KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary L. Deák Magnetic domains: theory and evaluation of diffuse resonant photon.
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KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary
L. Deák
Magnetic domains: theory and evaluation of Magnetic domains: theory and evaluation of diffuse resonant photon and diffuse resonant photon and
neutron scatteringneutron scattering
Nano-scale Materials: Growth - Dynamics - Magnetism,Nano-scale Materials: Growth - Dynamics - Magnetism,ESRF Grenoble, FranceESRF Grenoble, France 6-8 February, 2007 6-8 February, 2007
Outline Outline
• Introductiondomains as seen by theory (Synchrotron) Mössbauer Reflectometry (SMR) Polarized Neutron Reflectometry (PNR)
• Conclusions
• Off-specular SMRtheory (DWBA, DWA)simulations (2D and 1D scans)experimets (SPring-8, ESRF)EFFI2 (Environment For FItting)
Antiferromagnetic domains in multilayersAntiferromagnetic domains in multilayers
Layer magnetisations:
sample
p,,II kk
source detector
',,II p kk
p,,II kk
source
detectorin out
sample
',','II pkk
inout coscos|||||| kkkK
insinkk
outsinkk
θ in − θ out (detector scan)
p,,II kk
source
detector
2
',','II pkk
samplesample
sample
2θ − ω scan sinsin2|||||| kkkK
sinkk
2sinkk
Off-specular SMR: TheoryOff-specular SMR: Theory
rr 2kV Scattering potential:
Homogeneous wave equation:
Distorted wave Born approximation (DWBA)
2221 kkVVV
Off-specular SMR: TheoryOff-specular SMR: Theory
Next problem: E,r
DWBA is too slow for diffuse SMR!!
rrr cohlloff kIk II
22 rr offlk II2
Distorted wave approximation: rrr offcoh
11stst DWA DWA
Condition: Θout >> ΘCr
5-10 times faster algorithm
Off-specular SMR Off-specular SMR
MgO(001)[MgO(001)[5757Fe(26Å)/Cr(13Å)]Fe(26Å)/Cr(13Å)]2020
22 @ AF reflection @ AF reflection
Correlation length:
= 2π/KII
Fit result: = 5 m
D.L Nagy et al., ESRF
0 5 10 15 200
5
10
15
20
in
out
1E-31.26E-31.58E-32E-32.51E-33.16E-33.98E-35.01E-36.31E-37.94E-31E-21.26E-21.58E-22E-22.51E-23.16E-23.98E-25.01E-26.31E-27.94E-21E-11.26E-11.58E-12E-12.51E-13.16E-13.98E-15.01E-16.31E-17.94E-11E0
Off-specular SMROff-specular SMR: 2D : 2D ΘΘinin--ΘΘoutout scan scan
MgO(001)[MgO(001)[5757Fe(26Å)/Cr(13Å)]Fe(26Å)/Cr(13Å)]2020
0 5 10 15 200
5
10
15
20
in
out
1E-51.47E-52.15E-53.16E-54.64E-56.81E-51E-41.47E-42.15E-43.16E-44.64E-46.81E-41E-31.47E-32.15E-33.16E-34.64E-36.81E-31E-21.47E-22.15E-23.16E-24.64E-26.81E-21E-11.47E-12.15E-13.16E-14.64E-16.81E-11E0
Off-specular SMR: 2D Off-specular SMR: 2D ΘΘinin-Θ-Θoutout scan scan
MgO(001)[MgO(001)[5757Fe(26Å)/Cr(13Å)]Fe(26Å)/Cr(13Å)]2020
5 10 15 20
10-1
100
101
102
out
= in
inte
nsity
in (mrad)
Specular scan
Θcr
Θcr
ΘAF
ΘAF
ΘS
ΘS
= 4.6 m
Limits of validity: Θout >> ΘCr
0 5 10 15 200
5
10
15
20
in
out
1E-51.47E-52.15E-53.16E-54.64E-56.81E-51E-41.47E-42.15E-43.16E-44.64E-46.81E-41E-31.47E-32.15E-33.16E-34.64E-36.81E-31E-21.47E-22.15E-23.16E-24.64E-26.81E-21E-11.47E-12.15E-13.16E-14.64E-16.81E-11E0
ΘAF
Off-specular SMROff-specular SMR: 2D : 2D ΘΘinin--ΘΘoutout scan scan
MgO(001)[MgO(001)[5757Fe(26Å)/Cr(13Å)]Fe(26Å)/Cr(13Å)]2020
0 2 4 6 8 10 12
10-4
10-3
10-2
10-1
100
2= 2AF
Inte
nsity
(mrad)
= 4.6 m
ω - scan
Limits of validity: Θout = 2Θ - ω >> ΘCr
0 5 10 15 200
5
10
15
20
in
out
1E-51.47E-52.15E-53.16E-54.64E-56.81E-51E-41.47E-42.15E-43.16E-44.64E-46.81E-41E-31.47E-32.15E-33.16E-34.64E-36.81E-31E-21.47E-22.15E-23.16E-24.64E-26.81E-21E-11.47E-12.15E-13.16E-14.64E-16.81E-11E0
ΘAF
Off-specular SMROff-specular SMR: 2D : 2D ΘΘinin--ΘΘoutout scan scan
MgO(001)[MgO(001)[5757Fe(26Å)/Cr(13Å)]Fe(26Å)/Cr(13Å)]2020
0 5 10 15 2010-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
in =
AF
