dénes lajos nagy, márton major, dávid visontai kfki research institute for particle and nuclear...
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Dénes Lajos Nagy, Márton Major, Dávid Visontai
KFKI Research Institute for Particle and Nuclear Physics, Budapest
Nano-Scale Materials: Growth – Dynamics – Nano-Scale Materials: Growth – Dynamics – Magnetism Magnetism Grenoble, 6-8 February 2007.Grenoble, 6-8 February 2007.
Dynamics of magnetic domainsDynamics of magnetic domains(the pixel model)(the pixel model)
OutlineOutline
Experimental facts
Native patch-domain formation in antiferromagnetically coupled multilayers
Spontaneous and irreversible growth of the domain size during demagnetisation: the domain ripening
Spin-flop-induced domain coarsening
Supersaturation domain memory effect
Temperature-induced ripening
Pixel model of domains and domain walls; Monte Carlo simulation of domain dynamics
M. Rührig et al., Phys. Stat. Sol. (a) 125, 635 (1991).M. Rührig, Theses, 1993.
Ripple domains
Patch domains
Domains in an Fe/Cr/Fe trilayer Domains in an Fe/Cr/Fe trilayer
Patch domains in AF-coupled Patch domains in AF-coupled multilayersmultilayers
Layer magnetisations:
The ‘magnetic field lines’ are shortcut by the AF structure the stray field is reduced no ‘ripple’ but ‘patch’ domains are formed.
0.00 0.05 0.10 0.15 0.20 0.25 0.300
50
100
150
200
cou
nts
Qz [Å -1]
/2-scan: Qz-scand = 2/Qz
-scan: Qx-scan
= 1/ Qx-4 -2 0 2 4
0
20
40
60
80
100
co
un
ts (
no
rma
lise
d)
Qx [10 -4 Å -1]
Arrangement of an SMR experimentArrangement of an SMR experiment
2or
Hext
x
yz
k
APD
from the high-resolutionmonochromator
E
Field dependence of the magnetisation Field dependence of the magnetisation MM and of the intensity and of the intensity IIAFAF of the SMR AF of the SMR AF
reflectionreflection(easy direction)(easy direction)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0
0.2
0.4
0.6
0.8
1.0
Hsat
no
rma
lise
d v
alu
e
H (T)
IAF
M
HS = 0.85 T
From saturation to remanence:From saturation to remanence:the domain ripeningthe domain ripening
In decreasing field the domain-wall angle and, therefore, the domain-wall energy as well as its surface density is increasing.
In order to decrease the surface density of the domain-wall energy, the multilayer spontaneously increases the average size of the patch domains (‘ripening’).
The spontaneous domain growth is limited by domain-wall pinning (coercivity).
450 mT 300 mT
150 mT 9 mT 300 mT
600 mT 9 mT
600 mT
MgO(001)[MgO(001)[5757Fe(26Å)/Cr(13Å)]Fe(26Å)/Cr(13Å)]2020
+ + - - scatteringscatteringJINR Dubna, REMURJINR Dubna, REMUR
Qz
Qx
Domain ripening: off-specular PNR, easy axisDomain ripening: off-specular PNR, easy axis
ESRFID18
Correlation length: = 1/Qx
370 nm 800 nm
Domain ripening: off-specular SMRDomain ripening: off-specular SMRMgO(001)[MgO(001)[5757Fe(26Å)/Cr(13Å)]Fe(26Å)/Cr(13Å)]2020
22@ @ AF reflection, hard axisAF reflection, hard axis
From saturation to remanence:From saturation to remanence:the native statethe native state
The native domains do not change their shape and size (370 nm) from saturation down to 200 mT.
Between 200 and 100 mT the domain size increases to 800 nm.
The growth stops below 100 mT.
Domain growth is an irreversible process; the domain size does not change up to saturation.
Spin-flop induced domain coarsening Spin-flop induced domain coarsening (PNR)(PNR)
7 mT
14.2 mT
35 mT
MgO(001)[MgO(001)[5757Fe(26Å)/Cr(13Å)]Fe(26Å)/Cr(13Å)]2020, easy axis, easy axis
JINRDubnaSPN-1
non-spin-flip scatteringSn || M
spin-flip scatteringSn M
Qx (10-4 Å-1) Qx (10-4 Å-1)
Qz
(Å-1)
Spin-flop-induced domain coarsening Spin-flop-induced domain coarsening (SMR)(SMR)
MgO(001)[MgO(001)[5757Fe(26Å)/Cr(13Å)]Fe(26Å)/Cr(13Å)]2020
22 @ @ AF reflection, easy axisAF reflection, easy axis
0
50
100delayed in remanence
after 13 mT
50
100prompt
0
50
100delayed in remanence
after 4.07 T
refle
cted
inte
nsity
(%
of m
ax.)
-6 -4 -2 0 2 4 60
50
100delayed in remanence
after 35 mT
Qx (10-4
Å-1
)
90 rot.
ESRFID18
Correlation length: = 1/Qx
Delayed photonsbefore the spin flop
= 800 nm
Delayed photonsafter the spin flop
> 5 m = 800 nm
Domain coarsening on spin flopDomain coarsening on spin flop
Coarsening on spin flop is an explosion-like 90-deg flop of the magnetization annihilating primary 180-deg walls. It is limited neither by an energy barrier nor by coercivity. Consequently, the correlation length of the coarsened patch domains may become comparable with the sample size.
