Changes of magnetization ordering by increasing the
repetitions number N in (Co/Au)N multilayers
A. Maziewski, Maria Tekielak, M.Kisielewski, P.Mazalski, I.Sveklo,
V.Zablotskii,
Laboratory of Magnetism, University of Bialystok, Poland
R. Schäfer, J. McCord
Leibniz-Institut für Festkörper- und Werkstoffforschung Dresden e.V.,
Germany
B. Szymański, M.Urbaniak, F. Stobiecki
Institute of Molecular Physics, Polish Academy of Sciences, Poznan,
Poland
Influence of magnetic layer thickness on magnetic
ordering
RPT
d
M
M
small d
large d
Ea>0
Ea<0
easy axis
easy plane
For Co dRPT ≈ 1.79 nm=d1
strong influence of surface anisotropy
Ea = K1eff sin2θ + K2 sin4θ
K1eff [a.u.]
Easy
Plane
Easy Axisfor single Co
Ordering
layer
dCo [nm]
0
-2πM2 + K1V + (K1Sg+K1Sd ) / d
0,5
1
1,5
2
2,5
3
Stripe domain period as a function of film thickness
Q
1.4
1.0
1.2
Q*
p/lex
1
108
mz
d/d1=
0.56
106
0
1.04
104
d=1nm
1.00
0.96
102
* p*
0.6
0.7
lex=(A/(2π
πMS2))0.5
0.8
0.9
1.0
Q =K1/(2π
πMS2 )
M. Kisielewski, A. Maziewski, T. Polyakova, V. Zablotskii, Wide scale evolution of magnetization
M.Kisielewski, et al.. Phys. Rev. B. 69,184419 (2004 )
distribution in ultrathin films, Phys. Rev. B. 2004
d/d1
-1
0
0,5
x/p
1
Stripe domain period as a function of film thickness
p/2
E = Ly d
Q
∫
0
1.4
  dθ  2

2
 A
+ K1 sin (θ ( x)) − M S H // sin(θ ( x)) dx + E D
  dx 



1.0
1.2
Q*
p/lex
1
108
mz
d/d1=
0.56
106
0
1.04
104
1.00
0.96
102
* p*
0.6
0.7
lex=(A/(2π
πMS2))0.5
0.8
0.9
Q =K1/(2π
πMS2 )
M. Kisielewski, A. Maziewski, T. Polyakova, V. Zablotskii, Wide scale evolution of
Phys.
Rev.
B. 69,184419
magnetization
distribution
in ultrathin films, Phys.(2004
Rev. B. 2004 )
1.0
d/d1
-1
0
0,5
x/p
p*=8π lex2/d + 2 πd
p* ~ 200nm (for lex=3nm, d=1nm)
1
Questions
Q
1.4
1.0
1.2
Q*
p/lex
108
106
104
d=1nm
102
*p*
0.6
0.7
lex=(A/(2π
πMS2))0.5
0.8
0.9
Q =K1/(2π
πMS2 )
M. Kisielewski, A. Maziewski, T. Polyakova, V. Zablotskii, Wide scale evolution of
J.Ferré, et al.. Phys. Rev. B. 55,22 (1997)
magnetization distribution in ultrathin films, Phys. Rev. B. 2004
1.0
d/d1
Scheme of the sample
Si(100) / (Au 2nm / Si 1nm)10 / Au 2nm / (Co / Au 3nm)N
N=1, 3, 6, 12
Co d=(1, 2, 3) nm
10x
Au 2nm
Si 1nm
K1eff [a.u.]
Au 3nm
Ordering
for single Co Easy
layer Plane
Easy Axis
dCo [nm]
0
Si (100)
0,5
1
1,5
2
magnetic multilayers prepared by dc magnetron sputtering
in UHV conditions on oxidized silicon substrate
In the group of prof. F.Stobiecki, IFM, Poznan
2,5
3
Experimental results: Multilayers with dCo=1nm
N=3
N=6
N=12
P-MOKE
N=1
P-MOKE 150x150µ
µm
MFM
5x5µ
µm
MFM
5x5µm
State with out-of-plane magnetization
MFM
5x5µm
Experimental results: Multilayers with dCo=2nm
N=3
N=6
L-MOKE 300x300µm
L-MOKE 300x300µm
N=12
L-MOKE
P-MOKE
N=1
L-MOKE 300x300µm
State with in-plane magnetization
MFM
5x5µm
State with out-of-plane
magnetization
Experimental results: Multilayers with dCo=3nm
P-MOKE
N=1
N=3
N=6
N=12
N=18
N=24
90
90
90
90
90
90
0
0
0
0
0
0
-90
-90
-12
-6
0
6
12
-90
-12
-6
0
6
12
-90
-12
-6
0
6
12
-90
-90
-12
-6
0
6
12
-12
-6
0
6
12
-12
-6
0
6
12
H⊥[kOe]
L-MOKE 300x300µm
State with in-plane magnetization
MFM
5x5µm
State with out-of-plane magnetization
DS period p [nm]
Results of measurements
d=1nm
d=2nm
d=3nm
Number of repetition N
Dependence of the domain structure size on the number of repetitions N, for different
cobalt layer thicknesses. The lines are guides to the eyes.
