Exchange bias, training effect, hysteretic behavior of angular dependence,and rotational hysteresis loss in NiFe/FeMn bilayer: Effect ofantiferromagnet layer thicknessT. R. Gao, Z. Shi, S. M. Zhou, R. Chantrell, P. Asselin et al. Citation: J. Appl. Phys. 105, 053913 (2009); doi: 10.1063/1.3087450 View online: http://dx.doi.org/10.1063/1.3087450 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v105/i5 Published by the American Institute of Physics. Related ArticlesMagnetic and structural properties of (Ga,Mn)As/(Al,Ga,Mn)As bilayer films Appl. Phys. Lett. 102, 112404 (2013) Magnetization reversal and spintronics of Ni/Graphene/Co induced by doped graphene Appl. Phys. Lett. 102, 112403 (2013) Injection locking at zero field in two free layer spin-valves Appl. Phys. Lett. 102, 102413 (2013) Micromagnetic simulation of high-power spin-torque oscillator in half-metallic Heusler alloy spin valve nanopillar AIP Advances 3, 032132 (2013) Ultrathin magnetic oxide EuO films on Si(001) using SiOx passivation—Controlled by hard x-ray photoemissionspectroscopy J. Appl. Phys. 113, 17C505 (2013) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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Exchange bias, training effect, hysteretic behavior of angular dependence,and rotational hysteresis loss in NiFe/FeMn bilayer: Effect ofantiferromagnet layer thickness

T. R. Gao,1 Z. Shi,1 S. M. Zhou,1,a� R. Chantrell,2 P. Asselin,3 X. J. Bai,4 J. Du,4 andZ. Z. Zhang5

1Department of Physics and Surface Physics Laboratory (National Key Laboratory), Fudan University,Shanghai 200433, China2Physics Department, The University of York, York YO10 5 DD, United Kingdom3Seagate Research, 1251 Waterfront Place, Pittsburgh, Pennsylvania 15222, USA4National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China5Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China

�Received 8 September 2008; accepted 20 January 2009; published online 13 March 2009�

For NiFe/FeMn bilayers, the correlation among the exchange field, the coercivity, the training effect,the hysteretic effect of the angular dependence of the exchange bias, and the rotational hysteresisloss has been studied as a function of the antiferromagnet layer thickness tAFM. With increasingtAFM, all these quantities undergo nonmonotonic variations, except for the monotonic change in theexchange field. The maximal values of the coercivity, its relative change, and the rotationalhysteresis loss are almost located at the same tAFM of 3.8 nm. The maximal values of the relativechange in the exchange field and of the hysteretic effect of the angular dependence are located at 2.5and 3.0 nm, respectively. The rotational hysteresis loss and the hysteretic behavior of the angulardependence of the exchange bias have different characteristics. The variations of all physicalquantities with tAFM can be ascribed to the irreversible reversal of the antiferromagnet spins, whichare governed by the Arrhenius–Néel law, except for that of the rotational hysteresis loss. © 2009American Institute of Physics. �DOI: 10.1063/1.3087450�

I. INTRODUCTION

A ferromagnet�FM�/antiferromagnet�AFM� bilayer willexhibit a shifted hysteresis loop if it experiences a magneticfield-cooling procedure or it is deposited in a magnetic field.This phenomenon is called exchange bias �EB�; that is to say,the bilayer has a unidirectional anisotropy. At the same time,the coercivity HC is generally enhanced in comparison withthat of the corresponding free FM layer with fewexceptions.1–8 The effect of AFM spins on the EB has beenstudied extensively in many EB-related phenomena as shownbelow.5–19 Since very few direct techniques can be employedto probe the AFM spin motion due to the zero net magneti-zation in the AFM layer, however, it is difficult to reveal theeffect of AFM spins and thus the mechanism of the EB stillremains open.

First of all, as a signature of the EB, the rotational hys-teresis loss occurs between torque curves of clockwise �CW�and counterclockwise �CCW� rotations even if the externalmagnetic field Ha is much larger than the saturation field ofthe FM layer.11,12 That means that the rotation process of theFM magnetization is asymmetric for CW and CCW rotationsdue to the irreversible rotation of the AFM spins and that theexchange field acting on the AFM layer is less than the satu-ration field of the AFM layer. Second, the magnetization re-versal mechanism is found to be different at the descent andthe ascent branches of hysteresis loops, as revealed by mea-surements of magnetometry, anisotropic magnetoresistance,

and neutron scattering.13,14,20,21 Furthermore, the training ef-fect, as an important phenomenon of the EB, is often ob-served, which suggests that the AFM spins approach equilib-rium states after subsequent cycles of hysteresis loops.15,16

Finally, the hysteretic behavior of the angular dependence ofthe EB �ADEB� has very recently been reported although theADEB has been studied for more than 10 years.17–19

