or spin glass like). Hence the couplingcannot be as effective as expected from a crystalline AFM. A clear indication of this effect is given in some cases, whichwhen the samples are annealed at moderate temperatures the oxide shell improves its crystallinity and consequentlythe properties, e.g., coercivity enhancement, improve [349,350]. Nevertheless, other studies point towards a reductionof the exchange bias properties after the crystallization of the oxide shell, ascribed to the growth of the crystallites inthe oxide shell [358,366,367]. Another trend also exhibited by surface treated fine particle systems is the existence of asin � (i.e., unidirectional) component of the anisotropy [1–3,327,334,380,381], although in recent years torque studiesof the different components of the anisotropy are scarce. Moreover, as expected, some of the studied systems have alsobeen reported to exhibit training effects [293,354,364,368], even if this effect is seldom systematically studied. A moreintriguing result displayed by many core–shell nanoparticles is the presence of significantly large vertical shifts tiedin with the existence of HE [1–3,82,282–284,290,291,293,300,301,322,323,333,334,337,363,368]. Although verticalshifts have been observed in thin film systems [392,393], and they have been found to be correlated with exchangebias, for example due to uncompensated spins [394,395], those observed in some nanoparticle systems can be consid-ered rather large to arise solely from uncompensated AFM spins. Hence, although in some cases a clear correlationbetween the vertical shift and HE has been observed [363], more experiments will be necessary to elucidate the originof vertical shifts in exchange biased nanoparticles. An intriguing effect observed in some systems is the existence of


magnetization perpendicular to the applied field for large ranges of fields, hinting a possible perpendicular couplingbetween the FM core and the AFM or ferri shell [321,374]. Another interesting property occasionally reported, whichcan be technologically important, is a squareness enhancement (i.e., an enhancement of the remanence to saturationratio) [328,360,363,369,371]. In some cases, a strong dependence of HC and HE on the cooling field has been reportedand has been ascribed to the spin glass properties of the shell stemming from its disordered character [371]. Finally, itis noteworthy that virtually all the above studies report blocking temperatures clearly below the respective TN of theshell [82,282,284,293,294,300,301,304,308–310, 315,317,319–324,329,332,334,354,357,362,364,365,369,373,381].

There exists relatively few systematic studies of the effect of changing the different parameters in surface-treatednanoparticles (e.g., core diameter or shell thickness) [282,284,286,288,293,294,298,301,308,309,311,314,315,317,318,324,329–331,343,345,346,359,361,364,369,370,372,373], mainly due to interdependence of the different parametersin this type of systems: (i) the role of the core diameter, dCore, has been found to be similar to the FM thickness inbilayer systems for a certain thickness range. Specifically, HE and HC decrease with increasing core diameter, roughlyinversely proportional to dCore. This would be expected from the interface nature of the exchange bias effect. However,more complex behaviors have been reported in some cases, where a decrease of HE is observed for sufficiently smalldiameters. This effect could be due to the tendency of the small particles to become superparamagnetic [47,57,62], henceresponding differently to the FM–AFM coupling (note that HE ∝ 1/MFM). Moreover, for very large dCore (i.e., largerthan the critical single domain radius—see Section 5.2) the 1/dCore is no longer valid and the shift becomes roughlyindependent of dCore. The change in behavior in this case could be due to a transition in the core from monodomain tomultidomain, which would cause a more complex behavior. Note that regarding the coercivity, the effect of exchangecoupling in nanoparticles is perhaps more striking, since for the range of dCore studied a decrease of coercivity (ratherthan the observed increase) with decreasing core diameter would be expected due to superparamagnetism. Hence, theFM–AFM must overcome the tendency to superparamagnetism; (ii) the role of the shell thickness, tShell, has been lessstudied. In agreement with thin film systems, the loop shift increases with increasing tShell (i.e., tAFM) for thin shells.Nevertheless, for thick shells different behaviors have been reported, i.e., in some systems HE reaches a constant valuefor large tShell, while in others it decreases, as reported for thin film systems [4–14]. The coercivity exhibits a similarbehavior, i.e., it increases when increasing shell thickness, although it tends to level off for large tShell, i.e., no decreasein HC (as often observed in thin films [145,157]), has been reported.

Remarkably, it has been recently demonstrated that isolated 4 nm Co nanoparticles with 1 nm CoO shell are superpara-magnetic down to 10 K and do not exhibit exchange bias properties [82,320]. On the other hand, when these Co–CoOnanoparticles are clustered together they are FM and show large exchange bias [82]. The small exchange bias in isolatedparticles may indicate that the CoO shells of independent Co–CoO nanoparticles may be exceedingly thin or disorderedto actually induce exchange bias when they are isolated. When the particles are clustered together, due to the exchangecoupling between the different oxide shells, they exert a “collective behavior” thus having a much larger effective AFM“thickness” and hence a much higher blocking temperature, which, in turn, increases the superparamagnetic blockingtemperature of the cores. Alternatively, the dipolar interactions between the different cores induce an increase of thesuperparamagnetic blocking temperature of the cores, which, as a result, due to the exchange between the cores and theshells increases the exchange bias blocking temperature. Note that an enhancement of the superparamagnetic blockingtemperature due to dipolar and exchange interactions has been observed both in AFM [396–398] and FM (and ferri-)systems [399–402]. Moreover, collective states, referred to as “superspin-glass” [403–405] or “superferromagnetism”[406–408] have been shown to arise in FM nanostructures due to interactions. This trend in the enhancement of HEwith clustering has also been observed in linear aggregation of Co–CoO nanoparticles, when compared to dispersearrangements [298]. Consequently, perhaps some of the early results in surface modified nanoparticles may need to bereinterpreted.

Unfortunately, the lack of control of the microstructure in this type of systems and the few systematic studies makethe analysis of the results, as a whole, difficult. Nevertheless, there are clear indications that very large exchange biaseffects can be attained in this kind of nanoparticles. Eventhough, from the available results it is challenging to pinpointthe exact origin of such effects.

3.3. FM nanoparticles embedded in AFM matrices

In a sense, compacted core–shell nanoparticles, where the AFM shells can strongly interact with each other, couldbe considered as FM nanoparticles embedded in an AFM matrix. In spite of this, there are certain systems where no


Fig. 12. Schematic representation of (a) a nanoparticle (FM)—matrix (AFM) nanocomposite and (b) FM nanoparticles on an AFM surface.

clear shell is present surrounding the nanoparticle, but rather there is a large area of AFM material embedding it [i.e.,an AFM matrix—see Fig. 12(a)].

There exist several examples of such systems (without trying to be exhaustive):

3.3.1. Co-evaporation of FM–AFM materialsDepending on the relative evaporation rate of the FM and the AFM the deposition results in FM rich areas (i.e.,

nanoparticles) embedded in an AFM rich matrix, or vice-versa, i.e., AFM nanoparticles in a FM matrix. Note that onlythe former has been studied in some detail.

A more controlled variation of co-evaporation is the so called sequential-multilayers [11,82,409,410]. In this case, adiscontinuous layer of FM material (or by direct deposition of nanoparticles) is followed by a layer of AFM material.This procedure can be carried out once [410] or repeated a number of times [11,82,409], resulting in nanoparticlesembedded in an AFM matrix.

Using standard co-evaporation three systems have been studied, Co–CoO [411], Fe-FeCl2 [412] and Fe–FeF2 [413].Exchange bias effects, i.e., increased coercivity and loop shifts, have been observed at low temperatures for all systems,e.g., for Co–CoO a maximum loop shift of HE = 2800 Oe at 10 K after field cooling has been reported [411], while theeffect is much smaller for FeCl2 and FeF2 (e.g., HE ∼ 40 Oe at 4 K for FeCl2 [412] and HE ∼ 240 Oe at 5 K for FeF2[413]). Interestingly, although all the CoO, FeCl2 and FeF2 matrices are continuous, the blocking temperature, TB, ofFeCl2 is close to TN, while for FeF2 and CoO TB is well below TN. In the case of FeF2 this effect probably stems fromthe small size of the FM nanoparticles [413]. For CoO, although HE vanished below TN, HC remained large even aboveroom temperature (T > TN) [411]. This could be due to the small CoO crystallites, which, if not properly exchangecoupled to their neighboring crystallites, could exhibit reduced TB (due to their small size) but the individual crystallitescould have enhanced TN (due to the coupling to the FM nanoparticle). Moreover, the authors report an increase in HEwith reduced FM nanoparticle size, as expected [411]. Yet, since in order to reduce the FM particle size the relativeFM–AFM evaporation rate has to be adjusted, the observed HE effects could also be influenced by structural changesin the AFM. Moreover, vertical shifts have been observed for the Fe–FeCl2 system [412].

Remarkably, in the Fe–FeCl2 system, due to the low AFM anisotropy of FeCl2, apart from the matrix affecting thenanoparticles (e.g., inducing HE), it has been shown that the nanoparticles can also modify the matrix properties byinducing local spin flip transitions. These metamagnetic transitions result in an overall increase of the magnetizationof the system [412].

In the case of sequential multilayers, 2–6 nm Co nanoparticles were directly sequentially deposited, using gascondensation of sputtered atoms in a so-called “cluster gun”, onto CoO or NiO layers [82,410] (in contrast with co-evaporated Co–CoO). In the case of multilayers of 4 nm Co nanoparticles into CoO, a rather large exchange bias,HE =7.4 kOe, and coercivity HC =7.6 kOe, were observed at 5 K after field cooling [82]. Similar values were obtainedfor 6 nm particles covered by a single CoO layer (e.g., HE = 5 kOe) [410]. Moreover, in both cases the blockingtemperature has been found to be close or equal to the Néel temperature of CoO [82,410]. Actually, occasionallyblocking temperatures above TN have also been observed [82]. Although the effect is not clear at present, issues suchas AFM susceptibility or short range AFM order (used to explain similar effects in bilayers [109,149–152]), should beenhanced by the fact that in this case the nanoparticle, due to its small size, interacts with a single AFM domain orcrystallite. Moreover, the temperature dependence of HC, which roughly follows a T 3/2 law [82], is rather differentfrom the T 1/2 behavior expected for non-exchange coupled nanoparticles [414]. Interestingly, a vertical shift has also


Fig. 13. (a) Temperature dependence of the remanent moment, mR, for Co–CoO oxidized core–shell (dCore = 4 nm + tShell = 1 nm) nanoparticlesembedded in a non-magnetic Al2O3 matrix (open symbols) and in anAFM CoO matrix (solid symbols). The superparamagnetic blocking temperaturesof both systems are indicated in the figure. (b) TEM images of the microstructure of the sample [82].

been observed in this system [82]. For Co nanoparticles in NiO the loop shift is rather small, HE =0.18 kOe (comparedto the CoO case), in principle due to the smaller AFM anisotropy [410].

