3420 IEEE TRANSACTIONS ON MAGNETICS, VOL. 39, NO. 5, SEPTEMBER 2003

Magnetic Force Microscopy Studies ofPatterned Magnetic Structures

Xiaobin Zhu and Peter Grutter

Abstract—Magnetic force microscopy is a very powerful tool forstudying magnetic nanostructures. In this paper, we demonstratethat magnetic force microscopy is a tool for imaging, manipulating,characterizing magnetization switching and switching-field vari-ability, and studying magnetostatic coupling.

Index Terms—Hysteresis loop, magnetic force microscopy, mag-netic nanostructures, magnetostatic coupling.

I. INTRODUCTION

RECENT state-of-the-art technology such as electron-beam[1], nanoimprint [1], and interferometric lithography [2],allows for patterning of magnetic nanostructures as small as10 nm. Unique magnetic properties can thus be tailored bycontrolling particle shape, size, and spacing [1], [3]. The studyof patterned magnetic particles is of great interest due to thefundamental research issues and their potential applications inultrahigh density storage and magnetoresistive random accessmemory (MRAM) [1], [2], [4].

This booming interest requires imaging these small struc-tures. The magnetic force microscope (MFM), which has beensuccessfully used in the magnetic storage community for char-acterizing reading and writing heads and recording media, al-lows imaging with the spatial resolution of 10–100 nm [5]. Dueto this high spatial resolution and high sensitivity, MFM is anideal tool for studying the magnetic structures and magnetiza-tion reversal of submicron sized magnets [6]–[8]. This paperreviews the MFM study of lithographically patterned magneticparticles at McGill University. An emphasis is put on somequantitative information that can be extracted from various ex-amples.

II. EXPERIMENTAL TECHNIQUES

In MFM, the magnetic contrast is obtained through detectingthe force gradient between a ferromagnetic tip and the magneticsample by amplitude, phase or frequency detection techniques.The principle, instrumentation, and applications of MFM can befound in several review papers [5]. An important issue related to

Manuscript received January 9, 2003. This work was supported in part bythe Le Fonds Pour la Formation de Chercheurs et I’Aid a la Recherche de lasProvince de Quebec (FCAR), the National Sciences and Engineering ResearchCouncil of Canada (NSERC), and the Canadian Institute for Advanced (CIAR).

X. Zhu is with the Department of Physics, McGill University, Montreal, QCH3A 2T8, Canada, and also with the Department of Physics, University of Al-berta, Edmonton, AB T6G 2J1, Canada (e-mail: xzhu@ualberta.ca).

P. Peter is with the Department of Physics, McGill University, Montreal, QCH3A 2T8, Canada (e-mail: grutter@physics.mcgill.ca).

Digital Object Identifier 10.1109/TMAG.2003.816170

Fig. 1. Operation modes of MFM: (a) constant frequency shift mode;(b) tapping/lift mode; and (c) constant height mode.

the MFM imaging is the separation of the topography and mag-netic contrast. Different operation modes, as shown in Fig. 1,can result in different levels of convolution.

In the conventional operation mode (constant frequency shiftmode) [5], the cantilever resonance frequency is maintainedconstant by changing the tip-sample separation, as shown inFig. 1(a). The image obtained in this mode can have a sub-stantial convolution between the magnetic and the topographicsignal, especially when a large bias voltage between the MFMtip and sample is applied.

The tapping/lift mode can efficiently separate the topographycontrast and magnetic signal [9]. As schematically shown inFig. 1(b), the sample is scanned twice in this mode. The sampletopography is obtained in the tapping mode scan using the can-tilever oscillation amplitude as a feedback signal. The magneticcontrast is subsequently obtained in the lift mode scan by mon-itoring the cantilever’s frequency or phase shift upon rescan-ning the previously measured topography with a user controlledheight offset . The typical problem associated with the tap-ping/lift mode scan is that the MFM-tip stray field can producesubstantial distortion to the sample magnetic structures duringthe tapping scan. This is because the MFM-tip stray field closeto the tip end is substantial, even for a conventional low mag-netic moment tip [10].

