Neutron and x-ray spectroscopy

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1 Neutron and x-ray spectroscopy B. Keimer Max-Planck-Institute for Solid State Research outline 1. self-contained introduction neutron scattering and spectroscopy x-ray scattering and spectroscopy 2. application to correlated-electron materials bulk interfaces

2 Neutron scattering neutron E 1 q 1 E 2 q 2 interaction excitation: E= E 2 -E 1 q=q 2 -q 1 strong (nuclear) interaction elastic lattice structure inelastic lattice dynamics magnetic (dipole-dipole) interaction elastic magnetic structure inelastic magnetic excitations

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

4 Elastic neutron scattering

5 Elastic neutron scattering

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

7 mass attenuation coefficient Neutron radiography

8 Neutron radiography

9 Elastic magnetic neutron scattering

10 Elastic magnetic neutron scattering

11 Elastic magnetic neutron scattering one electron classical electron radius σ z σ x, σ y non-spin-flip spin-flip (not possible for nuclear scattering) average for unpolarized beam

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

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

14 Neutron diffractometer powder single crystal

15 Example one-dimensional ferromagnet use interference between nuclear and magnetic scattering to create spin-polarized neutrons dσ ~ dω b 2 + ˆ η 2 + b ˆ η (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 ~ H c1 : electrodynamic interaction between flux lines H ~ H c2 : vortex cores overlap structure depends on superconducting coherence length

19 Inelastic neutron scattering elastic cross section dσ dω # of neutrons scattered into dω = (unit time) (incident flux) inelastic cross section dσ dedω # of neutrons scattered into dω = (unit time) (incident flux) (energy) 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 λ characterized by population n s of phonons of energy ω (k ) s 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 ω = ( k f ki ) 2m q = k k f i analyzer monochromator sample detector

22 Triple-axis spectrometer TRISP at FRM-II

23 Example C 60 lattice structure typical inelastic nuclear scattering scans with a triple-axis spectrometer

24 Example C 60 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 polarization factor spin-spin correlation function Heisenberg antiferromagnet, magnon creation ˆQηˆ a = 0, 1 q, K m K m ) K m, itinerant electrons next lecture

26 Example molecular magnetism Mn 12 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 photon energy ~ 10 kev phonon energy ~ 10 mev resolution ΔE/E < 10-7 required triple-axis spectrometer

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

37 Example MgB 2 B vibration - modulates Fermi surface - drives superconductivity (T c = 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 absorption cross section transitions into continuum

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

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

44 X-ray absorption fine structure

45 Example K-edge transition into unoccupied excited state selection rules 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 dichroism absorption coefficient μ f circular birefringence index of refraction n f

51 X-ray magnetic circular dichroism (XMCD) L-absorption edge of ferromagnet cobalt L-edge

52 Example GMR device Kortright et al., JMMM 207, 7 (1999)

53 Example GMR device Ni 0.8 Fe 0.2 Cu Co 3 2 Ni XMCD amplitude high resistance Co 1 low resistance Bonfim et al., PRL 86, 3646 (2001) H

54 XMCD microscopy

55 XMCD microscopy

56 Resonant x-ray scattering form factor

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