1. 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

2. 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)

3. Antiferromagnetic domains in multilayers Layer magnetisations:

4. sample source detector

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

6. source detector sample 2θ − ω scan

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

8. 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

9. 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

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

11. 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

12. 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

13. 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

14. 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

15. 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”

16. 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

17. Off-specular SMR: Theory 1 st DWA

18. THE COMMON FORMALISM: Method: EFFI

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