Folie 1 - University of Nebraska–Lincoln
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Transcript Folie 1 - University of Nebraska–Lincoln
Training of the exchange bias effect
Training effect:
reduction of the EB shift upon
subsequent magnetization reversal
of the FM layer
- origin of training effect
- simple expression for
0HEB vs. n
Examples: recent experiments and simulation
NiO(001)/Fe(110)12nm/Ag3.4nm/Pt50nm
Co/CoO/Co1-xMgxO
10
8
e
oHEB (n) oHEB
n
-µ0 HEB [mT]
empirical fit
n
6
0
2
4
6
8
10
n
J. Keller et al., PRB 66, 014431 (2002)
A. Hochstrat, Ch. Binek and W. Kleemann,
PRB 66, 092409 (2002)
oHEB (n) oH
e
EB
D. Paccard , C. Schlenker et al.,
Phys. Status Solidi 16, 301 (1966)
Monte Carlo
Simulations
n
U. Nowak et al., PRB 66, 014430 (2002)
oHEB (n) oH
e
EB
-Simple expression
n
- applicable for various systems
Simple physical basis ?
Phenomenological approach
Meiklejon Bean
0HEB
JS S
AF FM
MFM t FM
FM interface magnetization: SFM
coupling constant:
tFM
J
AF interface magnetization: SAF
const.
oHEB (n) K SAF (n)
MFM
:saturation magnetization of FM layer
confirmation by SQUID measurements
and MC simulations
SAF
- microscopic origin of n-dependence of SAF:
Sn3 SAF (n 3) SeAF
Change of AF spin configuration
triggered by the FM loop through
exchange interaction J
deviation from the equilibrium value
SeAF lim SAF (n) equilibrium AF
n
1
2
3
S
Increases free energy by
4
under the assumption
5
6
7
n
F
F(S) F(S)
1
1
2
4
F a Sn b Sn
2
4
interface magnetization
Relaxation towards equilibrium
F
S
S
Lagrange formalism with
potential F and strong dissipation
(over-critical damping)
Landau-Khalatnikov
G.Vizdrik, S.Ducharme, V.M. Fridkin, G.Yudin,
PRB 66 094113 (2003)
:phenomenological damping constant
Training not continuous process in time, but triggered by FM loop
discretization of the LK- equation
8
t2,3
n=1
-1
n=2
n=3
2
0
0
4000
n=4
8000
12000
t
16000
20000
-2
dSAF/dt,<dSAF/dt>
SAF
6
4
tn,n+1: time between loop
0
#n and n+1
n
: measurement time
of a single loop
: loop #
/2
dSAF
1
dSAF
dt
dt
/ 2 dt
SAF (n 1) S AF (n)
SAF
Discretization:
SAF (n 1) S AF (n)
LK- differential equation difference equation
S AF
F
Sn
SAF (n 1) SAF (n) Sn a b Sn
where
/
and
Sn SAF (n) SeAF
2
Minimization of free parameters:
SAF (n) SAF (n 1)
2
lim
a
b
S
a
lim
0
n
n
n
Sn
S AF (n) SeAF
a0
Physical reason :
1
a<0 ruled out
A B
2
n n
stable equilibrium at S=0
SAF
1
1
2
4
F a Sn b Sn
2
4
a<0
0
1
2
3
4
5
6
7
n
S
2
a>0 ruled out
Non-exponential relaxation
SAF (n 1) SAF (n) Sn a b Sn
2
0
SAF (n) ea n Seq
Sn Sn
n 1
3
Exponential relaxation
negligible spin correlation
Exchange bias: AF spin correlation
a0
non-exponential relaxation
Simplified recursive sequence
b
3
SAF (n 1) SAF (n) Sn
with oHEB (n) K SAF (n)
0 (HEB (n 1) HEB (n)) 0 (HEB (n) H )
where
b
2
K
e
EB
3
power law:
e
oHEB (n) oHEB
n
Correlation between:
recursive sequence:
0 (HEB (n 1) HEB (n)) 0 (HEB (n) H )
e
EB
3
Substitution
oH
e
EB
n 1
e
oHEB (n) oHEB
oHEB (n 1)
1
n 1
1
n
1
2n n
1
0.5
n
4
1
1
0.48...
3 6 3
error <5%
80
K
2b
F
60
b
40
20
Physical interpretation:
- Steep potential F
0
-3
large b
- damping
large
increases with increasing
relaxation rate
-1
0
1
2
3
S
deviations from equilibrium unfavorable
- Training triggered via AF/FM coupling
-2
small training effect,
JK
K
means strong decay of EB after a few cycles
increases with increasing
small
Comparison with experimental results on NiO-Fe
1st& 9th hysteresis of NiO(001)/Fe
400
T=5K
(001) compensated
12nm
1.
Fe
2
m [nA m ]
200
0
9.
NiO
-200
-400
-200
-100
0
µ 0 H [mT]
100
200
10
experimental data
9
recursive sequence:
e
0HEB
4.45 mT input from power law fit
1 N 0 HEB (n) HEB (n 1)
N 1 n2 H (n) He 3
7
0
EB
EB
6
5
3
start of the sequence
8
n
-µ0 HEB [mT]
0HEB (n 1) 0HEB (n) 0 (HEB (n) H )
e
EB
0
3
6
n
power law:
e
oHEB (n) oHEB
n
9
10
experimental data
HEB
9
recursive sequence
f HEB (n) 0 HEB (n) H
8
n
2
e
EB
f
f
,
0
0
e
(0HEB )
3
HEB (n 1)
2
min.
0.015 (mT)
and
7
0HeEB 3.66 mT
6
5
0
-2
3
n
6
9