Magnetization reversal of Co/Pt multilayers: Microscopic originof high-field magnetic irreversibility

Joseph E. Davies,1 Olav Hellwig,2,3 Eric E. Fullerton,3 Greg Denbeaux,4,5 J. B. Kortright,4 and Kai Liu1,*1Physics Department, University of California, Davis, California 95616, USA

2BESSY GmbH, 12489 Berlin, Germany3San Jose Research Center, Hitachi Global Storage Technologies, San Jose, California 95120, USA

4Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA5College of Nanoscale Science and Engineering, University at Albany, Albany, New York 12203, USA

(Received 26 August 2004; published 29 December 2004)

We investigate the magnetization reversal infCos4 Åd /Pts7 Ådg50 multilayers with perpendicular magneticanisotropy both macroscopically by the first-order reversal curve(FORC) technique and microscopically bytransmission x-ray microscopy(TXRM) and resonant x-ray small angle scattering(SAS). In particular, wefocus on the nucleation and saturation processes. The onset of magnetization reversal is dominated by irre-versible processes corresponding to the avalanchelike propagation of one-dimensional stripe domains thatoriginate from earlier nucleated zero-dimensional bubble domains. In a second stage we observe mainlyreversible behavior where the overall domain topology is preserved. Finally another irreversible process bringsthe sample to negative saturation, corresponding to the contraction and annihilation of domains. Interestingly,even well beyond the apparent major-loop saturation field, the FORC diagram exhibits pronounced irreversibleswitching and thus provides a direct measure of the true(and significantly higher) saturation field. TXRM andSAS measurements reveal on a microscopic level that some residual bubble domains with negligible momentsstill persist for fields well above the apparent saturation field. These residual domains, if unannihilated, sig-nificantly alter the subsequent magnetization reversal.

DOI: 10.1103/PhysRevB.70.224434 PACS number(s): 75.60.-d, 75.70.Kw, 75.70.Cn, 68.37.Yz

I. INTRODUCTION

In recent years there has been tremendous interest in mag-netic nanostructures, largely due to advances in the fields ofmagnetoelectronics and magnetic recording.1 Central to theinvestigation of magnetic nanostructures are hysteresis andmagnetization reversal processes. Fundamentally, the revers-ible versus irreversible magnetization switching often aremanifestations of the microscopic magnetic interactions. Forexample, the reversible switching in spring magnets is a re-sult of low crystalline anisotropy and interlayer coupling;2

the irreversible switching in exchange-biased systems couldbe due to interfacial pinning by antiferromagneticdomains.3,4 Technologically, the reversal characteristics, suchas the onset and end point of switching and the distributionof switching fields, are critical to devices that consist of largearrays of magnetic entities, such as magnetic random accessmemory5 and patterned magnetic recording media.6

In this work, we employ a first-order reversal curve(FORC) technique7–10 to examine the macroscopic magneti-zation reversal processes in Co/Pt multilayers, in particularthe degree of reversible versus irreversible switching. Toprobe the microscopic origin of this behavior we exploittransmission x-ray microscopy(TXRM) and resonant mag-netic x-ray small-angle scattering(SAS). The Co/Pt multi-layers chosen are an important material system due to theirperpendicular magnetic anisotropy and potential applicationsas future high-density magnetic recording media.11–14 Wedistinguish three distinct stages during a complete reversalfrom positive to negative saturation: an initial irreversibleprocess due to domain nucleation and primarily domainpropagation, then an extended reversible stage as the do-

mains expand and contract in width without changing theirtopography, and finally another irreversible process corre-sponding to the annihilation of domains. Interestingly, someresidual domains persist well beyond the apparent saturationfield determined from the hysteresis loop. These domains, ifnot annihilated, impede the avalanchelike domain propaga-tion during the subsequent field cycle and manifest them-selves as distinct features in the FORC diagram. The numberof unannihilated domains depends on the maximum reversalfield applied. Thus it is not trivial to determine the true satu-ration field of the system from the major hysteresis loopalone. Our results illustrate detailed magnetization reversalprocesses in Co/Pt and provide direct and quantitative mea-sures of the true saturation field and other reversal character-istics.