Operating MFM in the constant height mode, as schemati-cally shown in Fig. 1(c), can substantially reduce the MFM-tipstray-field-induced irreversible distortion. In this mode, insteadof tracking the sample’s topography, the tip is scanned across

0018-9464/03$17.00 © 2003 IEEE

ZHU AND GRUTTER: MAGNETIC FORCE MICROSCOPY STUDIES OF PATTERNED MAGNETIC STRUCTURES 3421

the surface at a predetermined constant height while the can-tilever frequency shift is monitored. Unavoidable sample tilt iscompensated by a tilt correction hardware [10].

Constant height mode has the best signal-to-noise ratio (nofeedback noise) and the potential of increased scan speeds;however, the disadvantage of this mode is that a flat sample isneeded, as the minimal tip-sample separation is determined bythe sample’s roughness.

Tapping/lift mode and constant height mode are complimen-tary in acquiring good images. For magnetic particles with alarge coercivity field, the tapping/lift mode can be confidentlyapplied; however, for magnetic particles with small switchingfields, the constant height mode should be adopted, since thelatter produces smaller distortion, and the distortion can beeasily detected [10]. The images in this paper were all acquiredin the constant height mode.

III. V ERSATILITY OF MFM

A. MFM as a Tool for Imaging

The primary function of MFM is to obtain sample magneticdomain structures. In the literature, MFM has been success-fully used to obtain the domain structures in lithographicallypatterned particles [6], [7], [11], [12]. The particle size, mag-netocrystalline anisotropy and shape have a strong influence onthe magnetic structure [13]. Elongated sub-100 nm particles canform a single-domain state. For example, the black-white con-trast in Fig. 1(a) indicates that the particle forms a single-domainstate. The black spot indicates the tip is repulsive to the particle,while the white spot indicates it is attractive. As the particle sizebecomes bigger, the domain patterns such as a flux-closure do-main configuration will be formed [13].

If the magnetic particles are disk shaped [12] or elliptical witha small aspect ratio [11], a magnetic vortex state is formed. Suchstructures have been observed by Lorentz electron microscopy[14], MFM [11], [12], [15] and even spin-polarized scanningtunneling microscopy [16]. Fig. 2(b)–(d) shows such a vortexstructure of a Permalloy disk with size 700 nm [15]. In Fig. 2(b),the MFM imaging shows the particle forms a low magnetic con-trast state with a bright spot in the center, which can be clearlyseen in the reduced scan area in Fig. 2(c). This bright spot is avortex core, which can be proved by imaging in the presence ofan external magnetic field. The vortex core moves closer to theedge perpendicularly to the magnetic field direction, as shownin Fig. 2(d).

The existence of the vortex core leads to irreproducibilityof magnetization switching [17]. Patterning the magnetic disksinto a ring shape can avoid the formation of vortex cores [18].Similar to a magnetic disk, the low magnetic contrast state of aring is energetically stable, where the magnetic moments rotatecircularly around the center of the ring. Beside this state, thereexists another energetically stable state in a magnetic ring. Thisstate can be formed at remanence after a large magnetic field isapplied [18]. If a large in-plane magnetic field is applied to thering, the ring will form a single-domain state. As the magneticfield is reduced, domain walls will be nucleated in the ring, andthis magnetic moment state is often called the “onion” state. De-pending on the size, thickness and materials of a ring, there are

Fig. 2. (a) Single-domain structure of a Ni particle, the particle size:200nm�70 nm�15 nm. (b) Vortex structure in a Permalloy disk, the disk diameter 700nm. (c) Zoom in (140 nm) of (b). (d) Vortex core displacement in the presenceof the external magnetic field of 23 Oe. (e) The “onion” state of a permalloy ringwith ring diameter 700 nm. (f) Magnetic moment configuration of (e) obtainedthrough micromagnetic simulation of OOMMF code. The arrow in (d) indicatesthe magnetic field direction.

