Asymmetric recovery effect of exchange bias in polycrystalline NiFe/FeMn bilayersX. P. Qiu, Z. Shi, S. M. Zhou, J. Du, X. J. Bai, R. Chantrell, and L. Sun Citation: Journal of Applied Physics 106, 063903 (2009); doi: 10.1063/1.3211314 View online: http://dx.doi.org/10.1063/1.3211314 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/106/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Exchange biased FeNi/FeMn bilayers with coercivity and switching field enhanced by FeMn surface oxidation AIP Advances 3, 092104 (2013); 10.1063/1.4821105 Exchange bias, training effect, hysteretic behavior of angular dependence, and rotational hysteresis loss inNiFe/FeMn bilayer: Effect of antiferromagnet layer thickness J. Appl. Phys. 105, 053913 (2009); 10.1063/1.3087450 Picosecond optical control of the magnetization in exchange biased NiFe/FeMn bilayers J. Appl. Phys. 95, 6613 (2004); 10.1063/1.1652416 Magnetization reversal in the pinned layer of PtMnCr/NiFe exchange biased bilayers J. Appl. Phys. 89, 6591 (2001); 10.1063/1.1359793 Asymmetry of coercivity dependence on temperature in exchange-biased FeMn/Co bilayers Appl. Phys. Lett. 77, 2731 (2000); 10.1063/1.1319511

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Asymmetric recovery effect of exchange bias in polycrystallineNiFe/FeMn bilayers

X. P. Qiu,1,a� Z. Shi,1 S. M. Zhou,1 J. Du,2 X. J. Bai,2 R. Chantrell,3 and L. Sun4

1Department of Physics and Surface Physics Laboratory (National Key Laboratory), Fudan University,Shanghai 200433, China2National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China3Department of Physics, The University of York, York, YO10 5 DD, United Kingdom4Department of Mechanical Engineering, University of Houston, Houston, Texas 77204, USA

�Received 7 May 2009; accepted 23 July 2009; published online 16 September 2009�

For exchange bias in polycrystalline NiFe/FeMn bilayers, the hysteretic behavior of the angulardependence and the recovery effect has been studied. In particular, the pinning direction �PD� at theending remanent state of each hysteresis loop is identified. In the hysteretic behavior, in addition tothe coercivity, the PD also demonstrates different angular dependence between clockwise andcounterclockwise rotations of the external magnetic field. Measurements of the recovery effectconsist of two major steps. In the first step, the PD is deviated from the initial one by using itshysteretic effect and training effect. For polycrystalline NiFe/FeMn bilayers, the rotated PD islocated at the maximal angle �PD0 of �22° with respect to the initial ones. As for the second step,an external magnetic field is applied at a specific orientation �H−RE and then switched off at the sameorientation. For the negative �PD0, the recovery effect only occurs for 0��H−RE�180° with themaximal effect at �H−RE=90° and vanishes for 180° ��H−RE�360°, and vice versa for the positive�PD0. Therefore, the recovery effect shows an asymmetric angular dependence on �H−RE. Therecovery effect of the PD also depends on the magnitude and the application time of the recoverymagnetic field. For the exchange field and the coercivity, similar recovery behaviors are observedand attributed to the recovery effect of the PD. These phenomena clearly show that the motion ofantiferromagnet spins not only obeys the thermally activated transition but also strongly depends onthe magnetization reversal mechanism of the ferromagnet layer. © 2009 American Institute ofPhysics. �doi:10.1063/1.3211314�

I. INTRODUCTION

Exchange bias �EB� is known as a phenomenon in whichthe hysteresis loop is shifted along the magnetic field axis inferromagnet �FM�/antiferromagnet �AFM� bilayers.1 ManyEB-related physical phenomena, including the rotational hys-teresis loss, the training effect, the recovery effect, the asym-metry of the hysteresis loop, and the hysteretic behavior ofthe angular dependence of the EB �ADEB�, have been stud-ied extensively.1–20 It is generally believed that the AFMspins play an important role in these phenomena.3–12 Forexample, in studies of the rotational hysteresis loss, it is sug-gested that the AFM spins rotate irreversibly during the ro-tation of the external magnetic field.10,11

For polycrystalline NiFe/FeMn bilayers, the ADEB isdifferent for clockwise �CW� and counterclockwise �CCW�rotations, exhibiting a hysteretic behavior.13 Micromagneticcalculations have suggested that this phenomenon is inducedby irreversible rotation of AFM spins. Moreover, the hyster-esis loop asymmetry also has different angular dependencefor CW and CCW rotations, that is to say, the zero asymme-try is located at different orientations of the external mag-netic field for CW and CCW rotations. Since the zero asym-metry indicates parallel alignment of the external field andthe pinning direction �PD� of the bilayer,21 it is implicated

that the PD is rotated during CW and CCW rotations. Directmeasurement of the PD rotation in the ADEB is required toreveal the underlying physics behind the hysteretic behavior.