II. EXPERIMENTAL PROCEDURES

The perpendicular films used for our experiments arefCos4 Åd /Pts7 Ådg50 multilayers that were simultaneouslymagnetron-sputtered onto Si3Nx-coated Si substrates(formagnetometry measurements) and Si3Nx membranes(for theTXRM and SAS measurements in transmission mode). A200-Å Pt buffer layer and a 20-Å Pt capping layer have beenused. The perpendicular easy axis in the system is obtainedvia the high surface anisotropy of the 4-Å Co layers. The Ptbuffer layer and the multilayer are(111) textured. More de-tailed information about the samples can be found in priorpublications.12–14

Magnetization reversal on the macroscopic scale has beenmeasured by the magneto-optical Kerr effect(MOKE) andby the FORC method utilizing a Princeton Measurements

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Corporation 2900 alternating gradient magnetometer(AGM)at room temperature with the magnetic field applied perpen-dicular to the sample. The AGM is used to measure a largenumbers,102d of partial hysteresis curves called first-orderreversal curves in the following manner. After saturation, themagnetizationM is measured starting from a reversal fieldHR back to positive saturation, tracing out a FORC. A familyof FORC’s is measured at differentHR, with equal field spac-ing, thus filling the interior of the major hysteresis loop[Fig.1(a)]. Since the FORC technique uses a large data set incomparison to the usual single major hysteresis loop, it canreveal much more detailed information about the reversal. Ifthe magnetization at the applied fieldH on the FORC withreversal fieldHR is defined asM sHR,Hd a FORC distribu-tion is then defined by a mixed second-order derivative(Refs. 7–9):

rsHR,Hd ; −1

2

]2MsHR,Hd]HR]H

. s1d

This derivative eliminates the purely reversible componentsof the magnetization.15,16A plot of the distributionr versusH and HR can then be created to probe the details of themagnetization reversal.

In order to correlate the macroscopic information ob-tained by the FORC with the microscopic evolution of spe-cific domain patterns, we perform TXRM and SAS on simi-lar samples grown onto Si3Nx-membrane substrates. Themagnetic contrast is obtained from the resonant magneticterm in the atomic scattering factor that is first order in themagnetization [x-ray magnetic circular dichroism(XMCD)].17,18Such techniques are excellent tools for micro-scopic reversal studies since this photon-in–photon-outmethod does not perturb the sample during measurement ascompared to magnetic force microscopy(MFM) and is in-sensitive to external fields applied to the sample. This isespecially important for studying domain nucleation and an-nihilation processes in an external magnetic field. X-raymeasurements were performed at the Advanced Light Source(ALS) at the Lawrence Berkeley National Laboratory. TheTXRM imaging used the XM-1 zone-plate imaging micro-scope on bending magnet beamline 6.1.2 while the SAS wasperformed on beamline 8.0. To enhance the magnetic con-trast we tuned the energy to the CoL3 absorption edges,778 eV,,1.59 nmd. The imaging was done with a two-dimensional change-coupled-device(CCD) camera using el-liptical polarization from above the synchrotron orbit planein applied fields up to 3.5 kOe.17,18The SAS was performedusing linear polarization.19 Both techniques are applied intransmission and are predominantly sensitive to the perpen-dicular magnetization of the sample.

III. EXPERIMENTAL RESULTS

A. FORC

The experimentally obtained family of the FORC’s for afCos4 Åd /Pts7 Ådg50 sample is shown in Fig. 1(a) where theouter boundary delineates the major hysteresis loop. Fivereference points are marked to illustrate the different reversal

stages. The major loop is characteristic of magnetic thinfilms with perpendicular magnetic anisotropy as first outlinedby Kooy and Enz.20 The initial stage of the reversal is thenucleation and propagation of reverse domains[point 1 ofFig. 1(a)]. Once these domains fill the sample the magneti-zation is characterized by mostly reversible changes of the“up” vs “down” domain widths(between points 2 and 3),while the overall domain topology is preserved. Finally, satu-ration occurs via annihilation of residual unswitched do-mains (points 3–5). The corresponding FORC distributionplotted versusH andHR is shown in Figs. 1(b) and 1(d) as acontour plot and a three-dimensional plot, respectively. Foreach curve shown in Fig. 1(a) with a specific reversal fieldHR, the magnetizationM is measured with increasing appliedfield H; the corresponding FORC distributionr is repre-sented by a horizontal line scan at thatHR alongH. Five linescans corresponding to the reference points in Fig. 1(a) arerepresented by dashed lines in Fig. 1(b). As HR decreases andthe family of FORC’s is measured,r is scanned in a “top-down” fashion in theH-HR plane, mapping out the irrevers-ible processes. We observe three regions of interest in theFORC distribution in Fig. 1(b) and 1(d): a horizontal ridge inthe upper right corner, an intermediate mostly flat regionwith little FORC features, and finally a vertical valley-peakpair in the lower left corner.