Above physical properties strongly depend on the con-stituent layer thickness. The effect of the FM layer thicknesstFM on both the EB and related phenomena has been under-stood very well.3 For example, due to the well known inter-facial nature, the exchange field HE is inversely proportionalto tFM and HC decreases with an increase in tFM. In contrast,the effect of the AFM layer thickness tAFM is more compli-cated although it can provide rich information to understandthe effect of the AFM spins.3 In general, at small tAFM, thesephenomena disappear. When tAFM is larger than the criticalvalue for the onset of the EB, these phenomena begin toappear and then may undergo nonmonotonic variations orapproach saturation with further increase in tAFM. However,the detailed evolutions of these physical quantities near theonset have often been neglected while it is of crucial impor-tance to get deep insight into the effect of AFM spins. At thesame time, the variation trends of these physical phenomenawith tAFM have been studied in various FM/AFM systems bydifferent groups. In order to explain specific experiments,theoretical models are proposed. For example, in order toexplain the asymmetrical hysteresis loops, the AFM spin mo-tion is proposed in some experiments but rigid AFM spinsare assumed in other ones.5,13 Therefore, it is expected thata�Electronic mail: shiming@fudan.ac.cn.

JOURNAL OF APPLIED PHYSICS 105, 053913 �2009�

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systemic experimental studies on all above physical proper-ties in a single series of FM/AFM bilayers might be helpfulto propose a unified theoretical model.

In this work, a series of NiFe/FeMn bilayers was pre-pared with various tAFM, HE, and HC, the EB training effect,the rotational hysteresis loss, and the hysteretic behavior ofthe ADEB were measured. Attention is paid to the correla-tion between variations of these physical quantities withtAFM, in particular, the training effect and the hysteretic be-havior of the ADEB. The difference between the hystereticbehavior of the ADEB and the rotational hysteresis loss isanalyzed. In order to explain variations of these physicalquantities, micromagnetic calculations are made based on thethermal activation model.

This paper is organized as follows. In the following part,the model of thermally activated transition of AFM spins isdescribed. In Sec. III, fabrications and measurements ofsamples are described. In Sec. IV, HE and HC, and the train-ing effect are given as a function of tAFM. In Sec. V, thehysteretic behavior of the ADEB is discussed. In Sec. VI, therotational hysteresis loss RW is discussed as a function oftAFM. Finally, a summary is given.

II. THERMAL ACTIVATION MODEL

A computational model was developed to calculate theEB, the training effect, and the hysteretic behavior of theADEB.22 The FM and AFM layers are modeled as a granularmicrostructure produced using a Voronoi construction �see,for example, Ref. 23�. Each layer has the same microstruc-ture, which describes realistic systems where the columnargrowth is continuous across interfaces. The AFM grains areconsidered to be exchange decoupled while the neighboringFM-FM and FM-AFM grains are strongly exchange coupled.The AFM layer is treated using a kinetic Monte Carloalgorithm.24 The coherent reversal of AFM spins is governedby thermally activated processes; that is to say, the grains areallowed to reverse with a probability psw given by theArrhenius–Néel law.25 In view of the hysteretic behavior ofthe ADEB, the planar domain wall in the AFM layer is ne-glected due to a much smaller tAFM than the domain wallthickness.26 psw is determined by the intrinsic energy barrier,i.e., determined by the local anisotropy energy Eanis, and theexchange field from the FM layer. Eanis

=a0tAFMKAFM sin2 �AFM, where �AFM is the angle betweenAFM spins and the easy axis. The anisotropy constant KAFM

is single valued and the lateral area of AFM grains a0 has alognormal distribution with a typical standard deviation �.The easy axes of the AFM grains are assumed to be planarrandomly orientated. The interlayer exchange energy is27

Eexch=−a0c0JintSFMSAFM, where Jint is the interface exchange

coupling constant, and SFM and SAFM are the unit vectors ofthe FM and AFM moments at the interface, respectively. Thecontact fraction c0 represents the magnetization imbalancebetween the two sublattices contacting the FM layer. Deter-mination of stationary states from the total free energyEexch+Eanis allows calculations of the energy barrier, fromwhich psw is determined. The FM layer is treated in a stan-dard micromagnetic approach with the cell size being the

grain size. The FM grains are coupled with the bulk ex-change energy. The magnetic equilibrium state is determinedby minimizing the Gibbs free energy, which includes theZeeman energy, the exchange interaction, the uniaxial aniso-tropy, the magnetostatic terms, and the interlayer exchangecoupling energy. Minimization of the energy is achieved us-ing a conjugate gradient method with a precision of 10−5.With the strong exchange coupling between FM grains, thenonuniform magnetization reversal process might exist.