In the commonly observed EB training effect, the ex-change field HE and the coercivity HC are reduced duringconsecutive hysteresis loops.14 It is believed that the trainingeffect comes from the switching or rotation of AFM spins asmanifested by the PD rotation.17,22 As another EB-relatedphenomenon, the recovery effect has recently been studied,in which the trained EB can be restored by a full cycle ofhysteresis loop perpendicular to the PD.23 Although the rota-tion of AFM spins has already been predicted theoreticallyduring the recovery procedure,22,23 direct observation of thePD rotation has not been performed yet. Moreover, the re-covery procedure is complex, consisting of six segments ofapplied magnetic field, i.e., 0 to the saturation magnetic field�HS�, +HS to 0, 0 to −HS, −HS to 0, 0 to +HS, and +HS to 0.In order to clearly reveal the mechanism of the EB recoveryeffect, it is essential to simplify the recovery procedure.

In this work, for polycrystalline NiFe/FeMn bilayers, thePD rotation is studied in both the hysteretic behavior of theADEB and the EB recovery effect. A hysteretic behavior ofthe PD orientation is found to accompany that of the ADEBbetween CW and CCW rotations. As the first step of therecovery procedure, the PD can be aligned along either posi-tive or negative angles with respect to the initial PD by ex-ploiting measurements of ADEB and the training effect. Asa�Electronic mail: xp.qiu@yahoo.com.

JOURNAL OF APPLIED PHYSICS 106, 063903 �2009�

0021-8979/2009/106�6�/063903/6/$25.00 © 2009 American Institute of Physics106, 063903-1

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the second step, an external magnetic field is applied andthen switched off at a specific orientation �H−RE. It is inter-esting to find that the recovery effect takes the maximum�vanishes� at �H−RE=90° and vanishes �takes the maximum�at �H−RE=−90° when the rotated PD is located along thenegative �positive� angles, respectively. Apparently, the re-covery effect shows asymmetric AD on �H−RE. Both the hys-teretic behavior of the ADEB and the EB recovery effect canbe explained as a result of the PD rotation. All experimentalresults can be explained after taking into account the effectof the FM magnetization reversal mechanism on thermallyactivated transitions of AFM spins.

II. EXPERIMENTS

A glass/Cu �15 nm�/Ni80Fe20�3 nm� /Fe50Mn50

�2.4 nm� /Au�60 nm� sample was grown at ambient tem-perature by dc magnetron sputtering. The base pressure ofthe sputtering system was 2�10−5 Pa and the Ar pressure0.4 Pa during deposition. The 15-nm-thick Cu buffer layerwas deposited to stimulate the fcc �111� preferred growth ofFeMn and to enhance the EB.24 Deposition rates of NiFe,FeMn, Cu, and Au layers were 0.3, 0.1, 0.2, and 1 nm/s,respectively. During deposition of the bottom NiFe layer, amagnetic field of about 130 Oe was applied parallel to thefilm plane to induce the uniaxial anisotropy in the NiFe layerand the EB in the NiFe/FeMn bilayer, where the magnitudeof the deposition magnetic field is large enough to saturatethe soft magnetic layer. Similar fabrication procedure wasdescribed elsewhere.25 X-ray diffraction shows that the con-stituent layers are polycrystalline with fcc �111� and fcc�200� textures. With a vector vibrating sample magnetometerof model 7407 from Lakeshore Co., the magnetic momentsmx �parallel to H� and my �perpendicular to H� were recordedsimultaneously. In this system, the mx pickup coil and theelectromagnet are stationary in the laboratory reference withthe same common axis, remarked as the �magnetic� fieldaxis. The mx versus H curve corresponds to the conventionalhysteresis loop. For the in-plane configuration, mx and my

were both parallel to the film plane. All measurements wereperformed at room temperature.

