Neutron and x-ray spectroscopy

1. Neutron and x-ray spectroscopy • self-contained introduction •  neutron scattering and spectroscopy • x-ray scattering and spectroscopy • application to correlated-electron materials • bulk • interfaces outline B. Keimer Max-Planck-Institute for Solid State Research

2. Neutron scattering neutron E1 q1 excitation: E= E2-E1 q=q2-q1 E2 q2 interaction strong (nuclear) interaction elastic lattice structure inelastic lattice dynamics magnetic (dipole-dipole) interaction elastic magnetic structure inelastic magnetic excitations

3. Neutron sources neutron flux Maxwellian profile energy ~ 30 meV spectrum example research reactor FRM-II Garching, Germany

4. Elastic neutron scattering

5. Elastic neutron scattering

6. Elastic nuclear neutron scattering Bragg peaks at reciprocal lattice vectors K scattering length b ~ size of nucleus ~ 10-15 m

7. Neutron radiography mass attenuation coefficient

8. Neutron radiography

9. Elastic magnetic neutron scattering

10. Elastic magnetic neutron scattering

11. Elastic magnetic neutron scattering one electron “classical electron radius” non-spin-flip average for unpolarized beam σzσx , σy spin-flip (not possible for nuclear scattering)

12. Elastic magnetic neutron scattering one atom approximated as magnetized sphere, magnetization density M(r)

13. Elastic magnetic neutron scattering magnetic reciprocal lattice vectors generalization for collinear magnets Bragg peaks magnetic structure factor polarization factor

14. Neutron diffractometer single crystal powder

15. Example one-dimensional ferromagnet use interference between nuclear and magnetic scattering to create spin-polarized neutrons (up to prefactors)

16. Example one-dimensional antiferromagnet

17. Example vortex lattice in type-II superconductor small-angle neutron scattering

18. Example vortex lattice in type-II superconductor structural phase transition in vortex lattice H ~ Hc1: electrodynamic interaction between flux lines H ~ Hc2: vortex cores overlap structure depends onsuperconductingcoherence length

19. Inelastic neutron scattering elastic cross section inelastic cross section inelastic nuclear neutron scattering initial, final state of sample energy of excitation created by neutron in sample partition function

20. Inelastic nuclear neutron scattering thermal average characterized by population ns of phonons of energy in branch s Debye-Waller factor due to thermal lattice vibrations K) K)} phonon creation neutron energy loss phonon annihilaion neutron energy gain

21. Triple-axis spectrometer analyzer detector sample monochromator

22. Triple-axis spectrometer TRISP at FRM-II

23. Example C60 typical inelastic nuclear scattering scans with a triple-axis spectrometer lattice structure

24. Example C60 fcc lattice at room temperature molecules rotate freely molecules “lock in“ at low temperatures unit cell becomes larger new optical phonon modes appear

25. Inelastic magnetic neutron scattering Heisenberg antiferromagnet, magnon creation Km) Km, a = 0, 1 q, Km itinerant electrons  next lecture polarization factor spin-spin correlation function

26. Example molecular magnetism Mn12 acetate molecule energy levels inelastic magnetic neutron scattering intensity Mn atoms

27. X-ray sources: tube setup spectrum

28. X-ray sources: synchrotron synchrotron primary spectrum insertion devices: wiggler, undulator

29. X-ray sources: synchrotron ESRF Grenoble, France

30. Interaction of x-rays with matter

31. Thompson scattering – one electron

32. Thompson scattering – one electron differential cross section: one electron

33. Thompson scattering – one atom approximated as charged sphere, charge density ρ(r) atomic form factor × (polarization factor)

34. Thompson scattering – crystal lattice equilibrium positions thermal vibrations + … expansion of Debye-Waller factor Bragg reflections at reciprocal lattice vectors K thermal diffuse scattering

35. Inelastic x-ray scattering triple-axis spectrometer photon energy ~ 10 keV phonon energy ~ 10 meV  resolution ΔE/E < 10-7 required

36. Inelastic x-ray scattering ID-16 ESRF Grenoble, France

37. Example MgB2 B vibration • - modulates Fermi surface • drives superconductivity (Tc = 39 K) IXS data

38. X-ray absorption interaction Hamiltonian absorption photon annihilated scattering photon number conserved absorption cross section

39. X-ray absorption mass absorption coefficient

40. X-ray absorption edges

41. Example K-edge transitions into continuum absorption cross section

42. Example Fe L-edge valence state chemical analysis example Fe thin film example TbFeCo alloy

43. X-ray radiography dual-energy x-ray radiography discriminate between carbohydrates and metals

44. X-ray absorption fine structure

45. Example K-edge selection rules transition into unoccupied excited state electric dipole matrix element

46. Example vanadium K-edge

47. Magnetic circular dichroism example single atom electric dipole selection rules

48. Magnetic circular dichroism

49. Magnetic circular dichroism classical calculation for bound electron analogous to Thompson scattering

50. Magnetic circular dichroism circular birefringence index of refraction circular dichroism absorption coefficient