III. FABRICATION AND MEASUREMENTS OFSAMPLES

A bilayer of Ni80Fe20�=NiFe��3 nm� /Fe50Mn50�=FeMn� was deposited on a 1�5 cm2 glass sub-strate at ambient temperature by dc magnetron sputteringfrom NiFe and FeMn composite targets. In order to avoid therun-to-run error, the FeMn layer takes a wedge shape acrossthe distance of 5 cm, in which each sampling location alongthe wedge direction corresponds to a specific tAFM as an ap-proximate linear function. A 1�5 cm2 NiFe/FeMn �4.2 nm�bilayer with the wedge-shaped NiFe layer and a 3 nm thickuniform single layer NiFe film were also prepared. The basepressure was 2�10−5 Pa and the Ar pressure was 0.33 Paduring deposition. Before deposition of the bilayer, a 30 nmthick Cu buffer was prepared to improve fcc �111� preferredorientation in FeMn layers and thus to stimulate the EB.28

Finally, another 30 nm thick Cu layer was used to avoidoxidation. Deposition rates of NiFe, FeMn, and Cu layerswere 0.3, 0.1, and 0.2 nm/s, respectively. During deposition,a magnetic field of about 130 Oe was applied parallel to thefilm plane to induce the EB in bilayers and uniaxial aniso-tropy in single layer FM films.

X-ray diffraction �XRD� shows an intense peak at 2�=43.3° and a weak one at 50.6°, corresponding to �111� and�200� preferred orientations of Cu, FeMn, and NiFe layers,respectively, as shown in Fig. 1. Apparently, constituent lay-ers are polycrystalline with preferred textures. Before mag-

40 45 50 55

(200)

(111)

Inte

nsit

y

2θ (deg)

FIG. 1. A typical XRD spectra of the NiFe�3 nm�/FeMn�6 nm� bilayer.

053913-2 Gao et al. J. Appl. Phys. 105, 053913 �2009�

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netic measurements, the specimen was cut into small piecesalong the wedge direction prepared at the same time butvarying in tAFM or tFM. No field cooling was made to avoidmorphology degradation at the FM/AFM interface. With avector vibrating sample magnetometer �VVSM� of model7407 from LakeShore Co., hysteresis loops were measured.mx and my are components of the magnetic moment paralleland perpendicular to Ha, respectively, where mx correspondsto the conventional hysteresis loops. Ha, mx, and my are allparallel to the film plane. At the left and right coercive fieldswhere mx=0, my usually has maximal values, namely, my−L

and my−R. Here, in the same way as in Ref. 13, my−AVE

= �my−R+my−L� /2 and the asymmetry factor �= �abs�my−R�−abs�my−L�� / �abs�my−R�+abs�my−L��. These two parametersare of crucial importance to reveal the magnetization reversalmechanism. For measurements of the angular dependence ofhysteresis loops, Ha was set to zero during rotating samples.Torque curves were also measured by the VVSM.29 Beforemeasurements of the rotational hysteresis loss, a large Ha

was applied to saturate the sample along the starting orien-tation and then it was set to designed values. During mea-surements of torque curves, mx and my were measured as afunction of the orientation of Ha with a fixed magnitude forthe CW and CCW rotations. With data of my, the torque andthe rotational hysteresis loss can be obtained. All measure-ments were performed at room temperature.

IV. EB AND TRAINING EFFECT

In literature, few reports have shown the detailed evolu-tion of the EB from the onset to the maximum or saturation.In this work, the detailed dependence of all HE, HC, and thetraining effect on tAFM near the onset is emphasized usingmany samples. Figure 2 shows the dependence of HE and HC

on tAFM, which were taken from the hysteresis loop of thefirst cycle along the easy axis of each sample. As tAFM is

larger than the critical value of 2.3 nm for the onset of theEB, HE increases slowly and approaches the constant ofabout 200 Oe. At the same time, HC starts to increase attAFM�2.3 nm and then reaches a maximum of 85 Oe at 3.8nm, and finally decreases as tAFM further increases. Althoughthe present results about variations in HE and HC are similarto reported ones,3 more samples were used to show the de-tailed dependence of the EB on tAFM in the region of smalltAFM.

Figure 3�a� shows the typical training effect of the EB inthe NiFe�3 nm�/FeMn�3.2 nm� bilayer. One can find that HE

and HC decrease with increasing cycle number n as an em-pirical linear function of 1 /�n, similar to the previousresults.3 In general, for samples just after the deposition orthe field-cooling procedure,14,15 there is a big change in thecoercive field of the descent branch between the first and thesecond cycles, resulting in serious reductions in HE and HC.The particular mechanism of the first magnetization reversalperformed just after the field-cooling procedure or at the as-prepared state is induced by the AFM spin flopping due tothe AFM biaxial magnetic anisotropy. It is noted that the spinflopping only exists in the first magnetization reversal.14

Since it can happen at all temperatures, it manifests itself asan athermal effect. The reductions in HE and HC for n�1 aregoverned by the thermally activated transitions triggered bythe exchange field from the FM magnetization.30 In thepresent work, for each sample, the n=1 hysteresis loop alongthe easy axis was measured and a recovery procedure per-formed subsequently to remove the athermal effect.14

In order to make more direct comparison, the relativechanges are defined HE/C, i.e., �HE/C /HE/C�n=1� to expressthe EB training effect, where �HE/C=HE/C�n=1�−HE/C�n

1 2 3 4 5 6 70

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(b)

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HC

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FIG. 2. �Color online� HE �a� and HC �b� vs tAFM for the NiFe�3 nm�/FeMnbilayers.