Domain ripening: off-specular SMR, hard Domain ripening: off-specular SMR, hard direction: the ‘supersaturation memory direction: the ‘supersaturation memory
effect’effect’
ESRFID18
Field dependence of the magnetisation Field dependence of the magnetisation MM and of the intensity and of the intensity IIAFAF of the SMR AF of the SMR AF
reflectionreflection
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0
0.2
0.4
0.6
0.8
1.0
Hsat
Hsupersat
no
rmá
lt é
rté
k
H (T)
IAF
M
HS HSSnorm
alis
ed v
alue
JINR Dubna, REMURJINR Dubna, REMUR
Polarised Polarised neutron neutron
reflectometry reflectometry on Sample 2on Sample 2
The lateral distribution of the saturation field in Sample 2 is much narrower than that in Sample 1.
The supersaturation effect is probably due to the still not saturated fraction of Fe. When the field is released from a value HS < H < HSS, the old domain pattern re-nucleates on the residual seeds of very strongly coupled regions.
Supersaturation: the explanationSupersaturation: the explanation
J. Meersschaut et al., Phys. Rev. B 73, 144428 (2006).M. Major PhD thesis (2006).
Supersaturation memory effect andSupersaturation memory effect andthe lack of ripening at the lack of ripening at TT = 15 K = 15 K
Initial state: coarsened domains
HS = 1.55 T HSS = 3.60 T
ESRFID18
The lack of low-temperature ripening is due The lack of low-temperature ripening is due to the temperature dependence of the Fe to the temperature dependence of the Fe
coercive field coercive field HHcc
V(110)/[Fe(1.2 nm)/Cr(26 nm)15/Fe(1.2 nm)/Cr(10 nm)
J. Hauschild et al., Appl. Phys. A 74, S1541 (2002)
Domain ripening with increasing Domain ripening with increasing temperaturetemperature
ESRFID18
0.0 0.2 0.4 0.6 0.81
10
100
1000
C
ount
s
(deg)
15 K, 3.7 T --> 0 T 15 K --> 288 K, 0 T 288 K, 4T --> 0 T
Rationale of the pixel modelRationale of the pixel model
A full micromagnetic simulation would include about 1010 spins a simplified model is needed.
The bilinear layer-layer coupling the
saturation field Hs has a lateral distribution
obeying, e.g., a Gaussian statistics.
Rationale of the pixel modelRationale of the pixel model
Pixels (small homogeneous regions) are defined on a (rectangular) lattice.
Domain-wall width << pixel << domain size.
Two-sublattice model of the multilayer characterised by one opening angle 2 is used.
The domain-wall angleThe domain-wall angle
Domain-wall angle = 2 (H) = 2 arccos H/Hs(r)
Rationale of the pixel modelRationale of the pixel model
The domain-wall energy is proportional to
the square of the domain-wall angle: Ewall=
4 D 2
In remanence
In external field H
Rationale of the pixel modelRationale of the pixel model
The total domain-wall energy is the sum of the wall energies with the next 8 neighbours.
2
sc 12
rH
HMH
The hysteresis loss of a pixel associated with changing the sense of rotation (‘red’ or ‘green’) stems from the field-perpendicular component of the layer magnetisation.
The Monte Carlo ‘movies’The Monte Carlo ‘movies’
Random values of Hs(r) are generated on a
rectangular lattice.
H and/or Hc(T) are varied step-by-step.
Subsequent pictures of the calculation always differ from each other only by the sense of rotation of a single pixel, the saturation state ( = 0) being considered to have a third, ’neutral’ (yellow) sense of rotation.
The Monte Carlo ‘movies’The Monte Carlo ‘movies’
8
31 2
? 4
7 6 5
On gradually changing H or Hc, a pixel will change its sense of rotation if the new state, taken into account the domain-wall energy and the hysteresis loss, will be energetically more favourable.
A Gaussian distribution of the saturation field of expectation value <Hs> = 0.8 and standard deviation = 0.13 were used.
The simulation depends from D and HcM only through their ratio D/HcM.
Formation, ripening, supersaturationFormation, ripening, supersaturation
Formation, ripening, saturationFormation, ripening, saturation
Temperature-induced ripeningTemperature-induced ripening
ConclusionsConclusions With suitable magnetic field program, it is
possible to shape the domain structure of AF-coupled multilayers.
On leaving the saturation region sub-m native patch-domains are formed in decreasing field.
On further decreasing the field, the domain size spontaneously and irreversibly increases and the domain shape changes (ripening).
The bulk spin flop leads to an explosion-like increase of the domain size (coarsening).
In some samples, the domain structure is erased only in a field significantly higher than saturation, a probable consequence of the existence of very strongly coupled regions.
Due to the increased coercive field, at low temperature no ripening takes place.
The native domains retained at low temperature in remanence ripen when increasing the temperature (and so decreasing the coercive field).
ConclusionsConclusions
The Monte Carlo simulation based on the rough and phenomenological pixel model describes with surprisingly high accuracy the
o formation of patch domains (without introducing an artificial smoothing to Hs(r)),
o domain ripening during demagnetisation from saturation,
o apparent supersaturation domain memory effect,
o domain ripening at remanence with increasing temperature.
ConclusionsConclusions
Acknowledgements to:Acknowledgements to:
ESRF Grenoble ILL Grenoble JINR DubnaKFKI RMKI Budapest KU Leuven University
Mainz
D. Aernout Yu. NikitenkoL. Bottyán O. NikonovA. Chumakov A. PetrenkoB. Croonenborghs V. ProglyadoL. Deák R. RüfferB. Degroote H. SpieringJ. Dekoster C. StrohmT.H. Deschaux-Beaume J. SwertsH.J. Lauter E. SzilágyiV. Lauter-Pasyuk F. TanczikóO. Leupold K. TemstJ. Meersschaut V. VanhoofD.G. Merkel A. Vantomme