The observed differences (e.g., smaller bias or lower TB) in exchange behavior, between Co–CoO, either prepared byco-evaporation or by sequential multilayers, are probably related to changes in the microstructure due to the differentgrowth methods. Note that, while co-evaporation can be considered rather “poorly controlled”, sequential evaporationcan be rather carefully controlled. In particular, the spherical morphology of the nanoparticles can be clearly observedfor the sequential multilayers [82,410] while the nanoparticles could not be clearly observed by transmission electronmicroscopy in the co-evaporation case [411].

SmCo nanoparticles embedded in CoO have also been studied using sequential multilayers. This system also exhibitsloop shifts and coercivity enhancement at low temperatures, accompanied by a small vertical shift of the hysteresisloop [409].

Remarkably, all the systems studied exhibit another important feature, which is an enhancement of the remanencewhen compared to the FM nanoparticles embedded in non-magnetic matrices (see Fig. 13) [82,409–411]. As it willbe discussed in Section 4, this property is essential in stabilizing FM nanoparticles above their superparamagneticblocking temperature.

Note that although only FM(metal)–AFM(oxide) type of systems has been studied using sequential multilayers, itcan be easily extended to other combinations of FM and AFM materials.

Using the same cluster gun technique another type of related structure has been studied. Namely, a layer of AFM(CoO, NiO or NiO/CoO) covered by nanoparticles has been investigated [410]. However, as can be seen in Fig. 12(b),in this case the particles are not embedded in the AFM layer, hence, it does not strictly belong to “FM Nanoparticlesembedded in AFM matrices”. Remarkably, the exchange bias and coercivity enhancement in this type of structures arerather small [410]. The origin of these reduced effects could arise from the small interface, i.e., contact area, betweenthe nanoparticles and the AFM layer.

3.3.2. Mechanical milling of FM–AFM materialsThe case of FM–AFM mixing is particularly interesting since the microstructure depends on the mechanical properties

of the constituents [415]. For example, during the milling of ductile–ductile systems, the particles first become elongatedand later they develop into platelet or laminar shapes. Sometimes, for intermediate milling times, “sandwich”-typemicrostructures develop. Such microstructure would be favorable to obtain a large FM–AFM interface area. In spite ofthis, for exceedingly long milling times the various metallic components can be alloyed and the FM–AFM nature ofthe systems can be lost. Hence, probably the most convenient for embedding FM nanoparticles in AFM matrices is themilling of brittle–ductile constituents. In this case, during the milling, the ductile powders acquire elongated shapes,


Fig. 14. (a) Scanning electron microscopy micrograph of ball milled Co–NiO powders. (b) Temperature dependence of the loop shift, HE(T ), afterfield cooling in HFC = 5 kOe [428,430].

while the brittle counterparts are simply fractured. At intermediate milling times, the ductile grains or lamellae becomeembedded in the brittle matrix, forming agglomerates. An example of such microstructure for Co (ductile)–NiO (brittle)can be observed in Fig. 14(a). Finally, brittle–brittle is perhaps the least favorable combination, since at intermediatemilling stages, some heterogeneous agglomerates, with granular morphology, i.e., without a good interface contact ofthe constituents, are formed.

Due to the nature of ball milling, the microstructure in the composite is rather complex to adjust. Nevertheless,certain control can be achieved by tuning the milling parameters (e.g., milling power, milling time or FM/AFMratio). Several systems have been studied using this technique [11], Fe–FeS [416], Ni–NiO [416,417], Co–CoO [416],Fe–FeMn [418], Fe–Fe3O4 [419–423], NiFe–Ni Ferrite [424], Fe–Ba-ferrite [425–427], Co–NiO [428–432], Co–FeS[428,429], SmCo5–NiO [80,81,429,433–436], SmCo5–CoO [80,81,429,433–435], Fe–NiO [436], FeNi–CoO [437],Sr-ferrite–�-Fe2O3 [438], Fe–MnO2 [439] and FeCo–MnO and Fe–MnO (although in this case MnO was obtainedfrom the oxidation of Mn after or during the milling) [436,440,441]. Note that several of these systems involveferrimagnetic–AFM or FM–ferrimagnetic components. Contrary to many of the other techniques used to produceexchange biased nanoparticles, by ball milling the possible combinations of FM–AFM (or ferri-) pairs is only limitedby their mechanical properties, so that a favorable microstructure (i.e., many FM–AFM interfaces) is indeed obtained.Hence, systems where the AFM and the FM are unrelated (e.g., not derived from the same transition metal) can beobtained using this technique. However, by ball milling, although crystallite sizes of a few nm are obtained, usuallythe FM and AFM particles can be several �m in size often with a broad particle size distribution [see Fig. 14(a)].

It is noteworthy that in certain cases annealing of the as-milled powders is necessary to induce the desired microstruc-ture. For example, milling of Fe + �-Fe2O3 can result in FeO1−x , which after annealing becomes Fe (FM) + Fe3O4(ferri-) [419–423]. Similarly, Sr-ferrite + FeS results in a complex mixture, which after annealing becomes Sr-ferrite(ferri-) +�-Fe2O3 (AFM) [424] or Ni + �-Fe2O3 results in NiFe + Ni-ferrite after annealing [424].

The most well-studied systems in this category are ball milled Co–NiO [11,428–432], Fe–FeMn [418], Fe–NiO [436],FeNi–CoO [437], Fe–Fe3O4 [419–423], and SmCo5–NiO [11,80,81,429,433–435]. For all systems an appropriatemicrostructure, i.e., consisting of FM particles embedded in an AFM (or ferrimagnetic) matrix is encountered. InCo–NiO, both loop shift and coercivity enhancement (with respect to the pure Co processed under similar conditions)have been observed after field cooling from above TN. Despite the disordering nature of ball milling (e.g., the NiOcrystallite size becomes 〈D〉NiO ∼ 14 nm after 20 h of milling [428–432]) a TB ≈ TN has been observed in this system[see Fig. 14(b)]. TB is not significantly reduced with respect to TN probably because although the crystallites are smalla good exchange contact between them is maintained and perhaps also due to the rather broad AFM particle sizedistribution. HE and HC have also been studied as a function of the FM/AFM ratio and milling time. HE and HCenhancement exhibit maxima for FM/AFM ratios around 1:1 [428–432]. Moreover, for a fixed FM/AFM ratio, HE andHC also exhibit a maximum with milling time. These effects are probably due to the evolution of the microstructureduring milling, i.e., FM particle size, distance between FM particles (in a sense equivalent to the AFM thickness) andthe milling damage to the FM and AFM phases. Consequently, an exact quantification of the effects is difficult. TheseFM–AFM composites also exhibit an increase of the squareness, MR/MS, of the hysteresis loop when compared to the


pure FM material with similar microstructure. This MR/MS enhancement, together with the HC increase brings aboutthe improvement of the energy product, (BH)max, when the composition (i.e., the FM/AFM ratio) is optimized. Notethat to observe such (BH)max enhancement, the reduction in the overall saturation magnetization of the composite (dueto the zero MS of the AFM) has to be overcome by the increase in HC and MR/MS [429,432].

The cases of Fe–NiO and FeNi–CoO are similar to Co–NiO, in which HE and HC depend on the milling conditionsand the FM/AFM ratios [436,437]. Moreover, in agreement with Co–NiO a remanence enhancement has also beenobserved in the FeNi–CoO system. In contrast to Co–NiO, the blocking temperature of FeNi–CoO appears to be lowerthan TN, due, perhaps, to more aggressive milling conditions [437].

In many aspects Fe–FeMn is analogous to the previous cases, although this system is fully metallic. HE has beenfound to depend on the FM/AFM ratio, with a maximum observed loop shift of HE = 40 Oe for 90% of AFM FeMn.Similarly, the maximum HC is also observed for samples with largeAFM content.As for the previous cases, a remanenceenhancement has been observed after field cooling. This system has a complex dependence of the magnetic propertieswith milling time, which is caused by the phase transition of FeMn into a non-AFM phase during the milling [418].

HC for Fe–Fe3O4 depends strongly on the FM/ferri ratio [419–423], similar to what has been observed for Co–NiO.In this system the effects are increasingly complex since the annealing procedure to which the samples are subjectaffects not only the microstructure but also results in phase changes in the system. Note that no exchange bias has beenreported for this system [419–423].

The properties of SmCo5–NiO show an interesting behavior. This system exhibits a coercivity enhancement relatedto the FM–AFM coupling without field cooling from above TN. Actually, this system cannot be warmed since SmCo5decomposes and loses its hard magnetic properties. Moreover, since no field cooling is carried out and due to theinherent random nature of ball milling no exchange bias is observed. The authors attribute this behavior to the localheating induced during the milling and the local magnetic field exerted by the dipolar field of the FM particles on theAFM particles, which, to some extent, can be thought of as a local field cooling procedure. Moreover, in this system,the rather large increase of coercivity (�HC ∼ 3000 Oe) could be due to the large anisotropy of SmCo5. Note thatin FM–AFM thin film systems it has been shown that �HC appears to be proportional to the FM anisotropy [257].Remarkably, similarly to Co–NiO, this system exhibits an important enhancement of the squareness, in some casesreaching MR/MS = 0.95 (rather unusual for an isotropic material) [80,81,429].

As will be discussed in Section 4, these effects can be used to improve the performance, i.e., the energy product, ofhard magnetic materials.

3.3.3. Incomplete reactive evaporationIf a reactive evaporation or sputtering, where the reacted product is anAFM (e.g., CoO), is carried out with insufficient

reactive gas (i.e., O2), this may result in areas of the reacted film rich in metal source (i.e., the case of CoO, Co). Hence,the creation of unreacted FM nanoparticles in the reacted AFM matrix is induced. Note that this procedure could becarried out with other reactive gases, e.g., nitrogen to produce CoN, although only reports of O2 reactive evaporation canbe found in the literature. The most studied of these systems is Co–CoO [442–449], not so much for its exchange biasproperties, which are only effective at low temperatures, but due to the resulting microstructure. With the appropriateconditions nanometric columnar Co grains isolated by a CoO matrix can be obtained [444–446]. This microstructure wasproposed for perpendicular magnetic recording (not based on the exchange bias properties since the Néel temperatureof CoO is below room temperature) [444–446]. In any case, this system exhibits very large coercivities and loop shiftsat low temperature (e.g., HC = 8 kOe and HE = 3.8 kOe at T = 10 K for a system with 50% FM Co in a CoO AFMmatrix [442]). Similar effects have been observed for Fe, CoNi, Ni, FeNi and CoFeSiB reactively sputtered in O2,where for certain O2 concentrations, nanocrystals of Fe3O4 (ferri-) embedded in FeO (AFM) [442,450,451], Ni (FM)particles in NiO (AFM) [452], FeNi (FM) particles in FeNiO (AFM) [453], CoNi nanoparticles (FM) in CoO (AFM)[447,448,454,455] and CoFeSiB (FM) surrounded by an undetermined oxide (probably ferrimagnetic) [456], havebeen reported. Alternatively, transition metal oxides with different oxidation states, in which one of them is FM or ferriand the other AFM [e.g., CrO2(FM) + Cr2O3(AFM)] also show an analogous behavior [457]. Similar to the Co–CoOcase, these systems exhibit coercivity enhancements and loop shifts [442,447,448,450–457], yet they are substantiallysmaller than for Co–CoO. Contrary to what is observed for core–shell nanoparticles, in these systems the blockingtemperature is usually close to the Néel temperature [444,447,449,450,454] with some exceptions [449,452,453]. Thisis probably due to the sizeable AFM matrix, which can keep its bulk TN. However, some of these systems have beenreported to exhibit training effects [455], probably because, despite the large amount of AFM matrix, it is composed of


small crystallites which are more prone to training effects [121,157,161–169]. Torque measurements in some of thesesystems confirm the presence of a sin � component, i.e., unidirectional anisotropy [442,454]. In some cases verticalshifts of the hysteresis loops [444–446,450] or more unusual effects such as positive exchange bias [452] or asymmetricmagnetization reversal [449] are also observed. It is noteworthy that the exchange bias properties of these materialsdepend strongly on the O2 partial pressure [442–457], probably indicating that the relative amounts of FM–AFM arechanging. Hence, in this type of process, the control of the microstructure is difficult and the independent manipulationof the FM nanoparticles and AFM matrix is particularly complicated.