For conventional single layer FM films with uniaxial an-isotropy, the FM magnetization will be aligned along theeasy axis under zero magnetic field H, that is to say, mx hasa positive or negative maximum and my equals zero when theeasy axis of the sample is aligned with the field axis. Fromthe angular dependence of mx and my measured under zeroH, the orientation of the easy axis can be identified.26 In asimilar way, the PD orientation of the present FM/AFM bi-layers is identified as that of the orientation of the magneti-zation vector at the remanent state. If the uniaxial anisotropyaxis and the unidirectional anisotropy direction are col-linearly aligned, the PD orientation is parallel to their orien-tations. In the case of noncollinear alignment,27 the PD ori-entation is determined by the equilibrium one of themagnetization vector at the remanent state, depending on theorientations and magnitudes of the uniaxial and the unidirec-tional anisotropies. Therefore, it can be identified by the an-gular dependence of my at zero magnetic field. Here, the

initial PD orientation of the sample at the as-prepared state isidentified from the angular dependence of mx and my underzero H, which was measured by rotating the sample in thefilm plane. �Rtn in Fig. 1 refers to the orientation of the mag-netic field axis with respect to the initial PD of the sampleand �PD to that of the rotated PD. For comparison, �H−LOOP isdefined as that of the external magnetic field to measure hys-teresis loops with respect to the initial PD.

For the present NiFe/FeMn bilayers, my is equal to zerowhen the hysteresis loop is measured along the direction ofthe deposition magnetic field at the as-prepared state. Moreimportantly, it is always equal to zero when the hysteresisloop is measured along the rotated PD at the trained state.Accordingly, the principal axes of uniaxial and unidirectionalanisotropies are parallel to each other based on previouslyreported results,21 unlike the noncollinear case.27,28 Actually,the AFM spins can only experience 180° switching duringthe hysteresis loop along the PD orientation22 and theuniaxial anisotropy axis and unidirectional anisotropy direc-tion are not rotated during the hysteresis loop, that is to say,before measurements of the hysteresis loop they are collin-ear. Since the intrinsic uniaxial anisotropy of the magneti-cally soft NiFe layers is negligible, the uniaxial and the uni-directional anisotropies are both induced by the AFM spinssuch that they are possibly collinear. It is noted that the anglebetween the uniaxial anisotropy axis and the unidirectionalanisotropy direction can be simulated from the measured an-gular dependence of the ferromagnetic resonance field.29 Inthe dynamic approach, however, the AFM spins are requiredto be fixed during the action of the external magnetic field.

III. RESULTS AND DISCUSSION

Before applications of any external magnetic field, theinitial PD was identified as the reference axis, as shown in

FIG. 1. �Color online� �a� Typical angular distribution of mx �black� and my

�red� under H=0 and �b� schematic picture of PD rotation.

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Fig. 1. Afterwards, hysteresis loops were measured withCCW rotation of H from �H−LOOP�−60° to �60° and thenwith CW rotation from �60° to �−60°. Between neighbor-ing hysteresis loops, the curves of mx and my versus �Rtn

under H=0 were measured to identify the PD. It is interest-ing to find that the angular dependence of �PD also shows thehysteretic behavior between CCW and CW rotations, in ad-dition to HC,13 as shown in Fig. 2. With CCW rotation of Hfrom �−60° to �60°, the PD first deviates away from andthen rotates toward the initial PD, where �PD acquires thepositive maximal value of �22°. With subsequent CW rota-tion of H from about �60° to �−60°, the PD continues torotate in an opposite way, leading to the negative maximal�PD of �−22° and then rotates toward the initial PD. Appar-ently, the PD rotation exhibits a chirality change duringADEB measurements. It is interesting to find that the maxi-mal HC is almost located at the same �H−LOOP as that of thepositive or negative maximal �PD. Furthermore, since �PD

��H−LOOP, that is to say, the external magnetic field is par-allel to the PD, the coercivity acquires the maximum. There-fore, the hysteretic behavior of �PD between CW and CCWrotations accounts for that of HC according to the conven-tional ADEB.30