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e)

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FIG. 3. �Color online� HE and HC vs the cycle number n for the NiFe�3nm�/FeMn �4.2 nm� bilayer �a�. Relative changes in HE and HC �b� as afunction of tAFM for the NiFe�3 nm�/FeMn bilayers.

053913-3 Gao et al. J. Appl. Phys. 105, 053913 �2009�

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=��. Actually, when n�20, the changes in HE and HC arenegligible. Therefore, �HE/C�HE/C�n=1�−HE/C�n=20�. Therelative changes in HE/C correspond to those AFM grains inrotatable/nonrotatable AFM grains, which undergo thermallyactivated transitions at finite temperatures from nonequilib-rium to equilibrium states. Figure 3�b� shows�HE/C /HE/C�n=1� as a function of tAFM. With increasingtAFM, �HE /HE�n=1� and �HC /HC�n=1� increase sharply.Remarkably, as tAFM is slightly larger than the critical valuefor the onset of the EB, �HE /HE�n=1� has a maxima,whereas HE has the largest slope. It is also interesting to findthat �HC and �HC /HC�n=1� have similar variation trends.

The results in Figs. 2 and 3 can be explained qualita-tively in terms of thermally activated transitions of AFMspins. At small tAFM, most of AFM grains are “superpara-magnetic,” HE=0, and no HC enhancement occurs. As tAFM

is close to the critical value for the onset of EB, most ofAFM grains are thermally stable, in which all grains arerotatable during the FM magnetization motion. The rotatableAFM grains enhance the “uniaxial anisotropy,” which resultsin an enhancement of HC. Without nonrotatable AFM grains,HE=0 and the training effect is negligible. As the AFM layeris slightly thicker than the critical value for the onset of EB,there are a small fraction of nonrotatable AFM grains and HE

is nonzero. With more rotatable ones, HC increases. A part ofrotatable/nonrotatable grains are suggested to have transi-tions from nonequilibrium to equilibrium states triggered bythe rotating exchange field from the FM magnetization.16

With high probability of thermally activated transitions, theshrinkage of HE and HC is serious and �HE /HE�n=1� and�HC /HC�n=1� are large. As the AFM grain volume is fur-ther increased with increasing tAFM, more rotatable AFMgrains become nonrotatable, and HE increases but HC de-creases. At the same time, the anisotropy energy barrier in-creases and thus the thermal transition probability is sup-pressed. Then, �HE /HE�n=1� and �HC /HC�n=1� becomesmall. Therefore, different behaviors of HE and its relativechange and similar variation trends of HC and its relativechange can be easily understood in the frame of the theoret-ical model. Above explanations also agree with the reportedresults that the training effect becomes weak as the AFMgrain size is increased.31

V. HYSTERETIC BEHAVIOR OF ADEB

In this part, the basic experimental features of the hys-teretic behavior of the ADEB are first discussed in the NiFe/FeMn bilayers, which has been reported before.17 After-wards, the dependence of the hysteretic behavior on theconstituent layer thickness is studied. Then, possible reasonsfor the difference of the hysteretic behavior between HE andHC are discussed. Finally, the correlation between the hyster-etic behavior of ADEB and the training effect is analyzed.

Hysteresis loops were measured in the CW rotation ofHa with �H from 180° to 180° and in the CCW rotationwith �H from 180° to 180°. Here, �H is the orientation ofHa and set to zero when HE in the CW rotation has a nega-tive maximum value. In experiments, it is found that at aspecific �H near either �H=0 or �H=180°, the hysteresis

loops are different for the CW and CCW rotations. Figure 4shows typical hysteresis loops at �H=10° during the CW andCCW rotations. One can find that for the CW and CCWrotations, HE=−52 Oe and 51 Oe, and HC=52 Oe and 30Oe, respectively. HC is different for the CW and CCW rota-tions while HE is close to each other. More importantly, themagnetization reversal mechanism is also different. In theCW rotation, my−R at the ascent branch is almost equal tozero, indicating the domain wall motion. In contrast, my−L atthe descent branch is nonzero but much smaller than thesaturation magnetic moment. Therefore, the magnetizationrotation occurs, in addition to the domain wall motion. Forthe CCW rotation, however, my−R and my−L, having the samemagnitude, are nonzero although they are much smaller thanthe saturation magnetic moment demonstrating a combinedmagnetization reversal mechanism during the magnetizationreversal process of either branch. Hence, near �H=0 and180°, the magnetization reversal mechanism depends on thesense of rotation.