Finally, note that large exchange bias effects on systems composed of AFM nanocrystallites (MnO) embedded in aFM (Co) matrix (e.g., by simultaneous reactive sputtering of Co and Mn) have been recently reported [458].

3.3.4. SegregationCertain AFM or ferrimagnetic materials, especially non-stoichiometric ones, can segregate FM or ferrimagnetic

nanoparticles during fabrication or after appropriate heat treatment. Some examples are: (i) mechanical milling andmechanical alloying, which has been used to induce reactions to partially segregate a ferrimagnetic + AFM compositefrom a ferrimagnetic powder, e.g., ball milled NiFe2O4 results in a mixture of a NiFe2O4 (ferri-) + FeO (AFM)[459,460]. Interestingly, this system exhibits very large coercivity, HC = 10 kOe and loop shifts (HE = 10 kOe atT = 4.2 K after field cooling [459,460]); (ii) nanocrystallization of amorphous materials: although most of the studiesof nanocrystallization of amorphous ribbons are FM nanocrystals embedded in FM matrices [50,51], some studies inwhich either FM nanocrystals are dispersed in an AFM matrix, e.g., in DyAl [461] or AFM nanocrystals embeddedin a FM matrix, e.g., in NdFeAl or PrFeAl [462,463] have been reported. These systems have been found to exhibitlarge coercivity enhancements below TN [461,462], similar to what has been observed for SmCo5–NiO composites[80,81] and large exchange bias (e.g., HE = 8 kOe at 5 K in the NdFeAl system [462]), although the loops appearednot to be completely closed, indicating that the saturation field was not reached [462]; (iii) similar effects have beenobserved by mechanical alloying of Pr–Fe–Co–Al–B elements. Annealing the as-milled amorphous alloys leads tothe segregation of FM Pr4Fe12B and AFM Pr6Fe14 based alloys. This microstructure induces a large coercivity andremanence enhancement of the alloy. For certain conditions loop shifts of up to HE = 2.5 kOe have been observed[464]. In addition, mechanical alloying of Fe, Cu and Mn results a mixture of FM, spin-glass and AFM (probably �-Fe)phases, which exhibits loop shifts and vertical shifts at low temperatures [465]; (iv) finally there exists a number ofother chemical processes that can result in FM–AFM mixtures. For example, in NiFeMn or CuMnAl alloys Mn tendsto segregate upon annealing forming Mn poor (FM) and Mn-rich (AFM) areas. In the NiFeMn system small loop shiftsand coercivity enhancement are observed at room temperature [466], while in CuMnAl both the coercivity enhancementand the loop shifts are rather large and accompanied by vertical shifts [467,468]. Strain effects, due to epitaxial growth,induce the segregation of MnAs when grown on GaAs into lamellae of �-MnAs (FM) and �-MnAs (AFM). This lamellarmicrostructure gives rise to exchange coupling effects such as loop shifts and coercivity enhancement [469,470]. Asimilar lamellae nanostructure is found in volcanic rocks, formed by ilmenite (ferri) and �-Fe2O3 (AFM) [471,472].The unusual magnetic stability of the magnetization of this type of rocks is probably related to exchange bias and couldhave important consequences in paleomagnetism [473,474]. Other processes, such as plasma spray deposition, resultin the decomposition of the compound during the growth, e.g., MnZn-ferrite converts into MnZn-ferrite (ferri)–FeO(AFM), leading to a coercivity enhancement and a small exchange bias in the material [475]. Another example is thepyrolysis of ferricene (an organic material containing Fe) and C60, which develops into a mixture of �-Fe (FM), Fe3C(FM) and �-Fe (AFM). In this case, a loop shift, which vanishes at a TB close to TN of �-Fe, is observed after fieldcooling. These systems have been reported to exhibit small HE, HC increase or training effects [476–479].

3.3.5. Partial reduction or overoxidationPartial reduction or overoxidation of certain oxides (powders, films and single crystals) have been used to obtain FM or

ferrimagnetic nanoparticles in an AFM or ferrimagnetic matrix. For example, the partial reduction of �-Fe2O3 results in�-Fe and Fe3O4, which exhibits a strong coercivity enhancement at low temperatures [480] or �-Fe2O3 (ferri) embeddedin Fe3O4, (ferri) [481]. An example of overoxidation is NiO- or Fe-doped NiO films and single crystals, which, whenannealed at high temperatures in air, precipitate spinel overoxidized NiO1+x or NiFe2O4. Although no loop shifts orcoercivity enhancement have been observed for these systems, such materials exhibit changes in the ferromagneticresonance field consistent with the existence of exchange bias [482–486]. Reduction of mixed oxides by annealingin the presence of H2 can also be used to obtain the desired microstructure, for example the controlled reduction of


Fig. 15. (a) Transmission electron microscopy micrograph of Fe nanoparticles embedded in a Cr2O3 matrix. Temperature dependence of (b) theloop shift, HE and (c) the coercivity, HC, for Fe nanoparticles embedded in a Cr2O3 matrix after field cooling in HFC = 50 kOe [487].

CrFeO results in FM Fe nanoparticles embedded in an AFM Cr2O3 matrix [see Fig. 15(a)] [11,487]. Likewise, partialreduction of Fe-doped Ba-ferrite results in Fe nanoparticles embedded in the Ba-ferrite [488,489] or the reduction ofnon-stoichiometric NiZn-ferrite becomes Fe + NiZn-ferrite [490]. Note that using this method nanoparticles and matrixdo not necessarily have to be composed of the same transition metal. Moreover, in many cases, isolated nanometricFM grains inside the AFM matrix can be readily obtained. Similarly, the reduction of NiO by reactive ball milling in aH2 atmosphere results in FM Ni nanostructures embedded in an AFM NiO matrix [11,491,492]. All these systems havebeen found to exhibit significant coercivity enhancements after field cooling from above TN, however, the reported HEare rather small or negligible [487,488,492], as can be seen in Fig. 15 for Fe–Cr2O3. Another interesting system isCo3O4 nanoparticles covered by a SiO2 layer. During calcination there appears to be a solid state partial reduction ofthe Co oxide nanoparticle by the SiO2 protecting shell, which results in an inverted core–shell structure, i.e., FM Coshell and AFM CoO–Co3O4 core. This structure exhibits a rather large coercivity at low temperatures, accompaniedby a moderate loop shift, HE = 580 Oe [493].

The inhomogeneous microstructures, typical of many of these structures, result in many FM–AFM interfaces, veryoften oriented at random. This brings about the observed variety of exchange bias responses. Most systems of FMnanoparticles embedded in an AFM matrix exhibit larger coercivity enhancements than loop shifts, probably dueto the random character of this type of materials. Nevertheless, some systems also show rather large exchange bias(several thousand Oe). This effect can arise from the fact that due to their small size the nanoparticles interact with asingle AFM crystallite or domain [82]. Consequently, the averaging effects observed in continuous films are drasticallyreduced, which could lead to an enhanced exchange bias behavior in certain models (see Section 5 for more details).This suggests that when lithographed exchange bias nanostructures reach the 10 nm regime probably new phenomenawill arise.

3.3.6. Coupled ferri–AFM nanoparticlesIn this subsection we include a study on the coupling of AFM and ferrimagnetic nanoparticles. In most cases the

ferrimagnetic nanoparticles are not embedded in an AFM matrix, but rather AFM and ferri particles are coupled toeach other [494,495]. Two systems have been studied, �-Fe2O3–NiO and �-Fe2O3–CoO. The latter one shows typicalexchange bias effects, in particular a large HC increase compared to isolated �-Fe2O3 nanoparticles. Perhaps the mostremarkable feature of this system is the slowing down of the relaxation time of the �-Fe2O3 nanoparticles due to thepresence of the AFM [494]. This result is analogous to the increase of the superparamagnetic blocking temperatureobserved in Co nanoparticles embedded in a CoO matrix [82]. Interestingly, �-Fe2O3–NiO not only does not showexchange bias effects (loop shift or coercivity enhancement) at low temperatures, but it induces an increase of the rateof relaxation. The authors argue that this effect is probably linked to the low AFM anisotropy not being able to pin theferromagnetic spins.

3.4. Controlled core–shell nanoparticles

In this section we refer to “controlled core–shell nanoparticles” to those systems where the materials and thicknessesof the core and shell can be controlled independently, contrary to the “surface chemically modified nanoparticles”


(Section 3.2). Hence, it would be possible to carry out systematic studies of several interesting exchange bias parameters,e.g., to grow diverse cores of different diameters with a fixed shell thickness, to produce a fixed core diameter withdifferent shell thickness or to fabricate nanoparticles with a fixed core material and different AFM shell and so on.Nonetheless, although there exist several chemical techniques for the growth of controlled core–shell particles and inspite of the recent advances in these growth techniques [496–501], the potential of controlled core–shell nanoparticleshas not been extensively exploited in exchange bias studies.

Most of the core–shell combinations of materials used to date have been basically limited to ferrimagnetic cores–ferrimagnetic shells with some exceptions. Some examples (core–shell) of these nanoparticles are Fe4N (ferri)–LaFeO3(AFM) [502], Sr-ferrite (ferri)–CoO (AFM) [503], Cr2O3 (AFM)–Ytrium-Iron Garnet (ferri) [377], �-Fe2O3 (ferri)–�-Fe2O3 (AFM) [504], �-Fe2O3 (ferri)–Co (FM) [505], FePt (FM)–Fe3O4 (ferri) [506–508], FePt (FM)–Co-ferrite(ferri) [507], Co-ferrite (ferri)–�-Fe2O3 (ferri) [509], �-Fe2O3 (ferri)–Ba-ferrite (ferri) [510], Co-ferrite (ferri)–Zn-ferrite (ferri) [509], Fe3O4 (ferri)–Co-ferrite (ferri) [511–513]. The most studied system, due to its important role inmagnetic recording media (see Section 4) has been �-Fe2O3 (ferri) core–Co-ferrite (ferri) shell [514–529].

