The origin of exchange Bias

The Origins of ExchangeBiasSadia ManzoorDepartment of PhysicsCOMSATS Institute of Information Technology, IslamabadCo-workers:K. O’Grady, L. E. Fernández-Outón and G.Vallejo-Fernández, Department ofPhysics, University of York, U.K.M. Farooq Nasir, Department of Physics, COMSATS IIT, Islamabad

Overview• Exchange bias … what is it?• No single theory … why??• Issues still open• Time dependence in AFMs• Measuring exchange bias» thermal activation effects• Modeling exchange bias• Conclusions» the independent AFM grain model2

Order in magnetic systemsferromagnetT > T CT < T CantiferromagnetT > T NT < T N3

Exchange bias• soft ferromagnetM• pinned ferromagnetInterfacial exchange anisotropyCoercivity H CHMHH cHferromagnet antiferromagnetT < T CT < T NH EX4

The ‘rigid’ AFM picture5

Issues still open• H ex obtained from the ‘rigid’ AFM model >> H exobtained experimentally• at least 5 different theories have been proposed• still no single working theory (i.e. one that can takeaccount of interfacial as well as bulk effects)• new phenomena and effects are still being found• despite this we all use exchange bias every day (!)Why is this so?6

Time Dependence inAntiferromagnetseasy axisαMEAFM grainΔ EManisotropy energy of the AFM: E = K V sin 2 α0 π/2 παAnisotropy energy barrier: Δ E = K Vfrequency of reversal: f = f o exp ( - ΔE / k B T)relaxation time: τ = τ o exp ( ΔE / k BT)small particles become thermally unstable at hightemperatures7

all polycrystalline samples have distribution of grain volumes …f(V)Δ E = KVdistribution of grain volume dependent energy barriers toreversal of the AFMFor a given (H, T), there exists a critical value of theanisotropy energy barrier ΔE C(or critical grain volume V C)such that all grains withΔE > ΔE Care thermally stable (blocked)(V > V C)and all those withΔE < ΔE Care thermally unstable (unblocked)(V < V C)unblockedblocked8

ΔE C= KV C= k BThigh temperatures cause parts of the AFto disorderunblockedblockedonly the blocked grains causeexchange biasHblocked AFM grainsUnblocked AFM grainsH ex should depend upon the degree of order in the AFM!9

Thermal activation measurementssetting the AFMΔE C= KV SET= k BT SETactivating the AFMsetΔE C= KV C= k BT ACTnot setV SET Vsetnot setHEX(H,T)=C*(H,T)HiEXVSET∫VCf(V)dVV Cset in oppositesenseV SET VHCiEX*::intrinsic exchange biasinterfacial coupling constant

Reversal in IrMn(5nm)/CoFe(10nm)H EX (Oe)3002001000-100-200-300100 150 200 250 300 350 400Tact (K)T B11

Si/FeMn(10 nm)/NiFe(10 nm)/ Ta(15 nm)Sample ASample Bfrequency (%)15105D m= 3.6 nm00 2 4 6 8 10 12 14grain diameter (nm)1000 10 20 30 40 50 60frequency (%)20D m= 16.8 nmgrain diameter (nm)12

Grain size distribution for sample SBSi/FeMn(10 nm)/NiFe(10 nm)/ Ta(15 nm)fVσm1 ⎡ {ln ( V VV ) = exp ⎢ −2πσV⎣ 2σ: median grain volumem(2: s tan darddeviation)}2⎤⎥⎦13

*iH ( H,T)= C ( H,T)H f ( V)EXEXVSET∫VCdVfVσm1 ⎡ {ln ( V VV ) = exp ⎢ −2πσV⎣ 2σ: median grain volumem(2: s tan darddeviation)}2⎤⎥⎦relaxation time: τ = τ o exp ( K V / k B T)using t SET = 5400 s and t ACT = 1800 sln (tf) kSET o B SETVSET= andKAFMTV =Cln (tACTfKo) kAFMBTACTwhere f o = 10 9 s -114

T B = 165 KHEX*i(H,T) = C (H,T) HEX∫VSETVC2π σ1( V/ VM⎛ −exp)⎜⎝[ ln (V/ V22σM) ]2⎞⎟ dV⎠VM:mediangrainvolumeσ:standarddeviation15

!NOTE: at T = T B , H EX = 0Exact halves of the AFM particle volumedistributions are ordered in opposite sensesV =Mln (tfKACToAFM) kBTBV MVK AFM (165 K) = 2.96 × 10 5 erg/cm 3K AFM (293 K) = 1.85 × 10 5 erg/cm 3(K AFM (293 K) = 1.35 × 10 5 erg/cm 3 reported by Mauri et al.)D. Mauri, E. Kay, D. Scholl, and J. Kent Howard, J. Appl. Phys. 62, 292 (1987)16

Exchange biased nanocomposites• core-shell nanoparticles• FM nanoparticles embedded in an AFM matrix“Beating the superparamagnetic limit withexchange bias”Vassil Skumryev, Stoyan Stoyanov, YongZhang, George Hadjipanayis, DominiqueGivord and Josep NoguésNATURE, Vol. 423, p. 850 (2003)17