In measurements of the recovery effect, two major stepsare required. First of all, the PD is aligned along a designatedorientation. As shown in Fig. 2�b�, the PD can be set at anyorientation near the initial PD by measurements of the ADEBof either CW or CCW rotations. Hysteresis loops were mea-sured with CW �CCW� rotation from �H−LOOP= �60° to 0.In this way, the PD is rotated toward negative �positive�angles, as shown in Fig. 2�b�. In order to let the PD rotationbe saturated, 50 hysteresis cycles were immediately mea-

sured at �H−LOOP=0 in the training effect, leading to the CW�CCW� rotation of the PD toward more negative �positive�angles.22 Afterwards, the angular dependence of mx and my

under zero H was measured to identify the saturated �PD. Thevalues of HE and HC along the initial PD, which were deter-mined from the last hysteresis loop in the training effect, and�PD0 were obtained. Second, a recovery procedure was per-formed, in which at a specific �H−REHRE was applied andpersisted for a time period of tRE and then switched off at thesame orientation. Finally, �PD was identified and HE and HC

along the initial PD were determined again. Accordingly, thechanges of HE/C and �PD induced by the recovery procedure,i.e., �HE/C and ��PD, are achieved. In experiments done byBrems et al.,23 however, consecutive hysteresis loops weremeasured along the initial PD before the recovery procedureand thus the PD is expected to be still aligned along theinitial PD.

Figures 3�a�–3�c� show the hysteresis loops at zero�H−LOOP and the curves of mx and my versus �Rtn under zeroH before and after the recovery procedure, where HRE

=6.0 kOe, tRE=0 and �H−RE=90°. Before the second step ofthe recovery measurements, �PD0�−22° and HE=80 Oe andHC=37 Oe. After the recovery procedure, HE=103 Oe,HC=60 Oe, and �PD=−4°. Apparently, by the recovery pro-cedure HE and HC are enhanced with �HE=23 Oe and�HC=23 Oe, and the PD is rotated with ��PD=18°. At thesame time, the asymmetry is also enhanced. However, Figs.3�d�–3�f� show that at �H−RE=−90°, no changes take placefor HE, HC, the asymmetry, and the PD orientation after therecovery procedure. Apparently, the recovery effect strongly

FIG. 2. �Color online� Angular dependence of HC �a� and �PD �b� as afunction of �H−LOOP.

FIG. 3. �Color online� Hysteresis loops of mx ��a� and �d�� and my ��b� and�e�� at �H−LOOP=0, and ��Rtn� angular dependence of my ��c� and �f�� before�black, solid� and after �red, dashed� the recovery procedure applied at 90��a�, �b�, and �c�� or �90° ��d�, �e�, and �f��. HRE=6.0 kOe and tRE=0during the recovery procedure.

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depends on �H−RE. In particular, the present results clearlydemonstrate that in the six segments of the work done byBrems et al.,23 the recovery effect acts in at most two seg-ments, i.e., 0 to HS, +HS to 0.

Figures 4�a�–4�c� show the ��H−RE� angular dependenceof �HE, �HC, and ��PD, where �PD0�−22°. With increasing�H−RE, all three physical quantities undergo nonmonotonicchanges and acquire the maxima at �H−RE=90°. It is remark-able that at �H−RE�180°, the recovery effect vanishes. Fig-ures 4�d�–4�f� show the results for �PD0�22°. The recoveryeffect exits only in the region from �H−RE=180° to 360° witha maximum at �H−RE=270°, and disappears in the region of�H−RE=0 to 180°. Apparently, the angular dependence of therecovery effect is asymmetric.

Figures 5�a�–5�c� show the dependence of �HE/C and��PD on the magnitude of HRE, where �PD0�−22°, tRE=0and �H−RE=90°. For a small HRE, the recovery effect initiallyincreases sharply and then changes gradually with the mag-nitude of HRE. This behavior can be understood as follows.Upon applications of HRE at �H−RE=90°, the orientation ofthe FM magnetization is determined by the magnitude ofHRE. When HRE is smaller than the anisotropic field HK, theFM magnetization is aligned along an orientation between�H−RE=90° and �PD0�−22°. According to the results in Figs.4�a�–4�c�, the recovery effect should be equivalent to thecase of �H−RE�90°. As the magnitude of HRE increases, theorientation of the FM magnetization approaches that of HRE,leading to an increase in the recovery effect. For H muchlarger than HK, the increase in the recovery effect can beattributed to the increase in the time needed to achieve HRE.This assumption is verified by the results in Figs. 5�d�–5�f�.As the application time tRE is increased from zero to about2.0 s, �HE and �HC increase and reach the maximal values.This can be explained by the conventional ADEB. At tRE

=2.0 s, ��PD=22° and thus �PD=0°, that is to say, the PD is

aligned again along the initial PD, resulting in the maximal�HE and �HC. This is because the external magnetic field isparallel to the PD. With further increasing tRE, ��PD in-creases and the PD is deviated from the initial PD, leading tothe reductions in �HE and �HC because the external mag-netic field makes an angle with the rotated PD.