The main exchange bias related property observed in this type of materials is coercivity enhancement. For Fe3O4(ferri)–Co-ferrite (ferri) [511–513], �-Fe2O3 (ferri)–Co (FM) [501], �-Fe2O3 (ferri)–Co-ferrite (ferri) [514–529], thisHC enhancement has been reported to increase with increasing shell thickness, levelling off for sufficiently thickshell thickness, similar to what was observed in some oxidized nanoparticles [282,286,293,331,361]. Loop shifts havebeen reported for Cr2O3 (AFM)–Ytrium-Iron Garnet (ferri) [377], in which HE ∼ 400 Oe has been observed at lowtemperatures, exhibiting also typical exchange bias effects, such as reduced blocking temperature (i.e., TB < TN) andtraining effects [377]. However, the presence of an underoxidized CrO2 smaller core within the Cr2O3 AFM coremakes the interpretation of the results more difficult [377]. The most systematically studied system involving an AFMis Sr-ferrite–CoO, in which the thickness of the shell has been controllably changed keeping the core diameter constant[503]. As expected, HE increases steeply for small tShell thickness and saturates at about HE ∼ 600 Oe, while HCshows a broad maximum (see Fig. 16). This system also exhibits a remanence enhancement [503], similar to what wasobserved in Co–NiO [428,429], SmCo5-NiO [80,81] ball milled nanoparticles, Co nanoparticles embedded in a CoOmatrix [82,411] and Fe dots deposited on FeF2 AFM films [204]. Note that remanence enhancement is also observedin core–shell �-Fe2O3 (ferri)–�-Fe2O3 (AFM) [504].

Since most of these materials were developed to improve the hard magnetic properties of ferrites, the fabrication andprocessing procedures were actually not selected to observe exchange bias effects. Namely, they were not field cooledfrom above TN (or TC of the ferrimagnet), or the shell thickness or core diameter were not optimized for exchange biaspurposes. Hence, in most cases the improved properties observed are in an as-made state, similar to the case of ballmilled SmCo5–NiO, where coercivity enhancement could be observed without the need of field cooling. Remarkably,many of these core–shell nanoparticles could be considered as “spring magnets” [530–534], i.e., systems composedof exchange coupled hard and soft ferromagnets (or ferrimagnets). Note that many of the effects observed in springmagnets, e.g., shifted loops of the soft phase [426,530–539], are closely related to exchange bias.

The fact that most of the systems were not optimized for exchange coupling implies that no clear conclusions can bereached about the possible size effects in exchange bias. In spite of this, due to their potential for size and microstructuralcontrol this type of systems holds the promise to answer some of the fundamental issues related to HE in nanoparticlesin the future.

3.5. Surface effects (AFM, Ferri, FM)

Pure ferromagnetic, ferrimagnetic and antiferromagnetic nanoparticles have been extensively studied due to their at-tractive properties, both from basic science and technology points of view. Since the magnetic properties of nanoparticleshave been exhaustively reviewed in recent years [47–62] (in particular surface effects [540,541]), it is beyond the scopeof this article to revise them again. On the other hand, certain magnetic nanoparticles, in particular oxide ferrimagnets,have been reported to exhibit exchange bias-like properties. For example, it is well known that many pure nanoparticlesshow coercivity enhancements at low temperatures which are much larger than the expected from simple single domainconsiderations [58,414]. Moreover, the main tell-tale indication of the existence of exchange bias properties in purenanoparticles is the observation of loop shifts along the field axis at low temperatures after field cooling.

Surface spin canting and surface spin disorder have been evidenced by Mössbauer spectroscopy [386,542–546],inelastic neutron scattering [547], X-ray absorption and dichroism [387,548,549] and polarized neutron diffraction


Fig. 16. Dependence of (a) the loop shift, HE, and (b) the coercivity, HC, on the amount of CoO shell for a SrFe12O19–CoO core–shell nanoparticleat T = 77 K [503].

[550]. Although surface defects introduced by the synthesis techniques (e.g., ball milling) should certainly inducesurface spin disorder, the change of coordination of the surface atoms, especially in oxides due to broken exchangebonds [551,552], can also render surface spin disorder. Shown in Fig. 17 is a schematic illustration of the spin structureof a Ni-ferrite nanoparticle evidencing the disorder of the spins at the surface [551,552]. When this spin disorder freezesat low temperatures it can behave as a “spin glass like” layer at the surface of the nanoparticles. These spin glass surfacelayers can play the role of an “AFM” in the case of FM or ferrimagnetic particles, but it can also act as “FM” onAFM nanoparticles. Even though this intuitive description is rather simple, the full understanding of the exchange biasproperties of pure nanoparticles is far beyond standard exchange bias models.

Perhaps the most studied system from the point of view of exchange bias properties is the ferrimagnetic oxide�-Fe2O3 [337,494,553–560]. In this system, loop shifts [553,554,559,560] and the related effect of shifts in the FMRfrequencies [337,555,556] have been observed. Remarkably, in some cases loop shifts in excess of HE = 1400 Oe havebeen reported [553,554]. Large coercivities and the concomitant increased resonance linewidths at low temperatureshave also been shown [337,553–560]. Studies of these effects as a function of the particle size indicate that the effects


Fig. 17. Calculated spin structure of a 4 nm NiFe2O4 nanoparticle in an applied field of H = 50 kOe [551].

Table 1Exchange bias blocking temperature and the maximum reported loop shifts for some ferrite and manganite nanoparticles

Loop shift, HE Blocking temperature, TB

�-Fe2O3 [553,554,556] HE = 1.4 kOe TB = 30–50 KNi-ferrite [561,567] HE = 1.2 kOe TB = 60–120 KBa-ferrite [568] HE = 500 Oe TB = 60 KCo-ferrite [569] HE = 4 kOe TB = 5 KCu-ferrite [570,571] HE = 280 Oe TB = 40 KMn-ferrite [572] HE = 70 Oe TB=—LaCaMnO3 [573] HE = 50 Oe TB = 50 KFe3O4 [574] HE = 800 Oe TB = 40 K

Note that the given values are not necessarily at the same temperatures, for the same cooling fields or for the same nanoparticle diameters, and arethus not readily comparable.

become larger as the particle diameter (d) decreases, roughly as a 1/d, as expected from a surface effect. Moreover,these �-Fe2O3 nanoparticles also exhibit training effects [553,554]. Finally note that most of these exchange biaseffects vanish at rather low temperatures, around TB ∼ 30–50 K, as expected from the thin surface layer (one or twomonolayers) of disordered spins [553,554,556].

Other ferrite and manganite systems, such as (without pretending to be exhaustive) Ni- ferrite [551,552,561–567],Ba-ferrite [343,568], Co-ferrite [569], Cu-ferrite [570,571], Mn-ferrite [572], LaCaMnO3 [573], and Fe3O4 [574] havealso been studied. In these systems loop shifts (see Table 1) and coercivity enhancements have been observed. Similar to�-Fe2O3, these ferrites and manganites exhibit rather low blocking temperatures (see Table 1). Other typical exchangebias features such as training effects, remanence enhancement or shifts in the M-axis (vertical shifts) have also beenobserved [343,565,569,572]. In some cases a strong reduction of exchange bias with increasing cooling field has beenreported, and linked to the critical field for spin glass in the system [574].

Antiferromagnetic oxides, such as (again without pretending to be exhaustive) NiO [551,552,575–578], CoO[579], CuO [580–584], Co3O4 [585,586], �-Fe2O3 [442,450], Cr2O3 [587,588], FeOOH [589–593], ferritin[(FeOOH)8(FeOH2PO4)] [594,595], and Fe-doped polyethylene oxide [596] have also been studied from theexchange bias point of view. In these cases, coercivity enhancement, loop shifts, vertical shifts, remanence enhancement[442,450,551,552,575–596] have been reported. Some representative values for these materials are given in Table 2.Moreover, in CoO, CuO, FeOOH and Co3O4 a strong dependence of HC and HE on the cooling field has also been


Table 2Exchange bias blocking temperature and the maximum reported loop shifts for some antiferromagnetic nanoparticles

Loop shift, HE Blocking temperature, TB

NiO [551,575] HE = 10 kOe TB = 160 KCoO [579] HE = 2.5 kOe TB = 200 KCuO [580–584] HE = 1.7 kOe TB = 50–100 KCo3O4 [585] HE = 800 Oe TB = 30 K�-Fe2O3 [442,450] HE = 3 kOe TB = 200 KCr2O3 [588] HE = 2 kOe TB = 160 KFeOOH [592] HE = 250 Oe TB = 25 K

Note that the given values are not necessarily at the same temperatures, for the same cooling fields or for the same nanoparticle diameters, and arethus not readily comparable.

reported [579–581,585,589]. This is probably related to the difficulty to saturate the shell layer before the coolingprocedure, which has been shown in thin films to play a role in the exchange bias properties [389–391].

Interestingly, in the case of NiO and CuO, HE appears to decrease with decreasing particle size. This can be understoodfrom the fact that the AFM core becomes “less” AFM (e.g., lower blocking temperature or lower anisotropy) and henceless effective at a given temperature in inducing exchange bias effects [575,582]. For CuO the increase of coercivityafter field cooling appears to be inversely proportional to the particle size [582].

Note that the exchange bias effects in Ni-ferrite, LaCaMnO3, NiO and other AFM have been numerically modeledand many of the experimentally observed features could be reproduced [551,552,561–564,573,575,597–600].

Although metallic FM nanoparticles have been shown to have surface spin disorder [601], its effect on the magneticproperties appears to be less important than in oxides. Perhaps the small effects can be easily masked by the largemagnetization of the core. Hence there exist very few reports of exchange bias surface effects on pure metallic nanopar-ticles. The few systems where such surface effects have been observed are mostly intermetallic nanoparticles, such asFeCu [602], FeNbCrBCu [603], FeRh [604], CoNiB [605] or SmCo5 [606]. Most of these systems have been far lesssystematically studied than ferri or AFM nanoparticles, although loop shifts from a few tens of Oe to 9 kOe have beenreported depending on the system [602,604–606].

Finally, it is important to point out that many of the pure nanoparticle systems described in this section exhibit high fieldirreversibilities. Specifically, hysteresis loops remain open even at very high fields [551–554,558,559,561–566,569,575,576,578,586,589,606]. Hence, effects related to minor loops might have some influence in the values of HE and HCobtained in some systems [173,174,607].