Understanding these systems is much more complex than FM/AFM bilayers in whichH ex∝ 1/t FMand H ex∝ t AFMIn nanocomposite systems….definition of ‘thickness’ is an issuefor FM …. particle diameter ~ FM thickness (but percolation effects)for AFM…. distance between FM particles ~ AFM thicknessPROBLEM: these cannot be controlled independently of one another as in thin films18

Co-Cr 2O 3nanocomposites prepared by sol gel:sample wt. % CoA 30B 40C 50D 60E 80fcc Co nanoparticles embedded in Cr 2O 3matrixIncreasing Co concentrationincreasing FM / AFM interface densityeffect on exchange bias??? ≈ 3 – 4 nm, ≈ 24 nmvalidity of the independent AFM grain modelfor super exchange coupled AFM’s??19

H ex (Oe)200150100500-50-100-150-200A0 50 100 150 200 250 300T ACT (K)H ex (Oe)T B= 148 KV SET∫V Cf ( V ) dVV SET∫V C10-1f ( V ) dVH ex (Oe)3002001000-100-200BH ex (Oe)T B= 148 K0 50 100 150 200 250 300T ACT(K)V SET∫V CV SET∫V Cf ( V ) dV10-1f ( V ) dV150100C1150100C1150500-50-100-150T B= 148 K-2000 50 100 150 200 250 300T ACT(K)0-10-50-100-150T B= 165 K0 50 100 150 200 250 300T ACT(K)0-1•T Bdepends only upon the median AFM particle volume V m.• data can be described by the independent AFM particle model, i.e.VSET*i 1 ⎛ − [ ln (V/ VHEX(H,T)= C (H,T) HEX∫exp22 ( V/ V )⎜2V π σM ⎝ σCM) ]2⎞⎟ dV⎠usingV =Mln (tfKACToAFM) kBTB20

For Cr 2O 3…T N= 310 K ⇒ T SET> T Nis possible! ⇒ entire f (V) can be setHEX*i(H,T) = C (H,T)H f (V) dV= 1Separation of bulk and interfacial effects !!!EX∫C * H EXidepends non-monotonically uponFM/AFM interface densityH exitself is governed by both bulk andinterfacial effectsC * Hex i (Oe)20015010030 40 50 60 70 80Co Concentration (wt. %)21

Conclusions• H exis controlled not only by the degree of order in the bulk antiferromagnetbut also by interfacial effects.• These effects relate to the stiffness of the exchange coupling acrossthe interface between the ferromagnetic layer and the antiferromagnet.• Theoretical models such as the rigid AF model oversimplify the role ofthe AF by merely taking into account an anisotropy and exchangestiffness constant. They are only valid as first order approximations.Others like the domain state model overcomplicate the picture.• The results presented provide evidence of the need to introduce thermalactivation and AF order related parameters in the Hamiltonian of themodels proposed to explain exchange bias.22

References• Interfacial Spin Order in Exchange Biased SystemsL. E. Fernández-Outón, G. Vallejo-Fernández, Sadia Manzoor, B.Hillebrands and K. O’GradyJournal of Applied Physics 104, 093907 (2008)• Bulk and Interfacial Effects in Co – Cr 2O 3NanocompositesM. Farooq Nasir, H. Hoon, K. O’Grady and Sadia ManzoorInternational Journal of Nanoscience and Nanotechnology (2010)(in press)Acknowledgements• Dr. Umair Manzoor for TEM images• Higher Education Commission, GoP• Commonwealth Foundation, U.K.• Hitachi Global Storage Technologies (HGST), San José, California• Seagate Technology, N. Ireland23

Acknowledgements• Dr. Umair Manzoor for TEM images• Higher Education Commission, GoP• Commonwealth Foundation, U.K.• Hitachi Global Storage Technologies (HGST), San José, California• Seagate Technology, N. Ireland24

Energy per unit area of FM/AFM bilayerE = - H M FM t FM cos (θ - β) + K AFM t AFM sin 2 (α) -J INT cos (β - α)M AFMK AFM• K AFM t AFM < J INT⇒ AFM spins rotate with θ the FM spinsM FMHβθαno loop shift• K AFM t AFM > J INT⇒ pinning of FM spins by the AFM loop shiftMinimizing energy with respect to β keeping α small (≅ const.)Hex=JMFMINTtFM25

High Target Utilization Sputtering(HiTUS)SIDE ARMPLASMA SOURCERFpowerunitRotating substrate tableLaunchelectromagnetReactivegas feedAr gasfeedTargetsHighly ionized plasma‘beam’ generated in sidearm and directed to targetby electromagnetsPumpsystemsDC/RF 0-1000Vtarget bias27

AFM pinning layer e.g. IrMn, FeMnFM (pinned) layer e.g. CoFe, NiFeNon-magnetic spacer layer e.g. CuFM (free) layer e.g. CoFe, NiFe} EXCHANGE BIASED BILAYERI inI outSV sensorRecordingmedium29

In order to obtain the intrinsicbehaviour of exchange biasedmaterials, it is essential to measurein thermal activation free conditionsDetermination of thermal activationfree temperatureRecoil loops for a IrMn(5nm)/CoFe(10nm)exchange couple⇒ T NA= 100 K30

Grain size control through control of V biasof the FM and AFM layersSample Layer composition V bias (V)ANiFe (10 nm) 200FeMn (10 nm) 600BNiFe (10 nm) 1000FeMn (10 nm) 1000SG1CoFe (3 nm)IrMn (10 nm)--31