Figure 5 shows the angular dependence of HE, HC,my−AVE, and � for the NiFe�3 nm�/FeMn �3.2 nm� bilayer.First of all, HC, my−AVE, and � have different angular depen-dence for the CW and CCW rotations. HC and � have themaxima and my−AVE=0 at �H=18° during the CW rotationand at �H=−18° during the CCW rotation. In order to ex-press the degree of the hysteretic behavior, the angular dif-ference between the coercivity peaks of the CW and CCWrotations, ��H, is defined. For the present sample, ��H is36°. Second, with maximal values at almost the same �H forthe CW and CCW rotations, HE has no apparent hystereticbehavior. The disappearance of the hysteretic behavior of HE

will be discussed below. Finally, at �H near 0, 180°, and180°, hysteresis loops are asymmetric. When �H is devi-

-400 -200 0 200 400H (Oe)

(b)

M(a

rb.u

nits

)

(a)

FIG. 4. �Color online� Typical hysteresis loops �mx �black line� and my �redline�� of the NiFe�3 nm�/FeMn�3.2 nm� bilayer for CCW �a� and CW �b�rotations, where �H=10°.

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ated far away from the easy axis, however, �=0 and my−AVE

are close to the saturation magnetic moment. The magneti-zation reversal process is accompanied by the magnetizationrotation at both ascent and descent branches, leading to sym-metric hysteresis loops. Similar results have very recentlybeen reported in Co/IrMn and NiFe/MnPt bilayers,13,32 inwhich �=0 for �H larger than a critical value.

The results in Fig. 5 are proved to arise from the hyster-etic behavior. First of all, as shown in Ref. 17, the ADEB forthe second CW rotation measured directly after 1 cycle ofCW and CCW rotations is found to be almost the same asthat of the first CW rotation and the accumulation effectduring the continuous measurements of hysteresis loops canbe excluded in the explanations of the shift of the ADEBbetween the CW and CCW rotations. Second, the ADEB ofthe CW and CCW rotations was measured within different�H regimes. As shown in Fig. 6, when �H changes within asmall range, such as −30° →0→−30°, the angular depen-dence of my−AVE is almost identical for the CW and CCWmeasurements. For large regimes of �H, like −30° →20°→−30°, the angular dependence of the my−AVE is different inthe CW and CCW rotations and ��H is not equal to zero. Forlarger enough �H regions, such as −30° →40° →−30°, ��H

will approach a constant. The curve of my−AVE versus �H isof basic feature of the hysteretic behavior. Unambiguously,the hysteretic behavior of the ADEB is demonstrated.

Figure 7 shows calculations for a system with a mediangrain size of ao=5 nm, �=0.3,22 tAFM=5 nm, tFM=3 nm,KAFM=4�106 ergs /cc, KFM=5�103 ergs /cc, MFM

=MAFM=750 emu /cc, and the exchange field between FM-AFM grains is 500 Oe. The hysteretic behavior of the ADEBis demonstrated, including HE, HC, my−AVE, and �. At �H for

the coercivity peak, my−AVE=0 and � have either the positiveor the negative maximum. As �H is deviated from 180°,my−AVE=ms and �=0. The present model reproduces majorfeatures of the experimental results in Fig. 5.

The hysteretic behavior of the ADEB can be explainedqualitatively. Consider a hysteresis loop for the FM layer,i.e., the starting positive saturation S1�+MFM�→negative

-180 -90 0 90 180-1

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(Oe)

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FIG. 5. �Color online� Angular dependence of HE �a�, HC �b�, my−AVE /ms

�c�, and � �d� on the CW �black line� and CCW �red line� rotations for theNiFe�3 nm�/FeMn�3.2 nm� bilayer.

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FIG. 6. �Color online� Angular dependence of my−AVE /ms for a typical NiFe/FeMn bilayer in the small �a� and large �b� �H regions �Ref. 17�.

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FIG. 7. �Color online� Calculated angular dependence of HE �a�, HC �b�,my−AVE /ms �c�, and � �d� at 300 K for the FM/AFM bilayer.

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saturation S2�−MFM�→ending saturation point S3�+MFM�.Calculations show that AFM spins switch irreversibly duringthe hysteresis loop of the FM layer. With respect to the di-rection �H=0°, the average orientation of the AFM spins��AFM� experiences an irreversible change, i.e., ��AFM� hasdifferent values at states S1 and S3, similar to previouslyreported results.33 Accordingly, the angular dependence of��AFM� at the starting saturation state S1 should exhibit thehysteretic behavior between the CW and CCW rotations.This can be seen from the results at 300 K in Fig. 8. Once thetemperature of the AFM layer is set to 0 K, thereby thethermally activated transitions will be removed and ��AFM�at the starting saturation state S1 is reversible for the CW andCCW rotations. The rotational hysteretic behavior of theADEB at 0 K will disappear. In other words, the hystereticbehavior of the ADEB arises from the irreversible motion ofAFM spins induced by thermally activated transitions.