3.6. Coupled AFM–AFM systems

FM–FM interactions have been extensively studied and, in particular, the effects of hard–soft interactions (i.e.,spring-magnets) resemble those induced by exchange bias [530–539]. However, AFM–AFM interactions have beenfar less investigated and therefore are less understood. Mössbauer studies of �-Fe2O3–CoO and �-Fe2O3–NiO indicatethat AFM–AFM coupling results in effects somewhat related to exchange bias. For example, CoO, with a high AFManisotropy, has been shown to increase the superparamagnetic blocking temperature of �-Fe2O3 [398,608,609], similarto what has been observed in �-Fe2O3 coupled to CoO [494] or Co nanoparticles embedded in a CoO matrix [82]. Onthe other hand, NiO, with a low AFM anisotropy, appears to be less effective in changing TB [608,609], although itinduces other effects in �-Fe2O3, such as restoring the Morin transition [608,609]. These differences between NiO andCoO could be ascribed to the differentAFM anisotropies in analogy to exchange bias, where differentAFM anisotropieswould cause diverse effects (e.g., loop shifts vs. coercivity enhancement) in FM–AFM systems. Clearly, more researchis needed in this field to elucidate the similarities and differences between FM–AFM and AFM–AFM couplings.

4. Applications of exchange biased nanostructures

Applications of exchange biased nanostructures were soon proposed after the discovery of exchange bias in oxidizedCo nanoparticles [1,2]. It was suggested that surface-modified nanoparticles exhibiting coercivity enhancement could


Fig. 18. Schematic representation of typical (a) spin valve devices with metallic–non-magnetic interlayers, e.g., Cu and (b) tunnel magnetoresistancedevices with insulating–non-magnetic interlayers, e.g., Al2O3. Depicted in (c) is a characteristic magnetoresistance curve for this type of systems,where the magnetization direction of the layers is indicated.

be used as hard magnets [610,611]. Actually, magnets based on oxidized FeCo nanoparticles, resulting in FeCo coreand a FeCoO3 shell (ferri-), were indeed commercialized during the 1960s [612–615]. Nevertheless, the low blockingtemperature (usually far below room temperature) observed in most of this kind of systems made their applicationsrather limited. However, it has been demonstrated recently that milling permanent magnet materials (e.g., SmCo5) withAFM materials (e.g., NiO) can improve their hard magnetic properties due to exchange bias, even at room temperature,where squareness and coercivity can be improved simultaneously [81,428,429,432]. Hence, these new systems havebecome very promising candidates for the application of exchange biased nanoparticles in powder form, although theFM–AFM ratio has to be optimized in order to overcome the effects of MS reduction of the composite due to the zeromoment of the AFM [81,429,432].

Powdered exchange biased nanoparticles have found applications in recording media. Although, in magnetic mediametallic nanoparticles, e.g., Fe, with oxidized layers are rather common, in this case the oxide layer (usually AFM orferrimagnetic) is used only for passivation and magnetic decoupling purposes [612–615].TheAFM properties of the shellin these systems, which usually only arise at low temperatures, are not exploited, perhaps with the exception of oxidizedFeCo particles [612–615]. During the 1970s and 1980s, controlled core–shell �-Fe2O3–Co-ferrite nanoparticles wereextensively used as magnetic recording media. The role of the ferrimagnetic shell was mainly to induce a coercivityenhancement, without the loss of saturation magnetization, in the �-Fe2O3 particles previously used in the recordingindustry [612–615]. Yet, as discussed earlier, this coercivity enhancement should perhaps be ascribed to a combinationof exchange bias and spring-magnet properties.

Finally, exchange biased core–shell, FM–AFM, nanoparticles have been proposed as possible flux amplifiers formagnetic resonance settings, e.g., in magnetic resonance imaging [616].

The development of “spintronics”, i.e., devices in which the spin degree of freedom has been added, holds thepromise of non-volatility, higher speeds and reduced power consumption [15–17]. The main exponents for this spin-based electronics are spin valves and magnetic tunnel junctions, of which exchange biased nanostructures constitutean essential part [12–46]. Actually, the structures of spin valves and magnetic tunnel junctions are rather similar. Theyare based on two FM layers separated by either a non-magnetic metal, usually Cu (spin valves) or an insulator, usuallyAl2O3 (tunnel junctions) (see Fig. 18). One of these FM layers is pinned using exchange bias, i.e., by coupling it toan AFM layer. Note that more complex pinning strategies, such as synthetic AFMs, are also being used [28,617–620].This pinning renders a FM layer relatively insensitive to moderate magnetic fields. Conversely, the magnetization ofthe other FM layer, usually denoted as “free layer”, can be easily reversed by using small fields. This means thatthe relative orientation of the magnetization of each layer can be chosen to be either parallel or antiparallel by usingsmall fields. The spin valve and tunneling devices use the difference of resistance between the parallel and antiparallelstates of the magnetization, either due to changes in scattering (spin valves) or in the tunneling probability (tunnel


Fig. 19. Cross-sectional TEM image of a cell in a MRAM memory. The cell is separated between the magnetic part (MRAM BEOL) and theelectronic part (CMOS FEOL). The bit line and word line, used to write and read information are shown in the image. The magnetic tunnel junctionis highlighted by a circle. Image courtesy of Freescale Semiconductors.

junctions) [12–46]. The ever-increasing industrial demand for miniaturization is pushing the dimensions of spin valveand tunneling devices deep into the submicron regime [26–28,34,35,41–43]. Two examples of such submicron devices,in the production stage are read heads for hard drives [621–628] (for example, the evolution of the recording headtechnology as the density has evolved from 3 Gbit/in2 — in 1996 — to 130 Gbit/in2 — in 2003 — [629–640]) andmagnetic random access memories (MRAM) [660–682]. For example, as the storage density surpasses 150 Gb/in2

the stripe width of the read head will reach dimensions well below 100 nm [28]. Moreover, current 1 Mbit MRAMtechnology utilizes bits of lateral sizes below 200 nm [43] (see Fig. 19).

Recently, a new prospective application of exchange bias in nanoparticles and nanostructures has been developed.It has been proposed theoretically that exchange bias could be used to stabilize the magnetization of nanostructuresagainst thermal fluctuations [683]. Experimentally, it has been demonstrated that FM nanostructures deposited on anAFM layer (see Fig. 8) exhibit improved remanence, MR (a clear indication of improved magnetic stability) with respectto particles deposited on non-magnetic substrates [204].

Most of the applications of nanostructures (not necessarily exchange biased), and, in particular, in high-density mag-netic recording, relay on their stable magnetic order, i.e., single domain state, of the nanostructures with time [46–78].However, with decreasing size, the magnetic energy per particle (or nanostructure), KUV (where KU is the magneticanisotropy and V the particle volume) holding the magnetic moment along a certain direction becomes comparable tothe thermal energy, kBT (where kB is the Boltzman constant and T the temperature). When this happens, the thermalfluctuations induce a random flipping of the magnetic moment of the nanostructure with time, consequently losingtheir stable magnetic order, i.e., the nanoparticles become superparamagnetic. The temperature at which superpara-magnetism sets in is usually denoted as blocking temperature, TB-SP [47,57,58,62,414] (not to be confused with theexchange bias blocking temperature, i.e., the temperature above which HE vanishes, with the same name!). Thus, thedemand for further miniaturization, i.e., reduction of V , comes into conflict with the concomitant superparamagnetismcaused by the reduction of the magnetic anisotropy energy, KUV . This effect can be, to a certain extent, countered byincreases in KU. It is noteworthy that superparamagnetism, together with other factors, sets a fundamental limit forthe increase of areal density in conventional recording media, i.e., the so-called “superparamagnetic limit” [684,685].Thus, it would be desirable to have an external and tunable source of anisotropy, which could give further stabilizationin the magnetization of nanostructures. The new anisotropies induced at the interface between FM and AFM systems


by the exchange bias coupling, have been shown to supply the necessary extra anisotropy for magnetization stability[82]. However, it has to be taken into account that the “superparamagnetic limit” in magnetic recording is actually notonly related to the nanoparticles becoming superparamagnetic at room temperature below a certain size, but also tothe “dilemma” that the anisotropy can not be increased arbitrarily, since the coercivity should be lower than maximumwrite-field available (limited by the saturation magnetization of FeCo alloys). Hence, like in antiferromagneticallycoupled media [686,687] or thermally assisted recording [688], if exchange bias coupled nanoparticles are to be usedin recording media, they should be engineered to fulfill this criterion.

Nevertheless, these magnetization stabilization schemes of nanostructures, provided by exchange bias, will certainlyplay a key role in the continuing miniaturization race. Exchange bias magnetization stabilization can probably be uti-lized in many different aspects of the applications of magnetic nanostructures. The first logical application could be, assuggested by Skumryev et al. [82], to beat the superparamagnetic limit in longitudinal and perpendicular magnetizationrecording media. Moreover, any application where single domain nanostructures are utilized, but where superparamag-netism would limit their miniaturization potential, could benefit from exchange bias coupling. A clear example couldbe patterned recording media [46,63,71,74,689], where each bit of information is stored in an individual single domainparticle. For example, a fcc-Co nanoparticle would become superparamagnetic at room temperature around a diameterd ∼ 10–15 nm [690]. However, using exchange bias, nanoparticles as small as d ∼ 3 nm have been demonstrated toremain ferromagnetic at room temperature [82]. It is noteworthy that although the superparamagnetic blocking tem-perature of nanoparticles can be enhanced by exchange coupling, it has been shown that the Curie temperature of FMthin films appears rather insensitive to the FM–AFM coupling [691].

Another property of exchange biased nanostructures which has been suggested for applications is their MR/MS =1 (if the loop is significantly shifted). That is, at H = 0 the FM–AFM systems are fully saturated, implying thatthe nanostructures could be single domain at remanence. Hence, magnetization reduction or noise effects due tothe presence of domains would be minimized. Two examples found in the literature are: magnetoresistive devicessuch as read heads [692–696] and magnetic force microscopy tips [697], which improve their performance whenexchange biased.

5. Theoretical implications

In this section we review some theoretical aspects of exchange bias in nanostructures. Some relevant models forexchange bias are summarized in Section 5.1. In Section 5.2 we discuss some characteristic length scales in FM andAFM materials. In Section 5.3 we briefly analyze how the reduction of the dimensions of the system can affect some ofthe main exchange bias theories and in Section 5.4 we comment on some models that have been specifically developedfor exchange biased nanostructures.

5.1. General exchange bias models

In this section we revise some of the existing theories, for thin film systems, for exchange bias and related phenomena.Following Coehoorn’s classification [12], we divide the models into three categories: macroscopic, mesoscopic andmicroscopic with regard to the lateral length scales. Other types of models such as those based on the propagation ofspin waves or more complex quantum mechanical effects [698–700] are not considered.