The first feature is a ridge along the applied field direc-tion. A vertical cross-sectional view of this feature[Fig. 1(c)]shows that the ridge rises abruptly asHR is decreased fromther=0 plane above the ridge. When magnetization reversalprocesses are completely reversible, the magnetizationMsHR,Hd would not change from reversal curve to reversalcurve, or successive reversal curves will overlap. Therefore itcan be solely expressed as a function of the applied fieldH,and not the reversal fieldHR. Thus the FORC distributiongoes to zero in these regions. That is,

r = −1

2

]2MsHR,Hd]HR]H

= −1

2

]2MsHd]HR]H

= 0 s2d

for reversible processes.The rise of the ridge corresponds to the FORC distribu-

tion becoming nonzero, signaling the onset of irreversibleprocesses. This onset is better seen in the projection of theFORC distribution onto theHR axis (equivalent to integrat-ing r overH): for the entire ridge, we take a series of equallyspaced cross sectional cuts alongH, spanning the ridge andsumming them together. Then a line fit is done along theright side of the ridge, as shown in Fig. 1(c), where theintersection between the line fit and the horizontal axis indi-cates the onset of irreversibility. The onset determined thisway is 1.4 kOe. It can readily be seen in Fig. 1(a) that thisfield (point 1) indeed corresponds to where the magnetiza-tion drops precipitously, signaling an avalanchelike growthof reverse domains in the film. After the ridge has peaked,rreturns gradually to ther=0 plane. The endpoint of the irre-versible switching(point 2) can be similarly determined tobe about 1.2 kOe. This first irreversible ridge in Fig. 1(b)also reflects the sudden separation in the successive reversalcurves visible in Fig. 1(a).

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FIG. 1. (Color) (a) A family of first-order reversal curves for afCos4 Åd /Pts7 Ådg50 sample, where the first point of each reversal curveis shown by a black dot and(b) a contour plot and(d) a three-dimensional plot of the corresponding FORC distribution, versus applied fieldH and reversal fieldHR. Reference points 1–5 are marked in(a) and(b) to illustrate the different reversal stages.(c) shows the projection ofthe horizontal FORC ridge in(b) onto theHR axis (sum of vertical cross-sectional cuts taken along the horizontal ridge), with dashed linesdrawn to determine the onset and end point of irreversibility.

FIG. 2. (Color) Kerr hysteresis loop withTXRM images along a field reversal of afCos4 Åd /Pts7 Ådg50 multilayer. The differentstages of the reversal process from positive tonegative saturation are represented by severalsegments of the major loop,a–i, as described inthe text. The different TXRM images, over thesame 2.232.2 mm2 area of the sample, exhibitthe characteristic domain pattern evolution duringreversal. Approximate external fields, within±0.1 kOe, are given for each image and are alsomarked on the hysteresis loop. TXRM imagesand corresponding marks on the hysteresis loopare connected by arrows.

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The second feature in Fig. 1(b) is a planar region betweenlines 2 and 3 s−2.5 kOe,HR,1.2 kOed, separating theaforementioned horizontal ridge from a vertical pair of avalley-peak feature. In this region,r is essentially zero andinvariant in theHR-H plane, indicating mostly reversibleswitching [Fig. 1(d)].21 The successive FORC’s in Fig. 1(a)are indeed closely packed and nearly overlap. The reversibil-ity of the sample in this region has been also observed usingTXRM, which shows that the domains fill the sample andreversibly widen and narrow as the field is varied aroundremanence.13

The third feature consists of a negative valley and a posi-tive peak inr that stretch in the nearly vertical direction,between lines 3 and 5s−3.8 kOe,HR,−2.5 kOed. The on-set of this feature indicates the reintroduction of significantirreversible processes showing domain annihilation as thesample approaches negative saturation. At −3.2 kOe[point 4in Fig. 1(a)], the major loop appears to have reached nega-tive saturation, and one might expect this would simulta-neously declare the end of the irreversible switching. Strik-ingly, the FORC distribution is far from vanishing[line 4 inFig. 1(b)]. In fact this is just the beginning of a negative-positive pair of peaks.

