1. The Structure and Dynamics of Solids
The Muppet’s Guide to:
The Structure and Dynamics of Solids
Magnetic Reflectivity

2. Electronic resonances
A core electron is excited and creates a spin polarised photoelectron
Exchange split final states act as a filter of the spin
Magnetic sensitivity comes through the spin-orbit coupling and exchange and has strong polarisation dependence (MOKE)
Courtesy W. Kuch, Freie Universität Berlin

3. XMCD Examples at Resonant Edges
From Magnetism by J. Stöhr and H.C. Siegmann, Springer

4. Circular Polarised Light
A photon is a spin-one particle which carries ±1 unit of L along its direction of motion. This angular momentum is transferred to the absorbing material. .
Faraday Effect
Right Circular, +Pc, s=+1 M
s=Helicity
Left Circular, -Pc, s=-1

5. Detecting XMCD Transmission Thin Samples Drain Current
PEEM – ESG group at the ALS
Detecting XMCD
Transmission
Thin Samples
Drain Current
Field Sensitive, Anisotropic
Escape Depth ~3nm
Fluorescence
Escape Depth ~1mm, Anisotropic
Secondary processes

6. Element Specific M-H loops
FeCoZr
MnSb Mn

7. Resonant X-ray ‘Magnetic’ Scattering
Circular polarised x-rays. Element specific. 3d 2p
Absorption spectroscopy sensitive to the exchange split final state and the split core levels (spin-orbit). Basis behind XMCD.
Resonant elastic scattering is sensitive to the same terms but contains both the real and imaginary terms to the scattering factor.

8. On Resonance – Scattering Factor
Resonant processes enter the scattering factor through f’ and f’’ and must describe the initial and final state.
From XAS obtain f’’
From XMCD obtain m’’
Use Kramers-Kronig transforms to obtain the real parts of the scattering factors and thereby f(q,w).

9. Scattering amplitude
Scattering is sensitive to both the real and imaginary components which are related via the Kramers-Kronig transforms.....
The magnetic dependent absorption (XMCD) gives a magnetic dependence on the real part of the scattering factor Fe
From Magnetism by J. Stöhr and H.C. Siegmann, Springer

10. Electric Dipole Transition
Resonant and non-resonant charge scattering
Circular Dichroism and Kerr Effect
Linear Dichroism and the Voigt Effect
F0, F1, F2 are all complex numbers containing the scattering factors and depend on the incident energy, and therefore resonance.

11. q-space
Diffraction
Small Angle
Scattering &
Reflectivity

12. Reflections from Surfaces

13. Reflectivity from layered systems
Based on Simple Optical Theorems:
Snell’s Law
Fresnel’s Law
Intensity is proportional to layer thickness and the refractive index of the layers (electron density).
Roughness modifies the reflection and transmission coefficients - interface roughness
Sensitivity <1Å. Max. thickness Å. Max Roughness - 35 Å

14. [FeCoZr/AlZr]x20
Periodicities in the sample give rise to different beat frequencies in spectra. Profile proportional to FT{electron density profile)
Roughness modifies the Fresnel reflection and transmission coefficients and hence the overall fall-off.
Phys. Rev. B 80 (13)  (2009),

15. Amorphous Multilayer Exampled b
Averaged:
Layer thickness
Interface width
Refractive index - Density
TPA Hase et al. Phys. Rev. B 80(13) (2009)

16. Anomalous Dispersion
Enhance the scattering factor difference between the layers.

17. Grazing Incidence Scattering
Out-of-plane q
In-plane q
M. Wormington et al. Phil. Mag, Lett. 74(3) 211 (1996) 

18. Resonant magnetic reflectivity
Refractive index now depends on the moment direction: n2 n3
On resonance the scattering becomes sensitive to both the structural and magnetic profiles of the element under consideration.
Extract magnetic signal through the flipping ratio:

19. Alloy – Pd resonant Scattering
Sum (left) and flipping ratio (right) determined by reversing the applied field for the alloy sample at 200 K . The flipping ratio shows the same periodicity as seen in the sum signal and changes sign when the incident helicity (±Pc) is reversed.

20. Structural
T=20K

21. Magnetic
Magnetic dead-layer at interface with buffer and an enhanced moment at the surface
T=20K

22. Compositional and Magnetic Profiles (Pd)

23. PNR from a single layer Directly proportional to mB.
Courtesy Sean Langridge, ISIS

24. Fe/Pd Example

25. Comparison of Profiles
1.4 and 0.5 ML profiles have the magnitude of the moments fixed by PNR.
The spatial extent of the Fe moment increases with increasing δ-layer thickness but the induced moment extent remains approximately constant.
Samples close to half integer coverage appear to induce a higher moment.

26. Hysteresis Loops – 1.4ML Fe in Pd
The remanent magnetisation is extracted by fitting each hysteresis loop to a pair of arctan functions:
Fe edge
Pd edge