5.1.1. Macroscopic modelsMacroscopic models are considered those that do not take into account the lateral magnetic structure of the layers.

Namely, these models assume that the layers are homogeneous in the x–y plane. Usually the spins of the AFM layerare assumed to be uncompensated (i.e., the net magnetization in the first layer of the AFM is different from zero) andto lay parallel to the interface plane. In some of the models included here the detailed spin structure in the z-directionof the FM and/or the AFM is actually considered. However, since no lateral effects, i.e., variations in the spin structurein the x–y plane, are taken into account, we do not treat them as mesoscopic or microscopic.

The first theoretical approach developed to explain exchange bias was the model by Meiklejohn and Bean [2,3]described intuitively in the Introduction. Two of the main assumptions of this model are that the magnetization rotates


coherently and that the FM and AFM easy axes are parallel. Within this approach, the energy per unit surface in theFM–AFM couple can be expressed as

E/S = −HMFMtFM cos(� − �) + KFMtFMsin2(�) + KAFMtAFMsin2(�) − JINT cos(� − �),

where H is the applied magnetic field, MFM is the saturation magnetization in the FM, tFM and tAFM are the thicknessesof the FM and AFM layers [701], KFM and KAFM are the magnetic anisotropies in the FM and the AFM and JINT isthe exchange coupling constant at the interface. The angles �, � and � are the angles between the spins in the AFM andthe AFM easy axis, the direction of the spins in the FM and the FM easy axis and the direction of H and the FM easyaxis, respectively.

As can be seen from the different energy terms, if no coupling exists between the FM and the AFM and the appliedmagnetic field becomes zero, the overall energy of the FM–AFM system reduces to the terms due to the FM and theAFM magnetic anisotropies (2nd and 3rd terms). When a magnetic field is applied, a certain work has to be carriedout to rotate the spins in the FM (1st term — Zeeman term). Finally, the 4th term represents the FM–AFM coupling.If the AFM is assumed to have very large anisotropy, the spins of the AFM do not rotate with the field (i.e., they keepaligned along the AFM easy axis, so that � ∼ 0 and sin2(�) ∼ 0 — i.e., for fields below the spin flop field). Then itcan be shown that the hysteresis loop will shift by an amount HE = JINT/MFMtFM along the magnetic field axis [702].

It is noteworthy that if the magnetic anisotropy in the AFM is low (this is usually expressed as KAFMtAFM < JINT)it is energetically more favorable that during the hysteresis loop the spins in the FM and the AFM rotate together, i.e.,� − � ∼ 0. In this case no loop shift is induced. On the other hand, the value of HC will be enhanced, since the overallmagnetic anisotropy is modified due to the coupling.

As discussed in the Introduction, within this model, choosing appropriate values of the interface exchange constant,JINT, the values predicted for HE for thin film systems are usually much larger than the experimental results.

The first important modification to this model was proposed by Néel [703,704]. The main novel feature of Néel’smodel was to consider that when the field is reversed, instead of having a sharp magnetic interface, a domain wall,or a partial domain wall, forms either in the FM or in the AFM parallel to the FM–AFM interface. Similar argumentshave been used more recently by different researchers in their exchange bias models, e.g., in the work of Mauri et al.[705], Kiwi et al. [706–708], Geshev [709] or Kim et al. [710,711]. Thus, terms related to the formation of domainsare included in the energy expression. Whether the domain wall forms in the FM, in the AFM or in both will dependon which is the most energetically favorable solution. The interface domain wall may strongly decrease the energy ofthe equilibrium magnetic configuration, and, consequently the values of the “effective” coupling. Hence, based on thisapproach, the obtained loop shift becomes, in the strong interface coupling limit:

HE ∝ √KAFMAAFM/MFMtFM or HE ∝ √

KFMAFM/MFMtFM

depending on whether the domain wall is formed on the AFM or FM side of the interface, where AAFM and AFM arethe exchange stiffness of the AFM and FM, respectively. When substituting suitable values for the anisotropy and theexchange, the new value for HE is usually much closer to experimentally observed loop shifts.

In order to explain diverse experimental observations, many variations of this type of macroscopic models, combiningthe different energy terms described or introducing new ones, such as higher-order anisotropy terms or perpendicularcoupling (see 5.1.3), have been reported in the literature [95,109,712–716].

5.1.2. Mesoscopic modelsIncluded in mesoscopic models are those models that take into account, in some way or another, the possibility of

differences in the spin configuration in the x–y plane.Probably the first model to include some lateral spin distributions was introduced by Kouvel [173,717]. The model,

conceived to explain exchange bias in CuMn alloys, establishes the possibility of domains in the AFM. Although themodel was devised for inhomogeneous alloys, the ideas developed could be extrapolated to thin film systems.

The second major contribution to mesoscopic models was by Fulcomer and Charap, who considered the effects ofgrain size distribution in exchange bias [718]. The model is based on AFM grains of different sizes that are coupledto the FM, but uncoupled between them. The novel approach of the model is to recognize that different grains cancouple differently to the FM and that small AFM grains will have a tendency to superparamagnetism. More recently,related models, based on different properties of AFM grains (e.g., distribution of the number of uncompensated spins,


of the direction of easy axes, of the AFM anisotropies or of the FM–AFM interface coupling strength) [394,719–729] ordifferent degrees of coupling betweenAFM grains [728,729], have been developed. More sophisticated models based onsimilar ideas, which include the possibility of more sophisticated effects such as partial domain walls or perpendicularcoupling in the AFM grains, are becoming the basis for exchange bias models in polycrystalline FM–AFM systems[719–729]. For example, Stiles and McMichael consider the AFM layer as constituted by an ensemble of crystalliteswith different sizes and different AFM anisotropy directions. They show that, in these systems, those grains withlarge FM–AFM direct coupling constant and easy axes closer to the field cooling direction will not easily switch theirmagnetization during reversal of the FM, hence contributing to exchange bias. Conversely, similar grains with strongexchange coupling and easy axes oriented at a certain angle beyond a critical angle from the FM easy axis, will switchtogether with the FM, contributing to the enhancement of HC. Additionally, those grains with weak direct couplingconstant will not strongly contribute either to HE or to HC. This model is particularly suitable to explain the widespreadresults in FM–AFM fine particle nanocomposites, where different microstructures may contribute to different observedeffects [727].

However, the main example of mesoscopic models tends to be attributed to Malozemoff’s model [730–732]. Themodel, based on the ideas of Imry and Ma [733] and Meiklejohn and Bean [2,3], includes the possibility of a notperfectly flat FM–AFM interface. The interface roughness (or other defects) produces a random field, which leadsto the break up of the AFM into domains with domain walls perpendicular to the interface and sizes roughly givenby �(AAFM/KAFM)1/2. The imbalance of AFM moments, due to statistical reasons, at the surface of these domainsgenerates uncompensated moments that couple to the FM, resulting in exchange bias. More recently models based onMalozemoff AFM domain formation have been developed to explain other phenomena such as coercivity enhancement[117,156,734,735].

Finally, it is important to point out that, in a sense, the concepts used in the domain models and the modelsbased on grain effects are actually quite similar, since one of the main effects of out-of-plane domains is to provideuncompensated spins.

5.1.3. Microscopic modelsMicroscopic models are those that take into account the detailed spin configuration of each atom (or groups of

atoms) in the volume of the system, i.e., in the x, y, and z directions. There exist several approaches to this type ofmodels: Monte Carlo simulations [736–746], micromagnetic calculations [747–752] and different types of spin latticemodels [753–757]. In the latter case, although the spin structures are considered, different kinds of approximations aredeveloped to simplify the search of the spin configurations with minimum energy [753–757].

Note that although microscopic models take into account the spin structure of the AFM, most of the models use thesimplest type of uniaxial AFM. Uniaxial AFMs are correct for FeF2 [743], however they are certainly not adequatefor common AFMs such as FeMn or CoO. These AFMs have more complex spin arrangements with either more thantwo sublattices (e.g., FeMn or IrMn) or multiple anisotropy axes (e.g., CoO or NiO). Since there are indications thattaking into account these effects can strongly influence the results [159,751], more realistic microscopic models wouldbe desirable.

One of the pioneering microscopic theoretical works for the modeling of compensated interfaces was due to Koon[747]. He argued that the configuration with minimum energy for a compensated AFM and a FM is to couple the FMand AFM spins perpendicular to each other, as was later demonstrated experimentally [96–98]. Thus, a new term inthe energy equation, of the type J ′(mAFMmFM cos �)2, i.e., biquadratic, is introduced to account for spin–flop likecoupling. Actually, this effect is now often implemented in macroscopic models. It has been demonstrated that this spinarrangement does not give rise to exchange bias but nevertheless, it does account for coercivity enhancement in somesystems [751].

Schulthess and Butler have shown that Koon’s perpendicular coupling, together with uncompensated spins (similarto Malozemoff or Takano et al. suggestions [394,730–732]) can explain simultaneously the loop shift and coercivityenhancement encountered in FM–AFM bilayers [751].

Miltényi, Nowak, Misra, Beckmann et al. used Monte Carlo at finite temperature to study a FM–AFM couple withdefects in the bulk of the AFM, i.e., not necessarily at the interface. They found the formation of domains in the bulk ofthe AFM, perpendicular to the FM–AFM interface, that gave rise to uncompensated spins at the interface, which wereresponsible for the hysteresis loop shift. They also found that increasing the number of defects, within certain limits,increases the number of AFM domains, leading to larger exchange bias [736–742].


Table 3Characteristic length scales: exchange length (lex), domain wall width (��o), critical single domain size for a sphere (RSD) for some ferromagneticmaterials estimated using bulk parameters [48,56,58,758,765–767]

lex (nm) ��o (nm) RSD (nm)

Fe 1.5 40 18Co (hcp) 2.0 12 70Ni 3.4 80 60Ni80Fe20 (permalloy) 4.0 ∼ 100 ∼ 22SmCo5 4.9 4 764

Suess et al. have developed a model based on perpendicular coupling and randomly distributed, exchange coupled,AFM grains. Interestingly, the origin of exchange bias is found to be in the energy stored in the domain walls betweenAFM grains with different orientations [748–750].

Lederman et al. have recently reported that if the FM layer couples differently to each of the two AFM sublattices,it could give rise to exchange bias. Actually, using this simple concept many of the experimentally observed effects inFM/FeF2 bilayers can be explained [743].

As shown above, some microscopic models actually lead either to mesoscopic effects or have imposed mesoscopiceffects, such as the formation of AFM domains [736–742,746,751,752].

5.2. Characteristic length scales

Before discussing the effects of lateral size reduction in some of the exchange bias models presented above, itis instructive to introduce some relevant length scales that control the behavior of magnetic materials. This willallow estimating the dimensions of the exchange biased nanostructures which could be most susceptible tosize effects.

