RAPID COMMUNICATIONS

PHYSICAL REVIEW B 68, 140404~R! ~2003!

Interface domain wall and exchange bias phenomena in ferrimagneticÕferrimagnetic bilayers

S. Mangin, F. Montaigne, and A. SchuhlLaboratoire de Physique des Mate´riaux, UniversiteNancy 1, Boıˆte Postale 239, F-54506 Vandoeuvre le`s Nancy, France

~Received 12 May 2003; published 3 October 2003!

In Gd40Fe60/Tb12Fe88 exchange-coupled bilayer system, both negative and positive exchange bias, depend-ing on cooling field, are observed. A full enlightenment of the magnetic configurations adopted by the systemis obtained through micromagnetic calculations in agreement with magnetization and susceptibility measure-ments. Magnetization shifts and exchange bias fields are then quantitatively correlated to the presence of afrozen interface domain wall. This model may be transposed to antiferromagnetically exchange coupledantiferromagnetic/ferromagnetic (Fe/FeF2 or Fe/MnF2) systems

DOI: 10.1103/PhysRevB.68.140404 PACS number~s!: 75.60.Ch, 75.30.Et, 75.50.Gg, 75.70.Cn

-

nras-a

ld

isereres

ne

n-

lyag

ic

fve

i--

ei-n

e-and

ticled

po-pen-d-

calatium

is

this in-

wasThe

byof

the

ted

t inter-

per

-

-

ge

Exchange bias~EB! has been widely studied in ferromagnetic ~FM!/antiferromagnetic~AFM! bilayers.1,2 This phe-nomenon which is often essential for magnetoelectrodevices3 is mainly characterized, below a blocking tempetureTB , by a shift of theM -H loop towards a field known athe exchange bias fieldHE . In some FM/AFM systems exhibiting antiferromagnetic exchange coupling suchFe/FeF2 or Fe/MnF2, it has been shown that a cooling fieH f c could triggerHE from positive to negative values at lowtemperature and induce a magnetization shift.4–6Also strongcorrelation betweenH f c , HE and magnetization shift of thehysteresis loop has been observed.5 Additionally severalauthors6,7 pointed a peak in the coercive fieldHC for HEclose to zero. Despite numerous studies, the mechanleading to the EB effect is not yet fully understood. Howevan estimation of theHE must rely on configurations of thinterface magnetization. Two different kinds of model aproposed. A first approach to model EB phenomena is baon the formation of lateral domains in the antiferromagresulting in the formation of lateral domain wall.8 On theother hand, various models proposed the presence of aterface domain wall~iDW! with a modulation vector perpendicular to the interface. The position of the iDW~in AFM orin the FM! and its shape (90° or 180°) are up to now widediscussed.9–11 These aspects are still in debate after 15 yeof intensive research, mainly because the magnetic confiration inside the AFM layer is not measurable using classmagnetometric methods~at least linear! due to its zero netmagnetization. Other exchange-coupled systems such‘‘spring magnet’’ made of two layers~ferromagnetic or/andferrimagnetic! have shown EB effect.12–14 The presence oan interface DW was clearly evidence in that case. Howethe interface exchange coupling wasferromagneticand onlynegative EB was observed.

In this paper, we have studied EB phenomena in ananti-ferromagnetically coupled ferrimagnetic/ferrimagnetic blayer, namely, Gd40Fe60/Tb12Fe88. We present here the evolution of the magnetic properties (HE , HC , andmagnetization shifts! of this system at low temperaturdepending onH f c . Using ferrimagnetic layers, we investgated the magnetic configurations of both layers, athen develop a quantitative model forHE and MShi f t