Draaisma - Jonge model of DS in MLs
H.J.G. Draaisma, W. J. M. de Jonge, J. Appl. Phys. 62, 3318 (1987)
Large perpendicular anisotropy – all domains are up
or down oriented
• the domain walls are assumed to be infinitely thin
• the domain walls are freely mobile
• the domains period is the same in all layers
Draaisma de Jonge model of DS in MLs
H.J.G. Draaisma, W. J. M. de Jonge, J. Appl. Phys. 62, 3318 (1987)
Applying D-J model to our systems
τ=2*lc lc=10 nm
Ks=0.44 103
A=1.3 10-11 J/m
Ms=1420 kA/m
DS period (nm)
KV=0.63 106 J/m3
500
dCo= 1
2
3
dCo=1
dCo=2
dCo=3
300
100
0
5
10
15
Number of repetition
20
25
Micromagnetic simulations of magnetization distribution in
„domain wall” in Co/Au multilayers far from RPT
d=1nm
Q 1.4
p/lex
1.2
1.0Q*
OOMMF NIST free
software was used
108
106
104
d=1nm
102
0.6
0.7
0.8
0.9
1.0
K1=1,01
10π6MJ/m
2))30.5 Q =K1/(2π
πMS2 )
lex=(A/(2π
S
Ms=1420 103 A/m
* p*
d/d1
Parameter from M.Kisielewski,
Phys.Rev.Lett. 2002
Simulated magnetization distribution in (AuCo)N multilayers
for d1<d=3nm
N=2
N=3
Experimental results: Multilayers with dCo=3nm
P-MOKE
N=1
N=3
N=6
N=12
N=18
N=24
90
90
90
90
90
90
0
0
0
0
0
0
-90
-90
-12
-6
0
6
12
-90
-12
-6
0
6
12
-90
-12
-6
0
6
12
-90
-90
-12
-6
0
6
12
-12
-6
0
6
12
-12
-6
0
6
12
H⊥[kOe]
L-MOKE 300x300µm
State with in-plane magnetization
MFM
5x5µm
State with out-of-plane magnetization
Experimental results: Multilayers with dCo=3nm
P-MOKE
N=1
N=3
N=6
N=12
N=18
N=24
90
90
90
90
90
90
0
0
0
0
0
0
-90
-90
-12
-6
0
6
12
-90
-12
-6
0
6
12
-90
-12
-6
0
6
12
-90
-90
-12
-6
0
6
12
-12
-6
0
6
12
-12
-6
0
6
12
H⊥[kOe]
L-MOKE 300x300µm
State with in-plane magnetization
MFM
5x5µm
State with out-of-plane magnetization
Single magnetic layer, wedge
Thin regime
Ultra-thin regime
demagnetization effects
Co
d
M
dRPT1 ≈ 2 nm
strong influence of
surface anisotropy
K1eff = - 2πM2 +K1V+(K1St+K1Sb ) /d
Ea = K1eff sin2θ + K2 sin4θ
dRPT2 ≈ 20 nm
uniaxial „bulk”
anisotropy
period p (nm)
Domain structure changes as a function of cobalt film
(wedge) thickness
d=20nm
Domain structure period as a function of Co film thickness
M. Hehn, S. Padovani, K. Ounadjela, and J. P. Bucher, Phys.Rev.B, 54, 5 (1996)
d = 24nm
30nm
d > dRPT2 :
xz-cross-section equilibrium
zero-field magnetization
distribution
39nm
51nm
mx, mz - arrows
my - pixel
Ritta Szymczak type of domain structure
my
1
d = 99nm
z
0
M.KIsielewski 2007 JMMM
x Bloch wall
closure domains
CONCLUSIONS
Multilayer structure gives huge opportunities to
tune magnetic properties e.g.:
While increasing N, transition hard to soft
magnetic goes on
While increasing N, transition from in-plane into
out-of-plane magnetization ordering goes on
opp
We considered magnetostatic interactions,
additionally one can consider exchange
interaction,…