Ferromagnetic materials exhibit a range of length scales that influence their magnetic structure (e.g., the formationof domains) and ultimately their response to an applied field. From the basic magnetic parameters of FM systems,such as exchange stiffness constant A (proportional to the exchange integral J , which for a cubic structure becomesA = nJS2/a, where a is the lattice constant, n the number of atoms per unit cell, and S the magnitude of the spin),saturation magnetization Ms and anisotropy constant K , two of the basic length scales of ferromagnetism can be definedas follows [58]:

Exchange length lex =√

A/�0M2s

and domain wall parameter, also called exchange correlation length, �o =√

A

K.

The exchange length lex represents the length below which atomic exchange interactions dominate the effects ofmagnetostatic fields. To be precise, within lex the spins of the ferromagnet remain parallel. The values of lex are rathersimilar for most ferromagnetic materials, in the range of lex ∼ 1–6 nm (see Table 3). The domain wall parameter �ois related to the thickness of the domain walls that separates magnetic domains characterized by different orientationof the magnetic moment. In other words, the distance over which the variations of the spin orientation are correlated.In terms of lex, �o becomes, �o ≈ lex for hard magnets, while �o?lex for soft materials. The width of domain wallsis essentially determined by the competition between exchange energy, which tries to keep the spins parallel and thusfavors wide domain walls, and anisotropy energy which tries to keep the spins along certain directions and hencepromotes narrow walls. For example, in the case of a 180◦ Bloch wall of a uniaxial bulk material the domain wallwidth is given by �B = ��o. This parameter changes considerably from �B ∼ 1 nm in hard magnetic materials to over100 nm in soft ferromagnets (see Table 3). For other types of walls the multiplying factor will be different. Actually,the domain wall width may depend on other factors such as the film thickness. Moreover, the creation of magneticdomains arises from the need to minimize the magnetostatic energy. Thus, the formation of domains is only favoredif the reduction in magnetostatic energy is larger than the energy necessary to create a domain wall. This fact leadsto another characteristic length scale, i.e., the critical single domain radius, which for a sphere with large uniaxial


Table 4Estimated domain wall width, ��o,AFM, for some antiferromagnets assuming bulk parameters [726,768–772]

��o,AFM (nm)

NiO 11–2000FeF2 1.4Fe50Mn50 ∼ 50

anisotropy is given by [58]

RSD = 36√

AK

�0M2s

.

Materials with large cubic anisotropy or low anisotropies have other expressions of RSD [758–760]. Note that thislength scale depends very strongly on the shape of the structures [761,762]. The existence of a single domain radiusimplies that even if a nanostructure (e.g., a sphere) of a certain material is large enough to fit a domain wall, thatdoes not necessarily indicate that domains will be created. For example for hard magnetic materials RSD?�o (seeTable 3); Hence, although a SmCo5 sphere of 500 nm radius could enclose many domains, (�B ∼ 4 nm) due to thehigh energy necessary to create a domain wall, proportional to

√AK , it is favorable to remain single domain. In

the case of soft materials �B > RSD; this implies that in this kind of materials, inhomogeneous magnetization states,e.g., flower state or vortex state, will extend over the whole nanostructure [58,759]. Generally speaking, in very smallparticles magnetization reversal occurs ‘coherently’ during reversal, i.e., magnetization remains homogeneous with thesame magnitude and direction everywhere in the particle. For larger particles, incoherent modes of reversal, involving‘curling’ or ‘fanning’, will govern the magnetization reversal [58].

Another important length scale for nanostructures, which is perhaps not as fundamental as the previous ones, is thelength scale at which nanostructures form magnetic structures with zero or reduced net magnetization in zero field,e.g., closure domains or vortices [58,63]. Although in this type of magnetic arrangements the magnetostatic energywould be reduced to zero (in the case of complete flux closure), the energy of creating more walls or inducing spinstructures with high exchange energy, i.e., tilted neighboring spins, has to be taken into account. This length scale isstrongly dependent on the shape (e.g., round vs. square) and aspect ratio (e.g., elliptical vs. circular), i.e., ellipticalnanostructures can remain single domain, instead of forming a vortex state, for larger sizes than circular structures [63].

Different magnetic length scales should also be present in AFMs. However, they have not been studied systematically[237–253,763–765]. Exchange length effects should, in principle, be similar to the ones observed in FMs. That is tosay, non-collinear structures could arise for sizes larger than the exchange length, lex. Analogously to the FM materials,the domain wall parameter of the AFMs is defined as �o,AFM = (A/K)1/2 (see Table 4 for some examples of calculated�o,AFM). As for FM materials, AFM materials with sizes below �o,AFM should be in a single domain state. From Table4 it can be seen that materials with small anisotropy, such as NiO with a large �o,AFM (note that domain wall sizes inexcess of 200 nm have been observed experimentally in NiO single crystals [763–765]), could become single domainfor very large sizes, while materials with very large anisotropy, e.g., FeF2 with �o,AFM ∼ 1 nm, could have domainseven for sizes not reachable with conventional lithography.

AFMs have no net magnetization, thus the magnetostatic energy plays a negligible role in the domain formationof this type of materials. Hence, the concept of critical single domain size radius (and closure domains or vortices)will be drastically modified for an AFM. Other effects, such as magnetoelastic energy or gains in entropy (due toincreased disorder), will play a dominant role in domain formation [237–253]. The values for �o,AFM given in Table 4are for a “perfect” material, where the anisotropy is assumed to be of a purely magnetocrystalline origin. Nonetheless,magnetoelastic anisotropy, due to defects, twins, dislocations or even sample edges, should be taken into account tocalculate �o,AFM and it could actually have a dominant role for some real materials [251,773]. Hence, the values of�o,AFM given in Table 4 should be taken as an upper bound for the domain wall width. Moreover, defects, such asnon-magnetic dilution or grain boundaries, are known to promote the formation and stabilization of domains in AFMmaterials [774]. Actually, a clear correlation between AFM domains and grain size has been experimentally observedin NiO and LaFeO3 [252,763,764].


It should be stressed that in exchange biased systems the properties of AFM and FM are closely interlinked. Forexample, the magnetization state of the FM during cooling will affect the magnetic configuration of the AFM at lowtemperatures and in turn the AFM will control the reversal of the FM. Actually, other more subtle correlation effectsbetween AFM and FM in exchange biased samples probably take place [252,775–779]. For example, changes in �oand �o,AFM could arise since, due to the coupling, new anisotropies emerge in the FM–AFM system. Consequently,when addressing the effects of size reduction in exchange biased nanostructures length scale considerations for boththe FM and the AFM should be taken into account. Moreover, it has to be realized that the relevant length scales forthe AFM and the FM could be very different. For instance, it is not the same to deal with a FeNi/NiO nanostructurethan with a Co/NiO nanostructure, since, for example, for FeNi (permalloy) the domain wall width could be similar toNiO, yet the domain wall width of Co is substantially smaller than for NiO. Another parameter which needs to be takeninto account is the temperature, since for example the temperature dependence of the anisotropy of the AFM and FM,which controls some of the magnetic length scales, may be quite different, which in some cases could lead to oppositebehavior depending on the temperature. For example, the AFM domains in NiO have been observed to change size andorientation close to TN [764].

5.3. Consequences of lateral size reduction on standard models

After these considerations about relevant magnetic length scales, we next describe intuitively the possible effectsof lateral size reduction in some of the standard exchange bias models, mainly focusing on lithographed FM–AFMnanostructures of type I (see Fig. 5). Particularly, more complex systems such as core–shell particles or FM nanoparticlesembedded in AFM matrices are not discussed here, especially since many of the models would not be applicable insome of these morphologies.

Most exchange bias models do not specifically discuss the lateral magnetic structure of the AFM or FM layers intheir formulations. Hence, it is not straightforward to envisage the effects of patterning in most of the models.

In macroscopic models, since no lateral length scale is involved, size reduction should, a priori, not affect their mainfeatures. In spite of this, indirect effects could arise. For example, most macroscopic models assume coherent rotationof the FM. The FM layer in continuous films does not usually reverse by coherent rotation. On the other hand, innanostructures the FM magnetization could switch via this reversal mode, particularly if the size of the nanostructurefavors a single domain state in the FM. Hence, some of the consequences derived from certain macroscopic modelsmight be more adequate for nanostructures.

As discussed above, some of the mesoscopic and microscopic models do include explicitly or implicitly some laterallength scales in their formulation. Often, the length scales involved are of the same order of magnitude as the lateralsizes achievable by conventional lithography techniques. However, again, predicting the effect of lateral size reductionusing simple arguments is rather complex.

For systems based on a distribution of AFM grain properties (e.g., grain size or anisotropy), it can be argued that asthe nanostructures are reduced in size, the average properties observed in thin films will be modified. The number ofgrains in a nanostructure will be limited, thus the properties of the individual grains, rather than the average of all thegrains, can become significant. Moreover, each nanostructure will have a different set of grains, thus the properties ofeach nanostructure will probably be different if measured individually. If measured collectively, nanostructuring couldlead to typical effects of distribution of magnetic properties, such as sheared loops or broad switching field distributions.In the case of models based on grain size distribution or AFM anisotropy distribution, unusual effects could arise. Forexample, some nanostructures could be comprised of a few large (or high anisotropy) grains, leading to a large bias —eventually larger than that of continuous films, while other nanostructures could consist of smaller (or low anisotropy),superparamagnetic grains, giving no bias. Similar arguments could be presented for systems with a distribution of AFMeasy axes. For example, nanostructuring could improve, locally, the microstructural texture. This should result in anenhancement of exchange bias if the distribution of easy axes in the nanostructure is close to the FM easy axis. Though,if texture effects are favored in the nanostructures along a direction far from the FM easy axis, the overall HE wouldbe reduced with respect to continuous films. This effect would be similar to the tuning of HE observed by the relativeorientation of unidirectional and uniaxial anisotropies reported in certain nanostructures [196,209].

For models based on AFM domains similar effects may arise. First, as the nanostructure size decreases, averagingeffects of films will be altered, thus strong inhomogeneities in the magnetic properties of the individual nanostructureswould be expected. For even smaller lateral sizes, the AFM domain size will be limited to the physical size of the


nanostructure. In this case, a reduction of HE can be predicted (with respect to continuous films) since the amount ofAFM domain walls and the associated net uncompensated AFM magnetic moment will be reduced. However, if the sizeof the nanostructure is sufficiently reduced, as a consequence of Imry and Ma statistical imbalance concepts [730–733],the number of uncompensated spins per unit area should increase. This could lead to an increase of the exchange bias.Similar arguments can be used in the case of models based on uncompensated spins [719–726].

