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KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary L. Deák Magnetic domains: theory and evaluation of diffuse resonant photon and neutron scattering Nano-scale Materials: Growth - Dynamics - Magnetism, ESRF Grenoble, France 6-8 February, 2007

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Outline Introduction domains as seen by theory (Synchrotron) Mössbauer Reflectometry (SMR) Polarized Neutron Reflectometry (PNR) Conclusions Off-specular SMR theory (DWBA, DWA) simulations (2D and 1D scans) experimets (SPring-8, ESRF) EFFI2 (Environment For FItting)

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Antiferromagnetic domains in multilayers Layer magnetisations:

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sample source detector

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source detector sample θ in − θ out (detector scan)

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source detector sample 2θ − ω scan

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Off-specular SMR: Theory Scattering potential: Homogeneous wave equation: Distorted wave Born approximation (DWBA)

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Off-specular SMR: Theory Next problem: DWBA is too slow for diffuse SMR!! Distorted wave approximation: 1 st DWA Condition: Θ out >> Θ Cr 5-10 times faster algorithm

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Off-specular SMR MgO(001)[ 57 Fe(26Å)/Cr(13Å)] 20 2 @ AF reflection Correlation length: = 2π/ K II Fit result: = 5 m D.L Nagy et al., ESRF

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Off-specular SMR: 2D Θ in -Θ out scan MgO(001)[ 57 Fe(26Å)/Cr(13Å)] 20

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Off-specular SMR: 2D Θ in -Θ out scan MgO(001)[ 57 Fe(26Å)/Cr(13Å)] 20 Specular scan Θ cr Θ AF ΘSΘS ΘSΘS = 4.6 m Limits of validity: Θ out >> Θ Cr

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Θ AF Off-specular SMR: 2D Θ in -Θ out scan MgO(001)[ 57 Fe(26Å)/Cr(13Å)] 20 = 4.6 m ω - scan Limits of validity: Θ out = 2Θ - ω >> Θ Cr

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Θ AF Off-specular SMR: 2D Θ in -Θ out scan MgO(001)[ 57 Fe(26Å)/Cr(13Å)] 20 detector - scan Limits of validity: Θ out >> Θ Cr = 4.6 m

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Off-specular SMR: 2D 2Θ - ω scan MgO(001)[ 57 Fe(26Å)/Cr(13Å)] 20 Limits of validity: Θ out = 2Θ - ω >> Θ Cr Experiment: L. Bottyán et al. 2002, SPring-8, Japan L. Bottyán et al., SPring-8, Japan = 4.6 m

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Conclusions 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”

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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, ESRF Grenoble, France 6-8 February, 2007 L. Bottyán D.L Nagy M. Major H. SpieringYu.N Khaidukov

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Off-specular SMR: Theory 1 st DWA

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THE COMMON FORMALISM: Method: EFFI

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Off-specular SMR: Theory 1 st DWBA -scan: 0 th approximation: EFFI (Environment For FItting) The solution: : exponential

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