The Origins of Exchange Bias

Sadia Manzoor

Department of Physics COMSATS Institute of Information Technology, Islamabad

Co-workers:

K. O’Grady, L. E. Fernández-Outón and G.Vallejo-Fernández, Department of Physics, University of York, U.K.

M. Farooq Nasir, Department of Physics, COMSATS IIT, Islamabad

2

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» the independent AFM grain model

• Conclusions

3

Order in magnetic systemsferromagnet

T > TC T < TC

antiferromagnet

T > TN T < TN

4

• soft ferromagnet

H

ferromagnet antiferromagnet

H

M

Coercivity HC

• pinned ferromagnet

Interfacial exchange anisotropy

HEX

H

M

Hc

Exchange bias

T < TC T < TN

5

The ‘rigid’ AFM picture

6

• Hex obtained from the ‘rigid’ AFM model >> Hex obtained experimentally

• at least 5 different theories have been proposed

• still no single working theory (i.e. one that can take account 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?

Issues still open

7

anisotropy energy of the AFM: E = K V sin2α

Anisotropy energy barrier: Δ E = K V

frequency of reversal: f = fo exp ( - ΔE / kB T)

relaxation time: τ = τo exp ( ΔE / kB T)

small particles become thermally unstable at high temperatures

Time Dependence in Antiferromagnets

Δ E

α

Eeasy axis

AFM grain

α

M

M

0 π/2 π

8

Δ E = KV

distribution of grain volume dependent energy barriers to reversal of the AFM

For a given (H, T), there exists a critical value of theanisotropy energy barrier ΔEC (or critical grain volume VC)such that all grains with

ΔE > ΔEC are thermally stable (blocked)

(V > VC)

and all those with

ΔE < ΔEC are thermally unstable (unblocked)(V < VC)

blockedunblocked

all polycrystalline samples have distribution of grain volumes …f(V)

9

blockedunblocked

H

blocked AFM grains

Unblocked AFM grains

Hex should depend upon the degree of order in the AFM!

ΔEC = KVC = kBT

high temperatures cause parts of the AF to disorder

only the blocked grains cause exchange bias

set in opposite sense

Thermal activation measurements

VSET V

activating the AFM

setting the AFM

VC VSET V

Thermal activation measurements

not set

set

not set

set

ΔEC = KVC = kBTACT

ΔEC = KVSET = kBTSET

∫=SET

C

V

V

iEX

*EX dV(V)fHT)(H,CT)(H,H

constantcouplinglinterfacia:C

biasexchangeintrinsic:H*

iEX

11

Reversal in IrMn(5nm)/CoFe(10nm)

100 150 200 250 300 350 400-300

-200

-100

0

100

200

300

H E

X (O

e)

Tact (K)

TB

12

0 2 4 6 8 10 12 140

5

10

15

fr

eque

ncy

(%)

Dm = 3.6 nm

grain diameter (nm)0 10 20 30 40 50 600

10

20

fr

eque

ncy

(%)

Dm = 16.8 nm

grain diameter (nm)

Sample A Sample B

Si/FeMn(10 nm)/NiFe(10 nm)/ Ta(15 nm)

13

deviationdardsvolumegrainmedianV

VVV

Vf

m

m

tan::

2)}({lnexp

21)( 2

2

σ

σσπ ⎥⎦

⎤⎢⎣

⎡−=

Grain size distribution for sample SB

Si/FeMn(10 nm)/NiFe(10 nm)/ Ta(15 nm)

14

relaxation time: τ = τo exp ( K V / kBT)

using tSET = 5400 s and tACT = 1800 s

AFM

SETBoSETSET K

Tk)f(tlnV = andAFM

ACTBoACTC K

Tk)f(tlnV =

where fo = 109 s-1

deviationdardsvolumegrainmedianV

VVV

Vf

m

m

tan::

2)}({lnexp

21)( 2

2

σ

σσπ ⎥⎦

⎤⎢⎣

⎡−=

∫=SET

C

V

V

iEXEX dVVfHTHCTHH )(),(),( *

15

TB = 165 K

deviationdardtans:

volumegrainmedian:V

dV2

])V/V(ln[exp)V/V(2

1H)T,H(C)T,H(H

M

2

2M

V

V M

iEX

*EX

SET

C

σ

⎟⎟⎠

⎞⎜⎜⎝

⎛σ

−σπ

= ∫

TB = 165 K

16

NOTE: at T = TB , HEX = 0!

Exact halves of the AFM particle volume

distributions are ordered in opposite senses

VM VAFM

BBoACTM K

Tk)f(tlnV =

KAFM (165 K) = 2.96 × 105 erg/cm3

KAFM (293 K) = 1.85 × 105 erg/cm3

(KAFM (293 K) = 1.35 × 105 erg/cm3 reported by Mauri et al.)

D. Mauri, E. Kay, D. Scholl, and J. Kent Howard, J. Appl. Phys. 62, 292 (1987)

17

Exchange biased nanocomposites

• core-shell nanoparticles

• FM nanoparticles embedded in an AFM matrix

“Beating the superparamagnetic limit with exchange bias”Vassil Skumryev, Stoyan Stoyanov, Yong Zhang, George Hadjipanayis, Dominique Givord and Josep Nogués

NATURE, Vol. 423, p. 850 (2003)

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Understanding these systems is much more complex than FM/AFM bilayers in which

Hex ∝ 1/tFM and Hex ∝ tAFM

In nanocomposite systems….definition of ‘thickness’ is an issue

for FM …. particle diameter ~ FM thickness (but percolation effects)

for AFM…. distance between FM particles ~ AFM thickness

PROBLEM: these cannot be controlled independently of one another as in thin films

19

Co-Cr2O3 nanocomposites prepared by sol gel:

fcc Co nanoparticles embedded in Cr2O3 matrix

Increasing Co concentration

increasing FM / AFM interface density

effect on exchange bias???