A careful examination of the reversal curves in Fig. 1(a)shows that reversing from the apparent saturation(point 4)leads to a rounded corner in the returning path, in contrast tothe sharp nucleation edge seen in the major loop. Further-more, for −3.8 kOe,HR,−3.2 kOe(between points 4 and5), the negative FORC distribution inH,−1.4 kOe [Figs.1(b) and 1(d)] corresponds to a decrease of the FORC slope[Fig. 1(a)]; the positive FORC distribution inH.−1.4 kOe[Figs. 1(b) and 1(d)] corresponds to an increase of the FORCslope[Fig. 1(a)]. Hence this negative-positive pair of peaksrepresents the formation of a sharp corner that is present inthe return path of the major loop. These results show thatirreversible switching persists well beyond the perceivedmajor-loop saturation field of −3.2 kOe for this sample, andthe larger(or more negative) the reversal fieldHR, the moreabrupt the subsequent reversal. In this region the macro-scopic magnetization differs by less than 1memu, the reso-lution of our measurement or 0.7% of the saturation moment.However, the small residual moments are reflected in dra-matic differences in the nucleation stage during the subse-quent reversal.

B. Transmission x-ray microscopy

To explore these macroscopic reversal stages, we use theTXRM technique to image and follow the domain patternson the microscopic scale. In Fig. 2 we exhibit the hysteresisloop of the sample used for TXRM imaging which has nomi-nally the same structure as the one shown in Fig. 1(a). Theloops are nearly identical; however, the TXRM sample hasslightly lower nucleation and saturation fields resulting fromsample-to-sample variations in deposition. For this samplewe show in Fig. 2 a series of representative TXRM images,over a 2.232.2 mm2 area, taken along a field sweep frompositive to negative saturation. The dark-bright contrast illus-trates the opposite “up”-“down” domains. The decreasing-

field branch of the hysteresis loop is color coded correspond-ing to the different reversal stages identified below.

Initially, the sample is fully saturated beyondH,3.5 kOe, on both macroscopic and microscopic level(seg-ment a, black). As a reversal field is applied, even in theapparent macroscopic saturation state and well above the ap-parent nucleation fields1.3 kOe,H,3.0 kOed, we begin toobserve isolated nucleation of a few reverse domains. Wefirst observe zero-dimensional spotlike bubble domains(typically 1–3 nucleation sites/100mm2 area) that grow insize with decreasing field(segmentb, green) but remain asbubbles. As the field is further reduced the zero-dimensionaldomains expand into one-dimensional isolated stripes(,1.1 kOe, segmentc).

At the sharp edge in the major loop, where the FORCdiagram begins to display irreversible switching, we observea sudden avalanche of labyrinth stripe domains, seeded fromthe few isolated reverse domains already present. These ava-lanches move through the whole sample very quickly(seg-ment d, yellow) and a characteristic domain periodicity de-velops. This process corresponds to the horizontal FORCridge over a narrowHR range[between lines 1 and 2 in Fig.1(b)]. Thus, the sharp drop in magnetization and the onset ofirreversible behavior are not directly associated with thenucleation of new reverse domains, but primarily with thesudden growth of already present stripe domains.

Next the magnetization decreases almost linearly with de-creasing field(segmente, red). The sample is now filled withlabyrinth stripe domains. The decrease inM is due to a rela-tive change in the width of “up” vs “down” domains. In thisstage the topology of the domains is preserved(see the threeimages at 0.5, −0.2, and −1.8 kOe in Fig. 2) and the ratio ofwhite versus dark regions agrees very well with the macro-scopic magnetization. This corresponds to the second featurein the FORC diagram, the planar region, where we observemostly reversible switching.

Continued reversal leads to a steeper drop inM approach-ing negative saturation(segmentf, yellow). Microscopically,the domains start to contract and annihilate. Compared to theearlier nucleation stage, there are now much more isolateddomains per area present towards saturation. Near the appar-ent saturation(segmentg, blue, e.g., at −2.8 kOe), there arestill isolated one-dimensional stripe domains and zero-dimensional bubble domains present, even though the mag-netic moment associated with them becomes negligible. Be-yond the apparent saturation(segmenth, green, e.g., at−3.3 kOe), the zero-dimensional bubble domains persist, andthey continue to contract in size down below the TXRMresolution limit (however, they are still present in thesamples as we will show below). These segments togethercorrespond to the third region in the FORC diagram, theirreversible valley-peak feature. Eventually a true negativesaturation is achieved(segmenti, black).