Fig. 3. (a) Mixture of parallel states and antiparallel states. (b) Two differentantiparallel states. Particles size: 550 nm long, 70 nm wide, with compositionof NiFe (6 nm)/Cu(3 nm)/Co(4 nm). Grayscale: (a) 1 Hz and (b) 0.1 Hz. Top:the magnetic moment configuration configurations in each magnetic layers.

two possible moment configurations in the domain wall at the“onion state”: one forms a transverse domain wall, and the otherforms a flux-closure domain configuration [19]. Careful MFMimaging can distinguish these two configurations [19]. For ex-ample, Fig. 2(e) shows a transverse domain wall configurationof a Permalloy ring. The corresponding micromagnetic simula-tion of this ring is shown in Fig. 2(f).

Besides characterizing the shape influence on magnetic struc-tures, MFM is also suitable to identify the magnetic momentconfigurations of patterned magnetic multilayers [20]. For ex-ample, for elongated sub-100-nm-wide pseudo-spin-valve ele-ments composed of two different magnetic layers separated by anonmagnetic spacer, the magnetic moment in each layer forms asingle-domain state. The magnetic moment configuration of themagnetic layers therefore can either be parallel or antiparallel, asschematically shown on the top of Fig. 3. For the parallel state,MFM imaging shows a strong bipolar contrast, while the strayfield above the element almost cancels in the antiparallel state,resulting in a weak contrast. The mixture of parallel state andantiparallel state is shown in Fig. 3(a), while Fig. 3(b) clearlyshows the two different antiparallel states coexisting.

3422 IEEE TRANSACTIONS ON MAGNETICS, VOL. 39, NO. 5, SEPTEMBER 2003

Fig. 4. MFM images at remanence of a single square shaped ring elementafter applying different magnetic fields. (a) SEM image of a single square ring.(b) Remanence after saturation with the field indicated in (a). (c) 130 Oe. (d) 147Oe. (e) 256 Oe. (f) 270 Oe. MFM tip: 30 nm CoPtCr. Lift height: 150 nm; invacuum. A, B, C, and D symbolize the four segments. The arrows in (b)–(f)indicate the magnetic moment orientation in each segment.

B. Magnetization Reversal Studied by MFM

One distinguishing characteristics of imaging by MFM is thatit is compatible with external magnetic fields. The implementa-tion of the MFM in the presence of controlled external magneticfields [21], [22] can be used to identify magnetic structures andmagnetization behavior of patterned particles.

There are two different ways to study the magnetization be-havior using MFM: imaging at remanence after a magnetic fieldis ramped to a certain value or imaging in the presence of anexternal magnetic field. Imaging in the presence of an externalmagnetic field is necessary when observing domain wall dis-placement or studying reversible magnetization switching. Forexample, the vortex core displacement as a function of externalmagnetic fields can be observed easily in a Permalloy disk [15].Imaging at remanence can eliminate the combined effect of thetip stray field and an external magnetic field [10], [23]. Thistechnique is very suitable to study the magnetic particles with afew distinct magnetic states, such as single-domain particles, asthe exact switching field of the imaged particle can be obtainedwith the precision determined by the field ramping step [10].In the following, several examples of imaging at remanence arepresented.

