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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