We look more closely at the saturation of the magnetiza-tion in Fig. 3. In the background we show the third quadrantof a major hysteresis loop when reversing at −4.0 kOe(solidline), together with a hysteresis loop reversing at −3.1 kOe(open circles), which appears sufficient to saturate thesample. However, in the subsequent reversal this second loophas a gradual corner near −1.2 kOe, deviating appreciably

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from the sharp edge seen in the major loop[similar to theFORC’s in Fig. 1(a)]. In order to reveal the microscopic do-main structures associated with this feature, we exhibit twosets of TXRM images taken along that second loop in Fig. 3:one at −2.5 kOe along the decreasing-field branch beforenegative saturation[(a) and (b)] and the other at −1.8 kOealong the increasing-field branch after reversing at −3.1 kOe[(c) and (d)]. As shown in Fig. 3(a), approaching negativesaturation, there is a mixture of isolated stripe and bubbledomains. When reversing from −3.1 kOe, at −1.8 kOe, weobserve a number of bubble domains[Fig. 3(c)], which canbe traced to the domains in Fig. 3(a). To highlight this wehave marked the positions of the bubble domains in Fig. 3(c)with open circles[Fig. 3(d)]. These same circles are thensuperimposed onto Fig. 3(a), and the resultant compositegraph is shown in Fig. 3(b). The circles in Fig. 3(b) highlighteither bubble domains or ends of residual stripe domains.Clearly all the bubble domains in Fig. 3(d) after reversalhave originated from residual domains in Fig. 3(b) approach-ing saturation. Interestingly, at −3.1 kOe, some of the bubbledomains apparently have vanished as they contract below theresolution limit of the microscope. Yet they have not beentruly annihilated and reappear during the subsequent increas-ing field sweep.

The number of such bubble domains nucleated during theearly stage of the subsequent reversal, where the major hys-teresis loop still appears as saturated, provides measure forthe number of unannihilated residual domains(even if theirsizes are below the imaging resolution) at the maximum ap-plied reversal field. We can repeat the process shown in Fig.3 for other maximum reversal fields and simply count thenumber of nucleated bubble domains at −1.5 kOe within acertain image area. As shown in Fig. 4, at increasingly nega-

tive reversal fields, the number of bubble domains graduallydecreases, suggesting a rather slow approach towards truesaturation.

Each of these bubble domains then nucleates separatelystripe domains that later propagate to the entire sample, cor-responding to the edge in the major hysteresis loop. It isclear that the smaller the maximum reversal field is, thelarger the number of unannihilated residual domains, and themore gradual becomes the avalanchelike domain propagationprocess. In essence, there is less and less space left for eachindividual avalanche if the number of nucleation sites in-creases. Eventually the avalanching is suppressed completelyand we observe a gradual rather than a sudden domaingrowth. This is better shown in Fig. 5, where two sets ofimages are compared at the same field after the sample hasbeen exposed to different maximum reversal fields of 3.5 and2.9 kOe, respectively. Note that the domain patterns nearpositive saturation are representative of those near negativesaturation discussed in Figs. 3 and 4, as these samples ex-hibit complementary point memory effect.22 When exposedto a field of 3.5 kOe, only very few nucleation sites are seenprior to the sharp magnetization drop[left panels of Figs.5(a) and 5(b)]. When exposed to a field of 2.9 kOe, manymore nucleation sites are seen leading to the gradual magne-tization drop[right panels of Figs. 5(a) and 5(b), and Fig.5(d)]. After the stripe domains have propagated, the domainpatterns are similar[Fig. 5(c)].