inte
nsity
out
(mrad)
detector - scan
Limits of validity: Θout >> ΘCr
= 4.6 m
Off-specular SMROff-specular SMR: 2D 2: 2D 2ΘΘ - - ωω scan scan
0 5 10 15 20 25 30 35 40 45
10
20
30
40
(mrad)
(
mra
d)
1E-51.47E-52.15E-53.16E-54.64E-56.81E-51E-41.47E-42.15E-43.16E-44.64E-46.81E-41E-30.001470.002150.003160.004640.006810.01000.01470.02150.03160.04640.06810.1000.1470.2150.3160.4640.6811.00
MgO(001)[MgO(001)[5757Fe(26Å)/Cr(13Å)]Fe(26Å)/Cr(13Å)]2020
Limits of validity: Θout = 2Θ - ω >> ΘCr
3 4 5 6 7 8
11
12
13
14
[mrad]
[m
rad]
1E-30,0010,0020,0030,0040,0060,0080,0110,0160,0220,0320,0450,0630,0890,1260,1780,2510,3550,5010,7081,000
3 4 5 6 7 8
11
12
13
14
[mrad]
[m
rad]
1E-30,0010,0020,0030,0040,0060,0080,0110,0160,0220,0320,0450,0630,0890,1260,1780,2510,3550,5010,7081,000
Experiment: L. Bottyán et al. 2002, SPring-8, Japan
L. Bottyán et al., SPring-8, Japan
= 4.6 m
ConclusionsConclusions
SMR and PNR are efficient tools of studying (magnetic) multilayers and thin films
The computer program EFFI2 is available from ftp://nucssp.rmki.kfki.hu/effi2 for fitting off-specular SMR (and soon polarized neutron reflectometry) spectra
A common DWA method was introduced for calculating off-specular SMR, x-ray and polarized neutron reflectometry spectra
The new approximation results in a faster algorithm then the standard DWBA, but has limited range of validity
L.Deák, L. Bottyán, D. L. Nagy, H. Spiering, Yu. N. Khaidukov and Y. Yoda, „Perturbative Theory of Off-Specular Synchrotron Mössbauer Reflectometry”
KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary
Joint Institute for Nuclear Research, Dubna, Russia
Johannes Gutenberg Universität Mainz, Germany
Nano-scale Materials: Growth - Dynamics - Magnetism,Nano-scale Materials: Growth - Dynamics - Magnetism,ESRFESRF GrenobleGrenoble, , FranceFrance 6 6--88 FebruaryFebruary, 200, 20077
L. Bottyán
D.L Nagy
M. Major
H. Spiering Yu.N Khaidukov
Off-specular SMR: TheoryOff-specular SMR: Theory homogeneous wave equation rrr 22 kIk ,
where
S
ll
1IIrr and l is the layer index.
Defining IIrll we can separate the rcoh (coherent) specular and roff off-specular fields
rr lkIk 22 rr llk II
2 with rrr offcoh
rrr cohlloff kIk II
22 rr offlk II2
11stst DWA DWA
T h e s a m e l i n e a r d i f f e r e n t i a l e q u a t i o n f o r N E U T R O N a n d M Ö S S B A U E R r e f l e c t o m e t r y :
zWzikMzWz
d
d.
I n t h e c a s e o f s t r a t i f i e d m e d i a , w h i c h c o n s i s t s o f S l a y e r s w i t h t h i c k n e s s d l : ( l = 1 . . . S )
M ( z ) = M l = c o n s t . f o r t h e l t h l a y e r , t h e s o l u t i o n m a y b e g i v e n b y t h e 44 c h a r a c t e r i s t i c m a t r i x L , t h a t i s t h e p r o d u c t o f t h e c h a r a c t e r i s t i c m a t r i c e s lll MikdL exp o f t h e i n d i v i d u a l l a y e r s
112212 expexp...exp... MikdMikdMikdLLLL sss .
D e n o t i n g t h e 22 s u b m a t r i c e s o f L w i t h ijL ( i j = 1 , 2 ) t h e 22 r e f l e c t i v i t y m a t r i x r r e a d s
22211211122211211 LLLLLLLLr
. T h e r e f l e c t e d i n t e n s i t y I r i s
rrTrI r , w h e r e i s t h e 22 d e n s i t y m a t r i x o f t h e i n c i d e n t r a d i a t i o n .
THE COMMON FORMALISM:THE COMMON FORMALISM:
rIrLMnf
Method:
EFFI
II2
IIIIIIII d rrrRR llllllC
rrr cohlloff kIk II
22 rr offlk II2
Off-specular SMR: TheoryOff-specular SMR: Theory 11stst DWBA DWBA
rILrILTl rrr 2221
sin
sinsin2'
II
k
k
k
K
-scan:
0th approximation:
EFFI (Environment For FItting)
The solution:
'
''II'
'2
4
Tr4 ll
lllloff TCTr
kI kKk
IIRllC : exponential Lorentzian:IIKllC
ll
lloff CI IIK
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