N

0163-1829/2003/68~14!/140404~4!/$20.00 68 1404

ic-

s

m,

edt

in-

rsu-al

as

r,

d

variation of antiferromagnetically coupled bilayers. ThGd40Fe60(100 nm)/Tb12Fe88(50 nm) sample has been prepared by coevaporation on a glass substrate kept at 77 Kprotected by a 30-nm Si capping layer.12 Both Gd40Fe60 andTb12Fe88 are ferrimagnetic alloys, Fe and rare-earth magnemoments being very strongly antiferromagnetically coupand thus antiparallel. In Tb12Fe88, the iron contribution tomagnetization is dominant for all temperatures. This comsition has been chosen to avoid the occurrence of a comsation temperature.16 The terbium moments present a spreaing of their direction because of the strong random loanisotropy. Tb12Fe88 becomes thus a hard magnetic alloylow temperature because of the large increase of the terbmagnetic anisotropy. On the contrary, in Gd40Fe60, the con-tribution of gadolinium is dominant and the magnetizationlocally parallel to that of the Gd moments~antiparallel to thatof iron!, the magnetic anisotropy is generated by the growprocess and GdFe exhibits a very clear in-plane easy axthe film plane.17 This anisotropy remains weak at low temperatures because of thes character of the Gd 4f band. Forall the measurements presented here, the magnetic fieldapplied in the sample plane along the GdFe easy axis.exchange coupling between the layers being dominatedFe-Fe ferromagnetic interactions, the magnetizationsGdFe and TbFe are antiferromagnetically coupled atinterface.

Equilibrium magnetic configurations have been calculaby using a simple unidimensional micromagnetic model.13,14

Due to the demagnetizing field, the magnetization is kepthe plane of the layers and the magnetic profile is characized by a single depth dependent angleu(z) referred to theanisotropy direction. The magnetic energy of the bilayerarea unit is calculated by considering, for each layer~GdFeand TbFe!: the exchange energy~characterized by the exchange stiffnessAGdFe or ATbFe), the anisotropy energy~minimum for u50° andu5180° and proportional to theanisotropy energyKGdFe or KTbFe), the Zeeman energy corresponding to the interaction of the magnetizationMGdFe orMTbFe with the applied fieldH, and finally the interfaceexchange energy~characterized by a negative exchanstiffnessJ).

©2003 The American Physical Society04-1

g-Wrg

d

tor

uie

ily

Thale

of

rte,b

er

ife

onret

eld

rgy

the

ofent.

-e

ou-

e

c

n

00

RAPID COMMUNICATIONS

S. MANGIN, F. MONTAIGNE, AND A. SCHUHL PHYSICAL REVIEW B68, 140404~R! ~2003!

E5E0

tGdFeFAGdFeS ]u~z!

]z D 2

1K GdFe sin2u~z!

2HMGdFe cosu~z!Gdz1EtGdFe

tGdFe1tTbFeFATbFeS ]u~z!

]z D 2

1KTbFe sin2u~z!2HMTbFe cosu~z!Gdz

1J cos~uTbFei 2uGdFe

i !,

whereuGdFei anduTbFe

i are, respectively, the angle of the manetization at the interface in GdFe and in the TbFe layer.determined the magnetic profiles which minimize the ene~stable and metastables states! from which we calculated themagnetizationM and the susceptibility]M /]H. The mag-netic parameters used for the calculation are summarizeTable I.

Magnetic measurements were first performed at 300 Kestablish the possible initial magnetic configurations befcooling the sample under a magnetic fieldH f c . Experimentalresults are reported in Fig. 1 for both magnetization and sceptibility. The hysteresis loops as a function of the applmagnetic field are plotted along with the results of the mcromagnetic calculations. For the clarity of the figure, onthe absolute minimum-energy solution is represented.agreement between measurement and micromagnetic clations is then very good for both magnetization and susctibility. The solutions corresponding to local minima~notrepresented in Fig. 1! reproduce satisfactorily the openingthe loops. The magnetic profileu(z) from the calculation forfive different fields are presented in inset in Fig. 2. For velarge positive fields (H570 kOe!, both magnetizations poinin the field direction with only a small shift at the interfacconsequently the angle between the interface GdFe and Tmagnetizations and the field direction are close to z(uGdFe

i .0° and uTbFei .0°). As the field is decreased the

balance between Zeeman energy and the interfacial antromagnetic coupling leads to the formation of an iDWmainly located in the TbFe layer~inset of Fig. 2!. Its thick-ness increases anduTbFe

i ~calculated! rises from 0° angletoward 180°~Fig. 2!. This ‘‘decompression’’ of the iDW isslightly visible from the slow decrease of the magnetizatibut it is clearly evidenced by the susceptibility measuments. Indeed, when a DW becomes larger, the amoun

TABLE I. Magnetic parameters of a single layer~thicknesst)Gd40Fe60 and Tb12Fe88 at 300 K and 5 K used to performed thmicromagnetic simulations on the bilayer.~The interface couplingJhas been taken to be21027 erg/cm2). They are found to be ingood agreement with the one obtained from measurements andculations~Ref. 16!.

