Training of the exchange bias effect reduction of the EB shift upon subsequent magnetization...
-
Upload
richard-wilkins -
Category
Documents
-
view
222 -
download
1
Transcript of Training of the exchange bias effect reduction of the EB shift upon subsequent magnetization...
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