C. Resonant small-angle scattering

To further confirm the slow saturation of residual domainswe complement the TXRM imaging results with resonantSAS. Scattering is not limited by the imaging resolution andis sensitive to magnetic heterogeneities of size comparable tothe x-ray wavelengths,1.6 nmd. The field dependence ofthe magnetic scattering intensity from the Co/Pt multilayer

FIG. 3. Partial Kerr hysteresis loop around negative saturation.The solid line is part of the major hysteresis loop, with a maximumreversal field of −4.0 kOe. Open symbols represent part of a loopreversed at −3.1 kOe. TXRM images are shown in(a)–(d), over asame 2.7mm35.2 mm area of the sample, at −2.5 kOe approach-ing saturation(a), (b) and at −1.8 kOe(c), (d) after exposure to a−3.1 kOe field. The open circles in image(d) mark the nucleationsites of image(c), and coincide with the residual white reversedomains before saturation in image(a). The composite is shown inimage(b).

FIG. 4. Number of nucleation sites(y axis) observed within a12-mm-diam circle, after bringing the sample from positive satura-tion to a maximum negative reversal field, whose value is plotted onthe x axis, and then reducing the field back to −1.5 kOe forimaging.

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is shown in Fig. 6(a) and is similar to that shown in Ref. 19.The SAS loop is measured with the detector set such thatthere is an in-plane scattering wave vectorq=0.024 nm−1.The scattered intensity results from deviations from the av-erage magnetization and is proportional to the square of theFourier transform of the magnetization distributions. Thefeatures in the SAS loop correlate closely with features in thehysteresis loop shown in Fig. 2. Beyond saturation, the mag-netization of the sample is uniform and the scattering is at aminimum. As the field is reduced scattering commences atthe nucleation point and increases its intensity by orders ofmagnitude to a maximum near the coercive field before fall-ing back to the saturation level again at the opposite satura-tion. As shown in Fig. 6(a), the apparent nucleation and satu-ration fields are around ±2.8 kOe and ±1.2 kOe, respectively,coinciding with the onset and completion of reversal as in-ferred from the major hysteresis loop(Fig. 2).

However, at an expanded scale shown Fig. 6(b), the slowapproach to saturation becomes apparent. A small but mea-surable scattering intensity originating from the residualbubble domains is reflected in this reversal profile. As thesystem approaches saturation, the reduction in scattering in-tensity can occur both from the reduction of the bubble do-main size and from the annihilation of the bubble domains,which cannot be easily distinguished. However, it is clearfrom the SAS measurements that significantly higher fieldsare required to fully saturate the sample, in agreement withthe FORC and TXRM results. For the example in Fig. 6(b),fields exceeding −4.0 kOe are required to reach the saturatedscattering intensity whereas the saturation appears much ear-lier on the full intensity scale[Fig. 6(a)] and the hysteresisloop, near −2.8 kOe. Similarly, on reduction of the field, thefirst increase in scattering signaling the formation of reversedomains occurs near −2.0 kOe, well before the pronouncedincrease in scattering that signals the avalanche of reversedomains at −1.2 kOe. This, again, corresponds nicely withthe imaging results in Fig. 2 where bubble domains are ob-

FIG. 5. (a)–(c) Comparison of three pairs ofTXRM images(all 5.6 mm34.5 mm), each pairof images collected at the same external field(a=1.5 kOe,b=1.2 kOe, andc=0.9 kOe) after ex-posing to different maximum reversal fields of3.5 and 2.9 kOe for the left and right panels ofeach pair, respectively.(d) shows the first quad-rant of the corresponding MOKE hysteresis loopsreversed at 2.9 kOe(open symbols) and 3.5 kOe(solid symbols). The fields at which the TXRMimages (a)–(c) are taken are also marked bylarger open and solid circles.

FIG. 6. (a) Resonant magnetic soft x-ray scattering intensityprofiles from a fCos4 Åd /Pts7 Ådg50 multilayer over a completefield cycle. (b) A plot zooms in on the saturation and nucleationdetails as marked by the grey box in(a). The solid and open sym-bols represent the decreasing-field and increasing-field branch, re-spectively, as indicated by the arrows. The magnified view in(b)reveals a gradual intensity drop towards saturation and a gradualincrease at nucleation reflecting the residual domains present atthese fields.

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served well before the formation of the stripe domain pat-tern.