In order to investigate the possible effect of the interfacemorphology on the training and the recovery effects, twoNiFe�3 nm�/FeMn �2.2 nm� bilayers were prepared underbase pressures of 2.1�10−5 and 3.9�10−6 Pa. For the highbase vacuum, larger HE and HC are acquired. With the high�low� base vacuum, HE and HC are 147�90� and 94�68� in theunit of oersted for the first loop at �H−LOOP=−12°, respec-tively. Apparently, it is expected that with high base vacuum,the interface morphology or the AFM grain distribution orboth of them are changed, which favors to enhance the EBeffect. For the high �low� base pressures, however, the maxi-mal PD rotation is 19�16�° in the ADEB measurements of theCW rotation. After the recovery procedure, �HE

=20�24� Oe, �HC=45�35� Oe, ��PD=19�18�°. In a word,HE and HC are enhanced by high base vacuum while the PDrotation in either the hysteretic behavior of the ADEB or therecovery effect is almost not influenced. Since the PD rota-tion is strongly modified by the size distribution of the AFMgrains as discussed below, it is also reasonable to suggestthat the size distribution of the AFM grains is not influencedby the base vacuum. Furthermore, the interface morphologyshould be modified by the base vacuum but it has negligibleeffects on the PD rotation.

The hysteretic behavior of �PD in Fig. 2 can be explainedusing the model of thermally activated switching of AFMspins.13,31 In this model, the AFM layer is assumed to consistof exchange-decoupled grains having different activation en-ergies. During hysteresis loops, AFM spins of some grainsare switched, resulting in the deviation of the average orien-

FIG. 4. �Color online� �HE ��a� and �d��, �HC ��b� and �e��, and ��PD ��c�and �f�� as a function of �H−RE, where HRE=6.0 kOe and tRE=0 in �a�–�f�,and �PD0�−22° �left column� and 22° �right column�.

FIG. 5. �Color online� Dependence of �HE ��a� and �d��, �HC ��b� and �e��,and ��PD ��c� and �f�� on the magnitude of HRE ��a�, �b�, and �c�� and theapplication time ��d�, �e�, and �f��, where �H−RE=90° in �a�–�f�, tRE=0 in leftcolumn and HRE=6.0 kOe in the right column.

063903-4 Qiu et al. J. Appl. Phys. 106, 063903 �2009�

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tation of overall AFM spins from the initial PD and the PDrotation, as observed experimentally in CoFe/IrMnbilayers.32,33 More remarkably, the PD rotation �CW orCCW� strongly depends on the magnetization reversal chan-nel. As seen from Fig. 6�a�, in the CW rotation of H from�H−LOOP�60°, the FM magnetization is rotated through thechannel marked by the arrows in Fig. 6�a� because �H−LOOP

��PD. With the exchange field from the FM layer, the AFMspins of some grains are deviated from the initial PD, leadingto the CW rotation of the PD toward negative angles anddecreasing �PD. Due to the exchange coupling from the non-rotatable AFM grains, however, the PD cannot rotate faraway from the initial PD, so the continuous CW rotation ofH will result in �H−LOOP��PD at a critical angle. At thismoment the FM magnetization will be rotated through an-other channel as marked by the arrows in Fig. 6�b�, the PDrotates in the CCW sense and exhibits a turning point, whichcan be seen from Fig. 2�b�. In a similar way, the PD rotationduring the CCW rotation of H from �H−LOOP�−60° to �60°can be well understood. It is concluded that for rotations ofthe PD and the AFM spins, the chirality change and thehysteretic behavior are induced by the channel change of theFM magnetization reversal during hysteresis loops at differ-ent �H−LOOP.