Alloy t ~nm! A ~erg/cm! K (erg/cm3) M ~emu!

Gd40Fe60 ~300 K! 100 631027 2.53104 500Gd40Fe60 ~5 K! 100 631027 105 1000Tb12Fe88 ~300 K! 50 831028 2.83104 225Tb12Fe88 ~5 K! 50 831028 .107 350

14040

ey

in

oe

s-d-

ecu-p-

y

Feo

r-,

,-of

magnetization having a component perpendicular to the fidirection increases, which increases the susceptibility.12 Thesusceptibility is maximum atH5100 Oe field at which theantiferromagnetic coupling takes over the Zeeman eneand the TbFe magnetization reverses abruptly~Fig. 1!. Themagnetizations are thus antiparallel and entirely alongapplied field (uGdFe

i 50° anduTbFei 5180°) without any iDW.

This transition leads to a drop of the susceptibility becausethe disappearance of transverse magnetization componFor a small negative field, the whole structure~GdFe andTbFe still antiferromagntically aligned! reverses its magnetization ~Fig. 2!, GdFe magnetization is now pointing in thnegative field direction (uGdFe

i 5180° anduTbFei 50°). For

H,2200 Oe, Zeeman energy takes over interfacial c

al-

FIG. 1. Normalized magnetizationM /MS ~a! and susceptibilityxac ~b! as a function of the magnetic fieldH applied along the easyaxis for Gd40Fe60(100 nm)/Tb12Fe88(50 nm) at 300 K. Experimen-tal data~open circle! are compared to calculated values~solid line!.

FIG. 2. Calculated angleuTbFei between the TbFe interface spi

and the cooling field direction as a function of the applied fieldH.In inset, magnetic configurations in the GdFe/TbFe bilayer at 3K, u(z), for various fields 70 kOe~full triangle!, 1 kOe ~opentriangle!, 150 Oe~full diamond!, and 0 Oe. For the zero field twoconfigurations are possible~open circle! and ~full square!.

4-2

adism

r talln-en

t

a

hi

f

i

r

r-s

ng

thur

nem

of

he

n-sisge

y

th a

i-

heFe

rst

for-

taltoer,se ofys-hift

RAPID COMMUNICATIONS

INTERFACE DOMAIN WALL AND EXCHANGE BIA S . . . PHYSICAL REVIEW B 68, 140404~R! ~2003!

pling and the TbFe magnetization aligns along the field, leing again to the creation of an iDW. Symmetric behaviorobserved while the field is swept back to positive. The rootemperature behavior of the GdFe/TbFe bilayer is similathe one obtained for GdFe/FeSn antiferromagneticcoupled systems.15 It is thus perfectly understood and coform to a simple micromagnetic model which allows to prdict the magnetic configuration at the TbFe interface, aparticularlyuTbFe

i represented in Fig. 2.The sample was then cooled down to 5 K under constan

magnetic fieldsH f c . Two examples of 5 K hysteresis loopare represented in the inset of Fig. 3. The net bias fieldpearing in the cycle depends clearly on the cooling fieldH f c .This phenomenon is accompanied by a magnetization swhose variation withH f c is reported in Fig. 4~b!. The twoswitching fieldsHC1 and HC2 are plotted as a function oH f c in Fig. 4~a!. As usual, we defineHE5(HC21HC1)/2and the coercivity asHC5(HC22HC1)/2, both plotted inFig. 3 as a function of the cooling field. The exchange fieldmaximal in negative values (HE52HE

max) for H f c50(uTbFe

i 5180°) and increases monotonically withH f c . It isremarkable that for large values ofH f c (uTbFe

