KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary L. Deák Magnetic...

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


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


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


ΘAF



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


ΘAF



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


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

KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary L. Deák Magnetic...

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