The domain wall configuration and propagation in patternedring structures are of great interest in recent studies [17]–[19],[24]. Square-shaped ring structures, as shown in Fig. 4(a), aresuch an example [24]. For a thin and narrow square-shaped ring,each segment of the four edges can be considered as a “singledomain” state. Depending on the orientation of these “singledomain” states, different domain patterns in the square can beformed. The MFM images in Fig. 4(b)–(f) shows the differentmagnetic moment states of a Ni square-shaped ring at rema-nence after various external magnetic fields are applied. The ar-rows in the figures indicate the magnetic moment orientationin each segment. The MFM images indicate that the externalmagnetic field can switch the four segments individually. If themagnetic field is applied with a small angle with respect to thesegments and [see the arrows in Fig. 4(a)], the segments

Fig. 5. MFM image: (a) at remanence after applying�304 Oe along the longaxis of the element; (b) after applying�510 Oe; (c) remanent hysteresis loopconstructed from MFM images; and (d) hysteresis loop obtained by alternatinggradient magnetometry. Particle size:240 nm � 90 nm � 10 nm, lift height100 nm. Tip: 50-nm CoPtCr; in vacuum.

and are switched at much smaller magnetic fields [24] thanthe segments and . Depending on the magnetic field direc-tion, the domain wall configuration patterns are controllable byshowing the bright and dark spots in the figure moving from onecorner to another [24].

By observing the domain configuration as a function of ex-ternal magnetic field, MFM imaging allows a hysteresis loopto be constructed. The hysteresis loop can be constructed bycounting the percentage of switched elements as a function ofexternal magnetic fields. For a single-domain particle array, ifthe MFM-tip stray field does not irreversibly switch a particlefrom one state to another, the image can be performed at rema-nence after the magnetic field is ramped to predesignated values.If we assign 1 or 1 to each individual particle based on whetherit is switched or not, a normalized hysteresis loop can thereforebe constructed according to the number of switched particles asa function of external magnetic field.

Fig. 5 shows an example of the hysteresis loop of a single-do-main Permalloy particles with size 90 nm240 nm. Fig. 5(a)and (b) shows the magnetic states at remanence after applyingmagnetic fields of 304 and 510 Oe, respectively. The rema-nent hysteresis loop constructed by MFM is shown in Fig. 5(c).This remanent hysteresis loop can be directly compared to thehysteresis loop obtained by alternating gradient magnetometeryas shown in Fig. 5(d). The coercivities (310 Oe) obtained byboth methods agree very well, which demonstrates the capa-bility of characterizing the magnetization switching behaviorsof nanomagnets by MFM. One of the advantages of obtaininga hysteresis loop from MFM images is that it builds a bridgebetween an individual element and the ensemble, whereasmacroscopic techniques only study switching behavior of anensemble.

The study of switching-field variability among differentparticles is very important for fabricating magnetic particle

ZHU AND GRUTTER: MAGNETIC FORCE MICROSCOPY STUDIES OF PATTERNED MAGNETIC STRUCTURES 3423

Fig. 6. Switching-field distribution of widely separated Permalloy disk arrayswith the particle size1:2 �m � 0:2 �m � 30 nm. 600 different individualparticles are studied.

array with a uniform switching field. With the ability ofobtaining precise switching fields of different individualparticles, MFM makes it possible to conduct comparisonamong different particles and to build connections betweenthe magnetization switching and particle microstructures. Forexample, Fig. 6 shows the switching-field distribution of awidely separated Permalloy particle array [10]. For this particlearray, a broad switching-field distribution among differentparticles is observed. This switching-field distribution is dueto switching-field difference of different individual particles.The broadness of switching-field distribution is a commonobservation for a variety of lithographically patterned struc-tures. Although the elements appear to be identical, they havedifferences in edge roughness and microstructure, and evenmodest variability in microstructure or roughness can cause awide range in the switching field.

Above examples demonstrate that MFM combined withan external magnetic field is a unique technique for studyingnanoparticle arrays as it can obtain the image of individualparticles while studying the collective magnetization behavior.

C. Local Hysteresis Loop Technique

The investigation of the switching behavior of an individualmagnetic element is essential to understand the switchingmechanism. MFM imaging in the presence of an external mag-netic field is a conventional way to characterize it. However, insome cases, it is possible to characterize the switching field andswitching mechanisms of individual particles without imaging.We call this technique alocal hysteresis loop technique[15],[20]. As schematically shown in the inset of Fig. 7(a), toperform this measurement, the MFM tip is located at the endof an element, and the cantilever frequency shift is monitoredwhile sweeping the external field. The cantilever frequencyshift is proportional to the force gradient between the tip and thesample, and is thus a measure of the local sample moment. Thistechnique is ideally suited to study the particles of submicronsize, especially single-domain particles.