i 50°), HE

tends toward1HEmax ~which is also the exchange field fo

H f c50 with uTbFei 50°). HC is minimum for low and large

values ofH f c and maximum for an intermediate value coresponding to anH f c for which HE is almost zero. It appearclearly thatHE is related toH f c and particularly to the inter-face magnetic configuration in the TbFe before the cooliIndeed fromHE52HE

max for uTbFei 5180°, HE increases to

1HEmax for uTbFe

i 50° going through HE50 for aboutuTbFe

i 5690°.To quantify this relationship, we suppose below that

300-K magnetic configuration inside the TbFe is frozen ding the cooling procedure and remained unchanged at 5Consequently, uTbFe

i (H5H f c) at 300 K is equal touTbFe

i (H f c) at 5 K. Micromagnetic calculations have beeperformed for various fixed TbFe configurations deducfrom 300 K calculations and using GdFe magnetic paraeters for 5 K~Table I! considering that the magnetizationTbFe is frozen. The fieldHC1

calc for which it is energeticallyfavorable for the GdFe magnetization to reverse was tdeduced and found to be a linear function ofuTbFe

i . The

FIG. 3. Variation of the exchange bias fieldHE and the coercivefield HC as a function of the cooling fieldH f c . In inset, hysteresisloops at 5 K for H f c570 kOe andH f c5150 Oe.HC1 andHC2 aredefined forH f c5150 Oe

14040

-

-oy

-d

p-

ft,

s

.

e-K.

d-

n

HC1calc variation as a function ofH f c is compared toHC1

variation in Fig. 4~a!. The agreement between the experimetal results and the frozen magnetic configuration hypotheis good, showing the relevance of iDW to explain exchanbias phenomena in our system. The difference betweenHC2andHC1, the coercivity, is superior to the intrinsic coercivitof GdFe and upon a certain value of cooling field (H f c

.4 kOe), HC2 is constant and equal to1HEmax. These

points suggest that during the GdFe reversal atHC1, a rear-rangement of the TbFe interface magnetization occurs wireduction ofuTbFe

i . For uTbFei ,90° ~corresponding toH f c

.4 kOe), the rearrangement leads directly touTbFei 50° and

HC251HEmax. The amplitude of the rearrangement is d

rectly given by the coercivity~represented in Fig. 3!. Theamplitude is maximum for low exchange bias fields. Ttorque ‘‘exerted’’ by the GdFe during its reversal on the Tbinterface is thus maximum foruTbFe

i 590°. Nevertheless, thisrearrangement does not limit our quantitative analysis in fistage of theM -H loop.

Let us point out that the results described aboveGd40Fe60/Tb12Fe88 are in all respect similar to previous observations done on Fe/FeF2 and Fe/FeMn2 systems.4,5 It ac-tually gives credit to new theoretical and experimendevelopment18 showing that in the AFM the moments tendalign along the field axis as it is the case for TbFe. Moreovthe magnetization shift@Fig. 4~b!# observed in both systemcan be easily explained by our model. Indeed the presencthe interfacial DW changes the net magnetization of the stem. We then defined the normalized magnetization sMShi f t

N (H f c) for a given cooling fieldH f c as MShi f tN (H f c)

FIG. 4. ~a! Evolution of the calculated fieldHC1calc at which GdFe

reverses~dash line! compared toHC1 ~full circle! and HC2 ~opensquare! as a function of the cooling fieldH f c . ~b! Cooling fielddependence of the experimental~full square! and calculated~dashline! normalized magnetization shiftMShi f t

N (H f c).

4-3

-n

ethou

i-intu

x-t

th

erfiaseti-ldtoed

ns-s

ltso

it-ticor

RAPID COMMUNICATIONS

S. MANGIN, F. MONTAIGNE, AND A. SCHUHL PHYSICAL REVIEW B68, 140404~R! ~2003!

5M2 kOe(H f c)/M2 kOe(H f c570 kOe) whereM2 kOe(H f c) isthe magnetization measured at 5 K under 2 kOe after coolingthe sample from 300 K underH f c . The calculated and experimental results are in very good agreement as showFig. 4. Moreover for Fe/FeF2 and Fe/FeMn2, theH f c depen-dence of the magnetization shift is qualitatively the samHowever, because the net magnetization of AFM is zero,shift is about 1% of the total magnetization whereas incase it reaches 10%.