IV. DISCUSSION AND CONCLUSION

The observed microscopic magnetization reversal pro-cesses resemble those seen in other systems with perpendicu-lar anisotropy, such as garnet, CoCr, and Co/Pdfilms.13,20,23–25 Towards saturation, the labyrinth domainscontract to form isolated stripe domains that contract furtherinto bubble domains. Eventually the bubble domains col-lapse at a critical fieldHbc and a true saturation is reached.Theoretically,Hbc can be calculated according to

Hbc = 4pMS− 8ÎsW/Ds1 +Îmd, s3dwhereMS, sW, D, and m are saturation magnetization, do-main wall energy density, film thickness, and permeability,respectively.20 For the present Co/Pt multilayers we estimateHbc,−3.4 kOe.26 Experimentally, the bubble collapse fieldHbc has been difficult to measure. Macroscopically, the majorhysteresis loop is not sensitive enough to reflect the smallfractions of unreversed bubble domains; microscopically, thebubble domains can contract below the resolution limit of themagnetic imaging techniques, making a precise determina-tion of Hbc difficult. In contrast, the FORC distribution, thesecond-order derivative of magnetization, is very sensitive tothis collapse field. Before saturation, any residual bubble do-mains result in increased irreversibility in the subsequentfield sweep, giving rise to a nonzeror. Only after reaching atrue saturation will the subsequent field sweep becomeHRindependent orr=0. As shown earlier, the true saturationfield determined by FORC isHS,−3.8 kOe. Note that it isnot unexpected thatHS is slightly different fromHbc: Equa-tion (3) calculates anaverage Hbc based on the known ma-terial characteristics of a homogeneous sample. The FORCHS reflects theactual Hbc which is modified by inhomoge-neities. The determination of this true saturation field is im-portant for the application of such materials in perpendicularmagnetic recording, where old data needs to be overwrittenby the recording head.

Reviewing the microscopic analysis of the reversal viaTXRM and SAS and the macroscopic analysis with FORC, itseems that nucleation and saturation are almost two inverselysymmetric processes: both are macroscopically irreversible.One creates, while the other annihilates domains. In addition,both exhibiting microscopic domains well before the macro-scopic nucleation and well beyond macroscopic saturationpoints that would be typically identified from the major hys-teresis loop. On the other hand, there are clear asymmetries.Irreversible FORC features are visible beyond macroscopic

saturation, but are not sensitive to the reversal domain for-mation before macroscopic nucleation. This originates fromthe fact that there is no minor loop visible before macro-scopic nucleation, since the moment connected with the fewdomains present at that stage is below the instrumental reso-lution. In contrast, the lack of saturation due to residual do-mains becomes significantly amplified due to its impact onthe domain avalanches during the subsequent nucleation(sharp edge in the hysteresis loop becomes gradual), asshown in Figs. 3 and 5. We also observe that the density ofisolated nucleation sites after “microscopic saturation” ismuch lower than the density of isolated residual domains justbefore saturation; i.e., the tendency to fracture into isolateddomains is rather high towards saturation: we typically ob-serve about 200 isolated domains/10mm2, while only veryfew isolated domains trigger nucleation(typically only 1–3domains/10mm2).

In conclusion, we have analyzed the magnetic reversal ofCo/Pt multilayers using a complementary combination ofmacroscopic FORC and microscopic TXRM and SAS tech-niques. A striking feature of the system is that irreversibleswitching processes can persist well beyond the apparentsaturation, where the macroscopic magnetization levels off.We find that in that stage a small but crucial amount ofresidual reverse domains are still present. While not readilyobserved in the major loop, these residual domains alter thesubsequent minor loop reversal process significantly sincethey provide the nucleation sites for the avalanchelikegrowth of the stripe domains. As a result the residual do-mains produce a characteristic feature in the FORC distribu-tion that has no counterpart in the major loop. Our resultsalso demonstrate that the FORC method is a sensitive mac-roscopic technique(particularly in theH-HR coordinate sys-tem) for probing the reversibility and irreversibility of mag-netic switching processes in perpendicular magneticmultilayers. Combined with TXRM and SAS, it is possibleto obtain a comprehensive and quantitative understanding ofmagnetic reversal processes.

ACKNOWLEDGEMENTS

Work at UCD has been supported by Lawrence LivermoreNational Laboratory UCDRD funds. The acquisition of analternating gradient magnetometer which was used exten-sively in this investigation was supported by NSF Grant No.EAR-0216346. G.D., J.B.K., and work at LBNL have beensupported by the Director, Office of Science, Office of BasicEnergy Sciences of the U.S. DOE under Contract DE-AC03-76SF00098. We thank C. P. Pike, G. Acton, A. Roth, K. L.Verosub, R. T. Scalettar, G. T. Zimányi, M. S. Pierce, C. R.Buechler, and L. B. Sorensen for helpful discussions.