<DCo> ≈ 3 – 4 nm, <DCr2O3> ≈ 24 nm

validity of the independent AFM grain model for super exchange coupled AFM’s??

sample wt. % CoA 30B 40C 50D 60E 80

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• TB depends only upon the median AFM particle volume Vm.

• data can be described by the independent AFM particle model, i.e.

usingAFM

BBoACTM K

Tk)f(tlnV =

dV2

])V/V(ln[exp)V/V(2

1H)T,H(C)T,H(H 2

2M

V

V M

iEX

*EX

SET

C

⎟⎟⎠

⎞⎜⎜⎝

⎛σ

−σπ

= ∫

0 50 100 150 200 250 300-200-150-100

-500

50100150200

-1

00

1

Hex (Oe)

T ACT (K)

∫S E T

C

V

V

d VVf )(

A

0 50 100 150 200 250 300

-200

-100

0

100

200

300

-1

00

1

TACT (K)

B

∫S ET

C

V

V

dVVf )(Hex (Oe)

0 50 100 150 200 250 300-200

-150

-100

-50

0

50

100

150

-1

00

1

TACT(K)

∫S E T

C

V

V

d VVf )(Hex (Oe)

C

0 50 100 150 200 250 300

-150

-100

-50

0

50

100

150

-1

00

1

TACT(K)

∫S ET

C

V

V

dVVf )(Hex (Oe)

C1

TB = 148 K TB = 148 K

TB = 148 K TB = 165 K

21

For Cr2O3 … TN = 310 K ⇒ TSET > TN is possible! ⇒ entire f (V) can be set

∫= dV)V(fH)T,H(C)T,H(H iEX

*EX

= 1

Separation of bulk and interfacial effects !!!

30 40 50 60 70 80100

150

200

C* H

exi (

Oe)

Co Concentration (wt. %)

C* HEXi depends non-monotonically upon

FM/AFM interface density

Hex itself is governed by both bulk and interfacial effects

22

Conclusions• Hex is controlled not only by the degree of order in the bulk antiferro-

magnet but 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 of the AF by merely taking into account an anisotropy and exchange

stiffness 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 the models proposed to explain exchange bias.

23

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 – Cr2O3 NanocompositesM. Farooq Nasir, H. Hoon, K. O’Grady and Sadia ManzoorInternational Journal of Nanoscience and Nanotechnology (2010)(in press)

• Higher Education Commission, GoP• Commonwealth Foundation, U.K.• Hitachi Global Storage Technologies (HGST), San José, California• Seagate Technology, N. Ireland

• Dr. Umair Manzoor for TEM images

Acknowledgements

24

• Higher Education Commission, GoP

• Commonwealth Foundation, U.K.

• Hitachi Global Storage Technologies (HGST), San José, California

• Seagate Technology, N. Ireland

Acknowledgements• Dr. Umair Manzoor for TEM images

25

Energy per unit area of FM/AFM bilayer

E = - H MFMtFM cos (θ - β) + KAFMtAFMsin2(α) - JINT cos (β - α)

• KAFMtAFM < JINT

⇒ AFM spins rotate with the FM spins

no loop shift

• KAFMtAFM > JINT

⇒ pinning of FM spins by the AFM loop shift

Minimizing energy with respect to β keeping α small (≅ const.)

FMFM

INTex tM

J=H

KAFMMAFM

MFM

H

α

θβ

θ

26

27

Targets

Highly ionized plasma ‘beam’ generated in side arm and directed to target by electromagnets

RF power unit

SIDE ARM PLASMA SOURCE

Launch electromagnet

Rotating substrate table Reactive gas feed Ar gas

feed

Pump systems

DC/RF 0-1000V target bias

Targets

Highly ionized plasma ‘beam’ generated in side arm and directed to target by electromagnets

RF power unit

SIDE ARM PLASMA SOURCE

Launch electromagnet

Rotating substrate table Reactive gas feed Ar gas

feed

Pump systems

DC/RF 0-1000V target bias

High Target Utilization Sputtering (HiTUS)

28

29

Iin Iout

Recording medium

SV sensor

AFM pinning layer e.g. IrMn, FeMn

FM (pinned) layer e.g. CoFe, NiFe

Non-magnetic spacer layer e.g. Cu

FM (free) layer e.g. CoFe, NiFe

} EXCHANGE BIASED BILAYER

30

In order to obtain the intrinsic behaviour of exchange biasedmaterials, it is essential to measure in thermal activation free conditions

Determination of thermal activation free temperature

Recoil loops for a IrMn(5nm)/CoFe(10nm) exchange couple

⇒ TNA = 100 K

31

Sample Layer composition Vbias (V)NiFe (10 nm) 200AFeMn (10 nm) 600NiFe (10 nm) 1000BFeMn (10 nm) 1000

SG1 CoFe (3 nm)IrMn (10 nm)

--

Grain size control through control of Vbiasof the FM and AFM layers