Training of the exchange bias effect

reduction of the EB shift upon

subsequent magnetization reversal

of the FM layer

Training effect:

- origin of training effect

- simple expression for

0 EBH vs. n

NiO(001)/Fe(110)12nm/Ag3.4nm/Pt50nm

Examples: recent experiments and simulation

A. Hochstrat, Ch. Binek and W. Kleemann,

U. Nowak et al., PRB 66, 014430 (2002)

Monte CarloSimulations

Co/CoO/Co1-xMgxO

J. Keller et al., PRB 66, 014431 (2002)

empirical fit

eo EB o EBH (n) H

n

eo EB o EBH (n) H

n

D. Paccard , C. Schlenker et al.,Phys. Status Solidi 16, 301 (1966)

PRB 66, 092409 (2002)

-Simple expression

- applicable for various systemse

o EB o EBH (n) Hn

Simple physical basis ?

Phenomenological approach

const.

o EB AFH (n) K S (n) confirmation by SQUID measurementsand MC simulations

FMFM

FMAFEB0 t M

SJSH

Meiklejon Bean

coupling constant: J

AF interface magnetization: SAF

FM interface magnetization: SFM

MFM :saturation magnetization of FM layer

tFM

- microscopic origin of n-dependence of SAF:Change of AF spin configurationtriggered by the FM loop throughexchange interaction J

equilibrium AF interface magnetization

eAF AF

n

S S (n)lim

deviation from the equilibrium valueen 3 AF AFS S (n 3) S

under the assumption F( S) F( S)

2 4n n

1 1F a S b S

2 4

n1 2 3 4 5 6 7

SA

F

Increases free energy by FS

Relaxation towards equilibrium

Landau-KhalatnikovF

SS

:phenomenological damping constant

Lagrange formalism withpotential F and strong dissipation(over-critical damping)

Training not continuous process in time, but triggered by FM loop

discretization of the LK- equation

tn,n+1: time between loop

#n and n+1

: measurement time of a single loop

n : loop #

/ 2AF AF

/ 2

dS 1 dSdt

dt dt

AF AFS (n 1) S (n)

G.Vizdrik, S.Ducharme, V.M. Fridkin, G.Yudin,PRB 66 094113 (2003)

AF AFAF

S (n 1) S (n)S

AF AFS (n 1) S (n)

Discretization:

LK- differential equation difference equation

n

F

S

AFS

where /

and en AF AFS S (n) S

2n nS a b S

Minimization of free parameters:

AF AF

nn

S (n) S (n 1)lim 0

S

2

nnlim a b S a

eAF AF 2

A BS (n) S

n n

a 0

n1 2 3 4 5 6 7

SA

F

Physical reason : 1 a<0 ruled out stable equilibrium at S=0

2 4n n

1 1F a S b S

2 4

0 S

a<0

Simplified recursive sequence

3AF AF n

bS (n 1) S (n) S

3e0 EB EB 0 EB EB(H (n 1) H (n)) (H (n) H )

where2

b

K

with o EB AFH (n) K S (n)

2 a>0 ruled out Non-exponential relaxation

n 1 3n nS S

a nAF eqS (n) e S 2

n nS a b S AF AFS (n 1) S (n) 0

Exponential relaxation negligible spin correlation

Exchange bias: AF spin correlation non-exponential relaxation a 0

Correlation between:

eo EB o EBH (n) H

n

power law:

3e0 EB EB 0 EB EB(H (n 1) H (n)) (H (n) H )

recursive sequence:

Substitution

eo EB o EBH (n) H

n

e

o EB o EBH H (n 1)n 1

1 1 1

n 1 n 2n n

1

0.54

1 10.48...

3 6 3

error <5%

K2b

Physical interpretation:

- Steep potential F large b

deviations from equilibrium unfavorable small training effect, small

- Training triggered via AF/FM coupling J K

- damping relaxation rate

increases with increasing K

large means strong decay of EB after a few cycles

increases with increasing

1st& 9th hysteresis of NiO(001)/Fe

Comparison with experimental results on NiO-Fe

NiO

12nm Fe

(001) compensated

eo EB o EBH (n) H

n

power law:

3e0 EB 0 EB 0 EB EBH (n 1) H (n) (H (n) H )

experimental data

recursive sequence:

start of the sequencee

0 EBH 4.45 mT input from power law fit

N0 EB EB

3en 2

0 EB EB

H (n) H (n 1)1

N 1 H (n) H

experimental data

recursive sequence

232 eEB 0 EB EB EB

n

f H (n) H (n) H H (n 1) min.

f0

and

0.015 (mT)-2

0 EB

f, 0

( H )

e

0 EBH 3.66 mTe