It is instructive to study the dependence of the hystereticbehavior on the constituent layer thickness. Figure 9 showsthe angular dependence of HC for NiFe/FeMn bilayers withdifferent tFM. The angular shift ��H is almost the same fordifferent tFM although HC changes with tFM due to the inter-facial nature of the EB. As expected, ��H is independent oftFM. This is because �� reflects the change in the averageorientation of the AFM spins, which is only determined bythe interfacial exchange field on the AFM spins and the en-ergy barrier height of the AFM spins. It can also be knownthat the distribution of the AFM grain size does not changesignificantly with tFM. Otherwise, ��H will also change withtFM. Figure 10�a� shows the measured ��H as a function oftAFM. At small tFM, ��H equals zero. It increases sharply toreach the maximum as tAFM is increased. Finally, ��H de-creases with further increasing tAFM. If the AFM grain size isinfinite such as in epitaxially grown FM/AFM bilayers or theanisotropy energy barrier is high enough to overcome the

thermally driven transitions, the hysteretic behavior is ex-pected to disappear; that is to say, the ADEB is identical forthe CW and CCW rotations. Only in this case, the simula-tions of the parameters such as the exchange coupling energyand the uniaxial anisotropy are rigorous from the measuredADEB.19,34

The tAFM dependence of the hysteretic behavior on theADEB can be addressed qualitatively. At a small tAFM, allAFM grains are so-called superparamagnetic, i.e., transitions

120 240

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<φA

FM>

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FIG. 8. �Color online� Calculated ��AFM� at the state S1 throughout CW�squares� and CCW �circles� rotations at 0 K �solid symbols� and 300 K�open symbols� for the FM/AFM bilayer, where ��AFM� is the average ori-entation of the overall AFM spins.

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FIG. 9. �Color online� Angular dependence of HC on CW and CCW rota-tions for the NiFe /FeMn �4.2 nm� bilayers with tFM=7:0 nm �a� and 4.2nm �b�.

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2 3 4 5 6 7

0.0

0.2

0.4

0.6

∆φH

(deg

) (a)

tAFM

(nm)

(b)

∆ΗC/H

C

FIG. 10. �Color online� Dependence of ��H �a� and relative change in HC

�b� on tAFM for the NiFe�3 nm�/FeMn bilayer.

053913-6 Gao et al. J. Appl. Phys. 105, 053913 �2009�

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are freely allowed between two stable states. Thus, ��H isnegligible. With increasing tAFM, the volume of AFM grainsand thus the product of the magnetic anisotropy constant andthe volume increases. Accordingly, AFM spins in moregrains become thermally stable and are irreversibly reversedduring measurements of hysteresis loops and a large ��H isachieved. For a large enough tAFM, the intrinsic energy bar-rier is further increased and the transition probability is sup-pressed thereby decreasing ��H. The hysteretic behavior ofthe ADEB can also be removed by measurements near 0 K.It can be accomplished using surface magneto-optical Kerreffect system, in which low temperatures can be set andsamples can be rotated with respect to Ha.

It is significant to compare the variation in the hystereticbehavior with that in the training effect. Figure 10 shows�HC /HC�n=1� and ��H as a function of tAFM. First of all,the position of 3.0 nm for the maximal ��H is located be-tween that of 3.8 nm for the �HC /HC�n=1� and that of 2.5nm for the maximal �HE /HE�n=1� in Fig. 3�b�. ��H and�HC /HC�n=1� have variation trends close to each other.This is because for a specific series of FM/AFM bilayers, thehysteretic phenomenon and the training effect are two result-ant aspects of irreversibly thermally activated transitions ofAFM spins, depending on the distribution of the AFM grainsize, tAFM, and the anisotropy constant of AFM grains. Sec-ond, the relative changes in HE and HC,35 and ��H are allindependent of tFM. Finally, above analysis can be furtherconfirmed by measuring the temperature dependence of thetraining effect and the hysteretic behavior of the ADEB. Thetraining effect has been found to decrease at low tempera-tures and to disappear near the zero temperature.36 Mean-while, as shown above, the hysteretic behavior should alsodecrease at lower temperatures and disappear at 0 K. Theyare expected to have similar temperature dependence.

The hysteretic behavior of the angular dependence of HE

can be ascribed to two major reasons. First of all, the ratio ofHE /HC is very important. This is because the angular depen-dence of HE is strongly related to the ratio of the unidirec-tional and the uniaxial anisotropies as well as that ofHE /HC.37 If HE is larger than HC, HE changes smoothly with�H near the easy axis and the hysteretic behavior of HE ishard to be observed. If HE is smaller than HC, HE has a peaknear the orientation of the easy axis or changes sharply with�H and the hysteretic behavior of HE is easy to be observed.As shown in Fig. 5 and in Ref. 17, the hysteresis behavior ofHE is weak at large tAFM, where HE is larger than HC. Asshown in Figs. 11�a�–11�c� and in Ref. 17, however, the hys-teretic behavior of HE can be observed clearly when tAFM isjust slightly larger than the critical value for the onset of theEB, where HE is smaller than HC. Second, in principle, thehysteretic behavior of HE should be less prominent than thatof HC. Since the average size of nonrotatable AFM grains islarger than that of rotatable ones, the transition probability ofthe nonrotatable grains is smaller than that of rotatable ones,leading to a weaker hysteretic effect of HE than that of HC.Here, it should be pointed out that the rigorous criteria forthe hysteretic behavior of HE are unclear. Further studies

about difference between the hysteretic behaviors of HE andHC will be helpful to reveal the effect of AFM spins on theEB.