It is instructive to examine in more detail one of the few cases which allows for a simple analytical analysis.Malozemoff’s model predicts that, for thin enough AFM layers (i.e., in the so-called Heisenberg regime), the magnitudeof the exchange bias field, HE, decreases as the thickness of the AFM layer, tAFM, increases [730–732]. It can be arguedthat for a given AFM domain size, DAFM, the number of AFM moments at the FM–AFM interface is N = (DAFM/a)2,where a is the distance between AFM spins. The interface random field energy can be expressed as −JFM–AFM/N1/2,where JFM–AFM is the exchange constant of the FM–AFM coupling. Therefore, the interface coupling energy per unitarea is

FM–AFM = −JFM–AFM/aDAFM.

Hence, the interface coupling energy decreases when increasing the AFM domain size. Additionally, the domain wallenergy in the AFM, assuming that domain walls are oriented perpendicular to the FM–AFM interface and extendingthrough the whole AFM layer can be written as

DW,AFM = �2JAFM/(4aDAFM).

This equation shows that AFM domain walls are more difficult to create for thicker AFM layers. In fact, DW,AFM canbe minimized by enlarging the AFM domain size. By minimizing the total energy per unit FM–AFM interface area,i.e., FM–AFM + DW,AFM one obtains the following relationship between the AFM domain size and tAFM:

DAFM = (JAFM/JFM–AFM)�2tAFM.

Hence, substituting the expression for the dependence of DAFM on tAFM into the interface energy FM–AFM, an inverseproportionality relationship between FM–AFM and tAFM is readily obtained.Actually, some exchange biased continuousbilayers, such as permalloy/IrMn bilayers, show an inverse proportionality relationship between HE and tAFM [780,781].Taking into account reasonable values of JFM–AFM and JAFM for IrMn from the literature, i.e., JFM–AFM=7.6×10−22 J

and JAFM = 16.1 × 10−22 J (as calculated from the Néel temperature of IrMn) [782], one can estimate, for example,that DIrMn is of about 150 nm for tIrMn = 5 nm and it increases progressively up to about 500 nm for tIrMn = 20 nm.Thus, although these values are only indicative, it seems reasonable to assume that for sub-100 nm dots, it is likely thatthe lateral dimensions of the dots will impose physical limitations to the AFM domain size, particularly for relativelythick AFM layers. As a consequence, it can be predicted that, if continuous FM–AFM bilayers exhibiting a decreaseof HE for larger tAFM are patterned, the magnitude of HE will remain roughly insensitive to the AFM layer thicknessfor thick enough AFM layers or small enough nanostructures. Eventually, this will lead to larger exchange bias in thenanostructures than in the continuous film of the same AFM and FM thicknesses. This effect has, in fact, been observedexperimentally [190].

At first approximation, the intuitive consequence of most of the “standard” exchange bias models is to reduce HE,compared to continuous films, as the lateral size of the nanostructures decreases. Nevertheless, for sufficiently smallsizes an increase of the loop shift, compared to larger nanostructures, may be observed. Yet, the exact behavior ofthe size dependence of the exchange bias properties will depend not only on the lateral size, but also on the exactstructure and conditions of the system, i.e., AFM and FM materials, tAFM, tFM, grain size distributions, temperatureand so on.

5.4. Models specific for exchange biased nanostructures

Recently some models have been proposed in order to specifically describe exchange bias in nanostructures. Forexample, Zhang and Li [783] have studied the behavior of the exchange bias field, HE, and the coercive field, HC, inpolycrystalline films when the lateral size of the system is reduced. They mainly take into consideration magnetostaticeffects appearing as a result of the reduced dimensions of the nanostructures, claiming that the intradot magnetostaticenergy acquires importance with respect to other energy contributions (exchange and anisotropy energies in the FM


and the AFM layers, random exchange coupling energy between FM and AFM layers and Zeeman energy due to theapplied magnetic field) as the lateral size of the nanostructures is reduced. This leads to the formation of new andsmaller magnetic domain structures during magnetization reversal of the FM, which impose changes in the magnitudesof HE and HC. It is worth noting that magnetostatic energy effects are usually not taken into account in macroscopicsystems because they are assumed to be negligible. Within this model, micromagnetic simulations are performed toobtain the hysteresis loops, solving the standard Landau–Lifshitz–Gilbert equation. The model provides a critical dotsize, LC, at which the domain size due to random FM–AFM interfacial energy becomes comparable to that due tomagnetostatic energy and below which magnetostatic energy contribution becomes significant:

LC =(

2J 3FMKm

J 4FM–AFM

)1/3

t5/3,

where Km = (1/2)�0M2S, JFM is the exchange constant in the FM. Since the magnetostatic energy increases with tFM,

this critical dot size becomes larger for larger FM thickness. From this approach one obtains, for example, that, forpermalloy, LC = 200 nm when tFM = 10 nm. The model predicts that both HE and HC can increase (as much as 30%)when the lateral size of the system is reduced while keeping the FM thickness relatively large, i.e., when magnetostaticenergy effects become predominant.

Another example of theoretical studies specific of nanostructures is the modeling of circular FM–AFM dots bymicromagnetic and scaled Monte Carlo simulations [191,192,784]. Vortex states have been found to nucleate, althoughtheir formation may intuitively appear to be energetically unfavorable due to the presence of a unidirectional coupling.That is, during the cooling procedure a favored direction is set in the AFM. Thus, having FM spins at different anglesfrom the field cooling direction, as it occurs in the vortex state, results in an increase of the exchange energy of the system.These vortex states have properties that differ from conventional vortex (i.e., in systems without AFM). For example,as observed experimentally [191,192,195], the loops appear shifted on the field axis and depending on direction of theapplied field, with respect to the unidirectional anisotropy, vortex states are no longer stable and coherent rotation isfavored. Other unusual phenomena, such as the vortex core not propagating perpendicular to the applied field axis, aswould be expected for uncoupled dots, or changes in the annihilation and nucleation fields have also been observed[191,192,784]. It is noteworthy that micromagnetic simulations of submicron rectangular spin valves with syntheticantiferromagnet pinned by an AFM, seem to indicate that exchange bias suppresses the formation of flux closure statesin the pinned FM layer [785].

Moreover, four models that discuss the coupling between FM nanostructures on continuous AFM films (i.e., type IIstructures, see Fig. 5) or embedded in an AFM matrix have been recently proposed. The main finding of these modelsis that the continuous AFM layer stabilizes the thermal fluctuations of FM nanostructures [82,683,786,787].

It is well known that thermal switching of a single domain FM nanostructure follows an Arrhenius behavior =0 exp(�E/kBT ), where 0 is the attempt frequency and �E = KV is the energy barrier the magnetization has toovercome [788,789].

The models show that the presence of a FM nanostructure on top of an AFM layer induces a canting in the AFM spins(in the immediacy of the FM nanostructure). The FM spins, due to the coupling to the AFM spins through the interfaceexchange, experience an enhanced energy barrier for reversal, �E′. This energy barrier, which should lead to coercivityenhancement, translates also in an increased thermal stability of the nanostructure, since �E′ > �E [82,683,786].While some models postulate that �E′ should increase for larger interface coupling JFM–AFM, and smaller AFMexchange, JAFM, [683,786] other models point to the AFM anisotropy, KAFM [82] as the critical parameter controllingthe enhanced energy barrier. It is noteworthy that this exchange bias enhanced energy barrier has been proposed as apossible route to overcome the “superparamagnetic limit” in magnetic recording media [82].

Finally, different efforts aimed at understanding, from a theoretical point of view, the exchange bias properties ofcore–shell nanoparticles and FM nanoparticles embedded in AFM matrices have been reported [307,348,436,598,790–793]. Most of the studies rely on uncompensated spins in the AFM, based on the surface intrinsic spin canting,to explain the observed loop shifts. The coercivity enhancement is usually related to an extra anisotropy induced bythe AFM shell on the FM core. Monte Carlo studies have actually reproduced many of the observed experimentalphenomena, such as tShell or temperature dependencies of HC and HE [791]. Moreover, in a recent model, based onthe Preisach hysteresis assumptions, some of the exchange bias features of ball milled FM–AFM structures have beenreproduced [436].


6. Conclusions

In conclusion, we have reviewed the exchange bias properties of different types of AFM–FM nanostructures. Con-cerning lithographed nanostructures several regimes can be envisaged where the exchange bias behavior of the systemsis expected to deviate from that of continuous materials: (i) when the role of the shape anisotropy and demagnetizationfield (and competition between different anisotropies) becomes important, (ii) when the physical size of the nanostruc-tures becomes commensurate with the magnetic length scales of the AFM or FM (e.g., domain wall size and criticalsingle domain size), and (iii) when the size of the nanostructure reaches the dimension of the structural constituents, i.e.,crystallite size of theAFM. The effects of size reduction in exchange bias depend strongly on the exact system (e.g., size,shape, FM material, AFM material, or microstructure) and measuring conditions (e.g., temperature, measuring angle,or cooling conditions) and actually opposite trends can be observed depending on the precise set up. Consequently,more systematic studies are needed to fully understand ‘size effects’ in exchange biased lithographed nanostructures.For example, comparative investigations expanding over a wide range of sizes (from tens of microns to a few tens ofnm), involving different FM and AFM materials (e.g., different anisotropy or different domain wall width) with diversemicrostructures (e.g., single crystal, twinned, or polycrystalline) would be very valuable. It is worth mentioning thatalthough some traditional models describing exchange bias properties in bulk FM–AFM materials can be adjusted toaccount for some of the peculiarities of exchange bias in nanostructures, a complete understanding of this phenomenonat the nanoscale probably requires more sophisticated models, which should take into account a variety of effectsdirectly related to the nanometric character of the system. As regards to surface chemically modified nanoparticles,core–shell nanoparticles or nanoparticles embedded in an AFM matrix, the microstructure and the AFM material playsa dominant role in the results. The few available systematic studies and the complexity of most of these systems, whichdoes not allow independent control of their microstructure, make the overall analysis of this type of nanostructuresrather challenging. However, significant exchange bias effects, such as large loop shifts, have been observed in severalof these structures. Moreover, some of the main exchange bias properties (e.g., HE dependence on the FM particlediameter) seem to obey similar laws than thin film systems, at least for certain particle radii ranges. Remarkably, noveleffects such as the enhancement of the superparamagnetic blocking temperature of the FM nanoparticles seem to openpossibilities for the novel applications of exchange bias at the nanoscale. In this case, investigations with increasedcontrol over all the microstructural parameters would also be enlightening.

Acknowledgements

Discussions with X. Illa, E. Vives, A. Planes, J. Geshev, A. Hoffmann, C. Portemon, R. Morel, A. Brenac,C. Leighton, A.S. Carriço, H. Ohldag, J. Akerman and U. Nowak, are gratefully acknowledged. Work supportedby the Spanish CICYT (MAT2004-01679), the Catalan DGR (2001SGR00189) and the European Union research net-work NEXBIAS (HPRN-CT 2002-00296). VL acknowledges the support, through a “Ramón y Cajal” Contract, fromthe Spanish MEC.

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