In conclusion, by using a ferrimagnetic/ferrimagnetic blayer, we have investigated the magnetic configurationsside an exchange-coupled bilayer system at a tempera~T5300 K! above the blocking temperature for which echange bias appears. The cooling field dependence ofexchange bias phenomena (HE , HC , MShi f t

N ) were then ex-plained considering laterally uniform magnetization and

y

F.

n

y

14040

in

.isr

-re

he

e

freezing of the magnetic configuration in the pinning lay~TbFe!. However no lateral domain formation in either othe two layer is required. More precisely the exchange bfield value is dominated by the angle between the magnzation of the interface pinned layer and the cooling fiedirection, whereas the magnetization shift is relatedthe interface magnetic configuration. The model develophere for antiferromagnetically coupled bilayers may be traposed from ferrimagnetic/ferrimagnetic to FM/AFM systemwhich explains all the reported experimental resufor Fe/FeF2 and Fe/MnF2 systems and gives credit tinterface domain-wall models.9–11

We thank M. Hehn and Y. Henry for interesting and fruful discussions, L. Joly for his help in the micromagnecalculations, and M. Alnot, F. Mouginet, and D. Pierre fhelp with experiments.

o-

.D.

ys.

r, J.

gn.

d

1W.H. Meiklejohn and C.P. Bean, Phys. Rev.105, 904 ~1957!.2A.E. Berkowitz and K. Takano, J. Magn. Magn. Mater.200, 552

~1999!; J. Nogues and I.K. Schuller,ibid. 192, 203 ~1999!; M.Kiwi, ibid. 234, 584 ~2001!.

3J.R. Childresset al., IEEE Trans. Magn.37, 1745~2001!.4J. Nogues, D. Lederman, T.J. Moran, and Ivan K. Schuller, Ph

Rev. Lett.76, 4624~1996!.5J. Nogues, C. Leighton, and I.K. Schuller, Phys. Rev. B61, 1315

~2000!.6C. Leighton, M.R. Fitzsimmons, A. Hoffmann, J. Dura, C.

Majkrzak, M.S. Lund, and I.K. Schuller, Phys. Rev. B65,064403~2002!; C. Leighton, J. Nogues, B.J. Josson-Akermaand I.K. Schuller, Phys. Rev. Lett.84, 3466~2000!.

7T.L. Kirk, O. Hellwig, and E.E. Fullerton, Phys. Rev. B65,224426~2002!.

8A.P. Malozemoff, J. Appl. Phys.63, 3874~1988!.9D. Mauri, H.C. Siegmann, P.S. Bagus, and E. Kay, J. Appl. Ph

62, 3047~1987!.

s.

,

s.

10M. Kiwi, J. Mejia-Lopez, R.D. Portugal, and R. Ramirez, Eurphys. Lett.48, 573 ~1999!.

11R.L. Stamps, J. Magn. Magn. Mater.242-245, 139 ~2002!.12S. Mangin, G. Marchal, and B. Barbara, Phys. Rev. Lett.82, 4336

~1999!.13E.E. Fullerton, J.S. Jiang, M. Grimsditch, C.H. Sowers, and S

Bader, Phys. Rev. B58, 12 193~1998!.14F. Montaigne, S. Mangin, and Y. Henry, Phys. Rev. B67, 144412

~2003!.15F. Canet, S. Mangin, C. Bellouard, and M. Piecuch, Europh

Lett. 52, 594 ~2000!.16P. Hansen, C. Clausen, G. Much, M. Rosenkranz, and K. Witte

Appl. Phys.66, 756 ~1989!.17S. Mangin, C. Bellouard, G. Marchal, and B. Barbara, J. Ma

Magn. Mater.165, 161 ~1997!.18U. Nowak, K.D. Usadel, J. Keller, P. Miltnyi, B. Beschoten, an

G. Guntherodt, Phys. Rev. B67, 014430~2002!.

4-4