In experiments, no hysteretic behavior of the ADEB isfound for single layer FM films. Figure 11�d� shows the typi-cal angular dependence of HC for the single layer NiFe filmwith uniaxial anisotropy. Although the shape of the hyster-esis loops and the magnetization reversal mechanism changewith �H, the angular dependence of HC almost overlaps witheach other for the CW and CCW rotations. As a result, thehysteretic behavior of the ADEB does not exist in the singlelayer NiFe film and only exists in FM/AFM bilayers and thuscan be used as a signature of the EB.

VI. ROTATIONAL HYSTERESIS LOSS

Figure 12 shows the typical torque curves of CW andCCW rotations for the NiFe/FeMn bilayers with thin AFMlayers. Apparently, as Ha is small enough, the magnetizationis always aligned along the easy axis for both CW and CCWrotations and there is no irreversible rotations of the FMmagnetization and the rotational hysteresis loss is equal tozero. In this case, the torque curve can be fitted by sin �H,corresponding to a contribution from the unidirectional an-isotropy. At an intermediate Ha, torque curves of CW andCCW rotations are different; that is to say, the FM magneti-zation is irreversibly rotated. In addition to sin �H, sin�2�H�must be considered, which corresponds to the uniaxial aniso-tropy. It is this term that induces the nonzero rotational hys-teresis loss WR. At higher Ha, the FM magnetization alwaysfollows the rotating Ha and irreversible reversal disappears,

102030

-200 -100 0 100 200-1

0

1

-40-20

02040

-90 -60 -30 0 30 60 900

5

10

15

HC

(Oe)

(b)

my-

AV

E/m

S (c)

CCWCW

HE

(Oe)

(a)

(d)

HC

(Oe)

φH

(deg)

FIG. 11. �Color online� Angular dependence of HE �a�, HC �b�, andmy−AVE /ms �c� for the NiFe �3 nm�/wedged-FeMn �2.9 nm� bilayer. In com-parison, angular dependence of HC for a 3 nm thick NiFe single layer film isgiven in �d�.

053913-7 Gao et al. J. Appl. Phys. 105, 053913 �2009�

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resulting in a reduction in WR. Similar results have beenobserved in NiFe/Mn–Ir and CoFe/IrMn.12,38 As shown be-low, for the NiFe/FeMn bilayers with large tAFM, however,WR is still not equal to zero at Ha much higher than thesaturation field.

Figure 13 shows the typical curves of WR versus Ha atvarious tAFM. At small tAFM, WR is very small at all Ha. Atintermediate and large tAFM, WR undergo nonmonotonicvariations with tAFM, exhibiting a maximum WR�max�.The

magnitude and the field position of WR�max� change as afunction of tAFM with the largest one at the intermediate tAFM.The results are shown in Fig. 14�a�.

Above results can be explained below. In the FM singlelayer films, the rotational hysteresis loss is caused by theirreversible reversal �rotation or switching� of the FM mag-netization under rotating Ha.39 Whether the FM magnetiza-tion reversal is irreversible depends on the ratio of Ha andthe �intrinsic� uniaxial anisotropic field HK. If HaHK orHa�HK, the reversal is reversible, giving rise to negligibleWR. If Ha and HK are comparable, the reversal is irreversible,leading to large WR. The magnitude of WR depends on that ofHa. For the FM/AFM bilayers, the rotational hysteresis lossis caused by the irreversible reversal of the AFM spins underthe rotating exchange field from the FM layer, which pro-vides an effective HK similar to that of single layer FM films.Whether the AFM spins irreversibly rotates or not dependson the competition between the exchange coupling energyand the product of the anisotropy constant and the volume ofAFM grains. At small tAFM, AFM spins always follow therotating FM magnetization through the interfacial exchangefield, giving rise to negligible HK and WR. As tAFM is in-creased, AFM spins in more AFM grains do not follow therotating FM magnetization and instead irreversibly rotate,leading to high HK and large WR. As tAFM is further in-creased, AFM spins in more grains are fixed; that is to say,AFM spins in less grains rotate irreversibly, resulting in re-ductions in HK and WR. Therefore, the nonmonotonic varia-tion in WR with tAFM can be understood. Moreover, for aspecific tAFM, the nonmonotonic variation in WR with Ha canbe explained in a similar way to that of single layer FMfilms. Furthermore, since the rotational hysteresis loss is de-termined by the ratio of the torques on the FM magnetizationfrom Ha and HK and HK increases with increasing tAFM at

0 90 180 270 360

-40

0

40

-40

0

40

-40

0

40

(c)0 Oe

φH

(deg)

(b)200 Oe

Tor

que

(erg

/cm

3 )

(a)400 Oe

FIG. 12. �Color online� Typical torque curves of the NiFe�3 nm�/FeMn�6.4nm� bilayer with Ha=400 Oe �a�, 200 Oe �b�, and 0 �c�.