Fig. 7 shows local hysteresis loops of a pseudo-spin-valveparticle (NiFe–Cu–Co) in the same particle array shownin Fig. 3 [20]. Fig. 7(a) is a minor hysteresis loop of thepseudo-spin-valve element as the magnetic field is swept in the

range of 250 Oe. In this field range, only the magneticallysoft layer (NiFe) is switched back and forth. The magneticlayers form parallel or antiparallel states, as indicated on thetop of Fig. 3. The parallel state gives rise to large frequencyshift of cantilever, while the antiparallel state only induceslittle change of cantilever resonance frequency. Two abruptfrequency jumps in the figure indicates such switching. If themagnetic field, however, is swept in a larger range550 Oe,both the magnetically hard (Co) and magnetically soft layer(NiFe) can be switched. Two additional frequency shift jumpsat larger fields corresponding to the switching of Co layerappear in the major hysteresis loop, as indicated in Fig. 7(b).The hysteresis loops clearly show that the switching of eitherlayer occurs at different magnetic fields, and demonstrate thattwo layers are coupled by showing asymmetric switching fieldsin Fig. 7(a).

Advantages of this technique include easy characterization ofthe switching behavior of individual particles [15], [20] and easycomparison among different particles [20].

D. Magnetostatic Interaction and Coupling

Magnetic particles will be strongly coupled, if they areplaced close to each other. Such coupling gives rise to achange of the switching field, switching mechanism, initialsusceptibility, and switching field distribution. Cowburnet al.demonstrates that coupled single-domain magnetic particlescould be used to propagate information [25]. In a simplepicture, the particles with low coercivities will be switched atsmaller magnetic field. The switched particles, however, can actas triggers for the switching of their nearest-neighbor particles.This coupling effect can spatially visualized through carefula MFM imaging. In a closely packed Permalloy disk arrayarranged in a square lattice [15], we found that the magneticcoupling induces switching-field anisotropy and the switcheddisks form chain-like structures [15].

This type of coupling can be visualized more clearly in atruncated chain structure [26]. The switching mechanism ofa submicron Permalloy disk is a vortex nucleation process(single-domain state to vortex state) and a vortex annihilationprocess (vortex state to single-domain state) [15]. For thenucleation process, we found that switched elements initiated atthe edge of a chain, while the annihilation occurs at the centerof a chain. The switched elements form a chain-like structure[26]. Fig. 8 shows the coupling during the annihilation process,starting from the initial vortex state, if the magnetic field of425 Oe is applied along the disk chain. One of the disks in onechain switches to a single-domain state, as shown in Fig. 8(a).At a larger field of 440 Oe, two additional disks in this chainare switched, as shown in Fig. 8(b). Fig. 8(c) shows the imagesafter a magnetic field of 455 Oe is applied. It can be clearlyseen that the switched disks form a chain-like structure. Ideally,the particles in the center of the disk chain is annihilated first,as its neighbor disk applies the highest magnetic field to it. Theswitched disks themselves produce larger effective fields totheir neighboring disks than before, and help their neighboringdisks to expel the vortices. Fig. 8(d) shows that all the elementsin two chains have almost switched, while there is no elementswitched in other chains within the scan area.

3424 IEEE TRANSACTIONS ON MAGNETICS, VOL. 39, NO. 5, SEPTEMBER 2003

Fig. 7. Hysteresis loop of a single pseudo-spin-valve element of Py(6 nm)/Cu(3 nm)/Co(4 nm) with size 550 nm� 70 nm. (a) Minor loop. (b) Major loop. Theinset schematically shows the local hysteresis loop technique.