The EB recovery effect in Figs. 3–5 can also be ex-plained in the framework of the thermal activation model.Here we take the negative �PD0 as an example. Before therecovery procedure, the PD has already been set to the nega-tive maximal angle after measurements of the ADEB in theCW sense and training effect. So the PD cannot rotate anymore in the CW direction but can rotate back toward theinitial PD. In Figs. 3�a�–3�c�, with a magnetic field of 6 kOeat �H−RE=90°, the spins in some AFM grains will be reversedor rotated due to the rotating exchange field from the satu-rated FM layer and thereby the PD rotates back toward theinitial PD, resulting in the recovery of EB. If the field is

applied at �H−RE=−90°, as seen from Figs. 3�d�–3�f�, the PDcannot rotate any more toward more negative angles, so therecovery effect vanishes. For �H−RE=90° or �90°, AFMspins have the highest probability of switching and the stron-gest recovery effect is obtained, as shown in Fig. 4. Fornonzero tRE, more AFM spins are switched and thus the PDcontinues to rotate back toward the initial PD, leading toincreasing ��PD, �HE, and �HC. With further increasing tRE,however, the PD crosses and deviates away from the initialPD. Therefore, although ��PD still increases, �HE and �HC

are reduced due to the ADEB,30 as shown in Figs. 5�d�–5�f�.In addition to the EB recovery effect, the thermal activationmodel can also be used to explain the dependence of thetraining effect on the AFM layer thickness in NiFe/FeMn andCo/FeMn bilayers.22,34–36

Many theoretical models have been proposed to explainthe features of the EB.3,33,37–39 For example, in order to ex-plain the ADEB in Co/IrMn bilayers, a thin spin-disorderedlayer is assumed to exist at the FM/AFM interface with itsuniaxial anisotropy axis making an angle with that of theAFM layer.33 The simulated value of the angle is about 20°,by accident close to the PD rotation of 22° for the presentNiFe/FeMn bilayers. In order to further verify the validity ofthe thermal activation model, more experimental and theo-retical investigations are required. With the thermal activa-tion model, the recovery and the training effects in the poly-crystalline FM/AFM bilayers should disappear near zerotemperature. In fact, for FM/AFM bilayers, the trainingeffect is found to become small when decreasingtemperature.40 On the other hand, however, the training ef-fect is experimentally observed to become pronounced atlow temperatures.32,41,42 Apparently, the thermal activationmodel fails to explain the temperature dependence if theuniaxial anisotropy and the energy barrier are assumed to beindependent of the temperature. Therefore, the temperaturedependence of the uniaxial anisotropy of the AFM layersshould be measured in order to explain the temperature de-pendence of the training effect.

IV. CONCLUSIONS

In summary, in order to deepen the nature of the hyster-etic behavior of ADEB and the EB recovery effect in poly-crystalline NiFe/FeMn bilayers, the PD rotation at the endingpoint of each hysteresis loop is identified. The angular de-pendence of the PD exhibits hysteretic behavior betweenCW and CCW rotations, in addition to the HC. The chiralitychange of the PD rotation is induced by the channel changeof the FM magnetization rotation. In the EB recovery proce-dure, with the maximal �PD0� 22°, which can be realizedby measurements of the ADEB and training effect, HE andHC are enhanced and the PD is rotated toward the initialdirection after the recovery procedure with 0��H−RE

�180° �180° ��H−RE�360°�. The largest recovery effecttakes place at �H−RE=90° �270°�. For 180° ��H−RE

�360° �0��H−RE�180°�, however, the recovery effect dis-appears. Therefore, the angular dependence of the EB recov-ery effect is asymmetric. Furthermore, the recovery effectalso strongly depends on both the magnitude and the appli-

FIG. 6. �Color online� Schematic picture for CW rotation of ADEB mea-surements in the cases of �a� �H−LOOP��PD and �b� �H−LOOP��PD.

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cation time of HRE. The thermal activation model can beused to explained all these phenomena. In particularly, theseresults have directly confirmed the theoretical prediction ofthe rotatable anisotropy in polycrystalline FM/AFM bilayersproposed by Stiles and McMichael,5 and shown the tunabil-ity of the PD and accordingly the EB.

Note added in proof. During the review process we be-came aware of the work done by Jiménez et al.,43 which hasstudied the magnetization reversal process and the asymme-try of the FM/AFM bilayers with or without misalignment ofthe unidirectional and the uniaxial anisotropies. In particular,it is found that with collinear alignment of these twoanisotropies, my is always equal to zero when the externalmagnetic field is applied parallel to the both of them. It sup-ports the conclusion of that in the present FM/AFM bilayers,the unidirectional anisotropy is always parallel to theuniaxial anisotropy and they are both rotated during the EBtraining effect and the EB recovery process.

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, 973-project under Grant No.2006CB921300, and Shanghai Leading Academic DisciplineProject under Grant No. B113.

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