*Electronic address: kailiu@ucdavis.edu.1For a recent review, see, e.g., J. I. Martín, J. Nogués, K. Liu, J. L.

Vicent, and I. K. Schuller, J. Magn. Magn. Mater.256, 449(2003).

2E. E. Fullerton, J. S. Jiang, and S. D. Bader, J. Magn. Magn.Mater. 200, 392 (1999).

3M. D. Stiles and R. D. McMichael, Phys. Rev. B59, 3722(1999).

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4V. I. Nikitenko, V. S. Gornakov, A. J. Shapiro, R. D. Shull, K.Liu, S. M. Zhou, and C. L. Chien, Phys. Rev. Lett.84, 765(2000).

5L. Savtchenko, B. N. Engel, N. D. Rizzo, M. F. Deherrera, and J.A. Janesky, US Patent 6,545,906 B1.

6G. M. McClelland, M. W. Hart, C. T. Rettner, M. E. Best, K. R.Carter, and B. D. Terris, Appl. Phys. Lett.81, 1483(2002).

7C. R. Pike, A. Roberts, and K. L. Verosub, J. Appl. Phys.85,6660 (1999).

8H. G. Katzgraber, F. Pázmándi, C. R. Pike, Kai Liu, R. T. Scal-ettar, K. L. Verosub, and G. T. Zimányi, Phys. Rev. Lett.89,257202(2002).

9C. R. Pike, Phys. Rev. B68, 104424(2003).10A. Stancu, C. Pike, L. Stoleriu, P. Postolache, and D. Cimpoesu,

J. Appl. Phys.93, 6620(2003).11D. Weller, L. Folks, M. Best, E. E. Fullerton, B. D. Terris, G. J.

Kusinski, K. M. Krishnan, and G. Thomas, J. Appl. Phys.89,7525 (2001).

12O. Hellwig, S. Maat, J. B. Kortright, and E. E. Fullerton, Phys.Rev. B 65, 144418(2002).

13O. Hellwig, G. P. Denbeaux, J. B. Kortright, and E. E. Fullerton,Physica B336, 136 (2003).

14M. S. Pierce, R. G. Moore, L. B. Sorensen, S. D. Kevan, O.Hellwig, E. E. Fullerton, and J. B. Kortright, Phys. Rev. Lett.90, 175502(2003).

15F. Preisach, Z. Phys.94, 227 (1935).

16I. D. Mayergoyz,Mathematical Models of Hysteresis(Springer-Verlag, New York, 1991).

17J. B. Kortright, D. D. Awschalom, J. Stöhr, S. D. Bader, Y. U.Idzerda, S. S. P. Parkin, I. K. Schuller, and H.-C. Siegmann, J.Magn. Magn. Mater.207, 7 (1999).

18P. Fischer, G. Denbeaux, T. Eimüller, D. Goll, and G. Schütz,IEEE Trans. Magn.38, 2427(2002).

19J. B. Kortright, S. K. Kim, G. P. Denbeaux, G. Zeltzer, K. Takano,and E. E. Fullerton, Phys. Rev. B64, 092401(2001).

20C. Kooy and U. Enz, Philips Res. Rep.15, 7 (1960).21The 45° line in Fig. 1(b) between reference lines 1 and 3 repre-

sents the boundary of our data set.22M. S. Pierce, C. R. Buechler, L. B. Sorensen, J. J. Turner, S. D.

Kevan, E. A. Jagla, J. M. Deutsch, T. Mai, O. Narayan, J. E.Davies, K. Liu, J. Hunter Dunn, K. M. Chesnel, J. B. Kortright,O. Hellwig, and E. E. Fullerton, cond-mat/0411698, Phys. Rev.Lett. (to be published).

23F. Schmidt and A. Hubert, J. Magn. Magn. Mater.61, 307(1986).24A. Hubert and R. Schäfer,Magnetic Domains(Springer-Verlag,

Berlin, 1998).25A. W. Rushforth, P. C. Main, B. L. Gallagher, C. H. Marrows, B.

J. Hickey, E. D. Dahlberg, and P. Eames, J. Appl. Phys.89,7534 (2001).

26Based on MS=700 emu/cm3, anisotropy K=33106 erg/cm3,

andsW=6 erg/cm2.

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