0 100 200 300 4000

100

200

0

100

200

0

100

200

(c)

H (Oe)

(b)

WR

(erg

/cm

3 )

(a)

FIG. 13. �Color online� Rotational hysteresis loss vs Ha for the NiFe �3nm�/FeMn bilayers with tAFM=6:4 nm �a�, 3.8 nm �b�, and 2.4 nm �c�.

0

50

100

150

200

2 3 4 5 6 7

0

20

40

60

80

(a)

WR

(erg

/cm

3 )

(b)

HC

(Oe)

tAFM

(nm)

FIG. 14. �Color online� Maximal rotational hysteresis loss �a� and HC �b� vstAFM for the NiFe�3 nm�/wedged-FeMn bilayers. The solid line in �a� servesa guide to the eye.

053913-8 Gao et al. J. Appl. Phys. 105, 053913 �2009�

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small tAFM, the critical value of Ha for the onset of WR andthe field for the maximal WR�max� increase with an initialincrease in tAFM. Finally, since WR�max� and HC depend ontAFM in similar ways, they vary with tAFM in similar trends, asshown in Figs. 14�a� and 14�b�.

It is significant to address the difference between thehysteretic behavior of the ADEB and the rotational hysteresisloss. First of all, the hysteretic behavior of the ADEB canbetter reflect the feature of the EB. Since the rotational hys-teresis loss also exists in single layer FM films,39 it is notunique for FM/AFM bilayers. As an evidence, however, thehysteretic behavior of the ADEB can exist only in the FM/AFM bilayer because such phenomenon does not exist insingle layer FM films. Second, they have different depen-dence on the constituent layer thickness. As shown in Figs.10�a� and 14, for tAFM�3.0 nm �� and WR�max� changessharply and slowly with tAFM, respectively. More remarkably,as shown in Fig. 9, �� is independent of tFM. For the FM/AFM bilayers, the magnitude of WR should increase withincreasing HK which decreases with increasing tFM due to itsinterfacial nature. Therefore, WR should decrease with an in-crease in tFM. Furthermore, they are expected to have differ-ent temperature dependences. The rotational hysteresis lossis expected to increase at low temperatures and to reach satu-ration at 0 K because the anisotropy constant of the AFMgrains usually increases at low temperatures, resulting in anenhanced effect of the irreversible rotation of AFM spin. Incontrast, the hysteretic behavior of the ADEB is suppressedat low temperatures because the thermal energy at low tem-peratures is much smaller than the energy barrier. Finally,they reveal the AFM spin motion in different ways.12,40 Forthe rotational hysteresis loss, the irreversible rotation ofAFM spins is dragged by the rotating exchange field fromthe FM layer while during the hysteretic behavior of theADEB, the irreversible transition of AFM spins is driven bythermal activation during measurements of hysteresis loops.

VII. SUMMARY

HE, HC, the EB training effect, the rotational hysteresisloss, and the hysteretic behavior of the ADEB have beenstudied in a single series of NiFe/FeMn bilayers as a func-tion of tAFM. Correlation and difference among above physi-cal quantities have been discussed.

First of all, for the NiFe/FeMn bilayers, HC,�HC /HC�n=1�, and �HE /HE�n=1� all change nonmonotoni-cally with tAFM in similar variation trends. In contrast, HE

increases monotonically with tAFM.Second, as a signature of the EB, the dependence of the

hysteretic behavior on the ADEB on the constituent layerthickness has been studied for the NiFe/FeMn bilayer. ��H

undergoes nonmonotonic variation with tAFM whereas it isindependent of tFM. Comparison between the hysteretic be-havior and the training effect is made. ��H and the relativechanges of HE and HC are of similar variation trends withtAFM because they all arise from thermally activated transi-tions of the AFM grains over local anisotropy energy barriersduring measurements of hysteresis loops.

Furthermore, the rotational hysteresis loss undergoes

nonmonotonic variation with tAFM and Ha. WR, and HC havesimilar variations with tAFM. Difference between the hyster-etic behavior of ADEB and the rotational hysteresis loss hasbeen discussed.

Finally, the variations of all physical quantities studiedhere with tAFM can be explained in terms of thermally acti-vated transitions of AFM spins, except for WR. This remark-able agreement between theory and experiments gives strongsupport to the granular model of EB in thin films. Studies oftheir correlation as a function of temperature are required,which is helpful to understand the validity of the thermalactivation model.

ACKNOWLEDGMENTS

This work was supported by the National Science Foun-dation of China under Grant Nos. 10874076, 50625102,50871030, 10574026, and 60490290, the National Basic Re-search Program of China under Grant Nos. 2007CB925104and 2009CB929201, the 973-project under Grant No.2006CB921300, and the Shanghai Leading Academic Disci-pline Project under Grant No. B113.

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