Fig. 8. MFM images of Permalloy disk chains after applying the magneticfield of: (a) 425 Oe (b) 440 Oe; (c) 455 Oe; and (d) 489 Oe. Images were takenat magnetic field of 250 Oe. The diameter of the Permalloy disks is 700 nm, andthe thickness is 40 nm. The separation between the disks in chains is 100 nm.The switched particles are circled.

E. MFM-Tip Stray Manipulation

It is well known that MFM tip stray field can produce dis-tortion to submicron sized magnetically soft particles. A severedistortion is that the tip stray field can directly flip a particlemoment state [27]. This distortion can used to locally controlthe sample magnetization states, i.e., to write a bit in patternedmagnetic media [1]. The prerequisite of this process is that theeffective tip stray field is larger than the switching field of theparticle [1].

The writing and reading process can be performed using twoMFM tips: the writing tip with a large magnetic moment andthe reading tip with very small magnetic moment [1]. Since theMFM-tip stray field applied to particles is tip-sample separa-tion dependent, alternatively, it is possible to use one tip to ac-complish the writing and reading process. A suitable MFM-tipmoment needs to be selected to accomplish this. For a large

Fig. 9. (a), (b) Two MFM images of the same magnetic particles. Tip: 50-nmCoPtCr, lift heighth = 120 nm. Schematic diagram of particle and tip positionis shown on the left side of the images. Experimental procedure of performingthe writing and reading process is shown at the bottom of the images.

tip-particle separation, MFM can be used to read the magneticmoment states of the particle, while at smaller tip sample sep-aration, the tip stray field can be used to control the particlemagnetic moment state. This process is demonstrated in Fig. 9through a Permalloy particle with size 600150 nm. For a largetip-sample separation (120 nm) we find that the particle forms asingle-domain state. For a small tip-sample separation (60 nm)by positioning the tip at and , respectively, the particle mo-ments can be switched as schematically shown at the bottom ofthe image. The resulting moment state can be imaged at a largetip-particle separation (120 nm) as shown in Fig. 9(a) and (b).

This local tip-manipulation mode is very useful. Besidesreading and writing bits in magnetic storage media, it is alsopossible to use the MFM-tip stray field as a local input signalfor a magnetic logical device [25]. The recent technique ofoperating more than 1000 atomic force microscopes in parallelmakes it promising to integrate MFM-tip arrays into a realdevice [28].

ZHU AND GRUTTER: MAGNETIC FORCE MICROSCOPY STUDIES OF PATTERNED MAGNETIC STRUCTURES 3425

IV. SUMMARY AND CONCLUSION

MFM is well suited to characterize lithographically pat-terned nanomagnets. In the imaging mode, MFM can be usedto characterize the magnetic structures. MFM is compatiblewith external magnetic fields, which makes it ideal to study themagnetization reversal of magnetic particles, and obtain preciseswitching fields of particles. By counting the percentage ofswitched particles as a function of the external magnetic field, ahysteresis loop comparable with macroscopic magnetometerymeasurements can be obtained through imaging at remanenceor at a suitable magnetic field [15], [29]. The advantage ofstudying magnetization reversal by MFM over macroscopicmeasurement is that it directly determines the individualparticle differences and studies switching-field distributions.

MFM is able to study local hysteresis loop by monitoring thecantilever status versus external magnetic fields, which can beused to study switching mechanism of individual elements, andis potentially ideal to study the switching-field distribution of anindividual particles, e.g. thermal switching. The magnetic fieldemanating from the tip can be used to apply a localized magneticfield to a sample, and can also locally switch the magnetizationof a particle.

ACKNOWLEDGMENT

The authors would like to thank V. Metlushko, B. Ilic,J. Beerens, Y. Hao, F. J. Castano, S. Haratani, B. Vogeli, C. A.Ross, and H. I. Smith for fabricating the samples.

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