Resonant inelastic x-ray scattering studies of elementary excitations
Ament, L.J.P.
Citation
Ament, L. J. P. (2010, November 11). Resonant inelastic x-ray scattering studies of elementary excitations. Casimir PhD Series. Retrieved from https://hdl.handle.net/1887/16138
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Resonant Inelastic X-ray Scattering Studies of Elementary Excitations
Luuk Ament
ii
Resonant Inelastic X-ray Scattering Studies of Elementary Excitations
P R O E F S C H R I F T
ter verkrijging van
de graad van Doctor aan de Universiteit Leiden,
op gezag van Rector Magnificus prof. mr. P. F. van der Heijden, volgens besluit van het College voor Promoties
te verdedigen op donderdag 11 november 2010 klokke 13.45 uur
door
Lucas Johannes Peter Ament
geboren te Winterswijk in 1982
Promotiecommissie:
Promotor: prof. dr. J. van den Brink
Overige leden: prof. dr. J. P. Hill (Brookhaven National Laboratory) prof. dr. J. M. van Ruitenbeek (Universiteit Leiden) prof. dr. C. W. J. Beenakker (Universiteit Leiden) prof. dr. M. A. van Veenendaal (Argonne Nat. Lab. &
Northern Illinois University) prof. dr. G. Ghiringhelli (Politecnico di Milano)
ISBN 978-90-8593-087-7
Casimir PhD Series, Delft-Leiden 2010-25
The research presented in this thesis was supported by FOM.
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Contents
1 Introduction 1
1.1 Resonant Inelastic X-ray Scattering (RIXS) . . . 1
1.2 Excitations of strongly correlated systems . . . 9
1.3 This thesis . . . 11
2 Theory of Resonant Inelastic X-ray Scattering 13 2.1 Introduction . . . 13
2.2 Electron-photon coupling . . . 14
2.3 Kramers-Heisenberg equation . . . 20
2.4 Direct and Indirect RIXS . . . 26
2.5 Ultra-short core hole lifetime expansion . . . 28
3 Charge excitations 31 3.1 Introduction . . . 31
3.2 UCL approach to charge scattering . . . 32
3.3 Corrections to the cross section for strong core hole potentials . . . 48
3.4 Polarization dependence of transition metal K edge RIXS . . . 50
3.5 Comparison to experiments . . . 52
4 Magnetic RIXS on 2D cuprates 53 4.1 Introduction . . . 53
4.2 Theory of magnetic excitations . . . 55
4.3 Magnetic RIXS scattering amplitude . . . 60
4.4 Copper K edge . . . 64
4.5 Copper L edge . . . 80
4.6 Copper L edge of doped cuprates . . . 93
4.7 Oxygen K edge . . . 98
4.8 Two-magnon screening of holes in the t-J model probed by angle- resolved photoemission . . . 106
vi CONTENTS
5 Orbital RIXS 115
5.1 Introduction . . . 115
5.2 Theory . . . 116
5.3 RIXS spectra of 2D eg systems . . . 119
5.4 RIXS spectra of YTiO3 . . . 126
6 RIXS in systems with strong spin-orbit coupling 151 6.1 Introduction . . . 151
6.2 Theory of Sr2IrO4 . . . 153
6.3 Iridium L edge cross section . . . 156
7 Phonon RIXS 171 7.1 Introduction . . . 171
7.2 Electron-phonon coupling . . . 173
7.3 RIXS cross section for phonons . . . 175
7.4 dd excitations dressed by phonons . . . 181
7.5 Conclusions . . . 183
8 Outlook – X-ray Free Electron Lasers 185 8.1 Bosonic enhancement in an XFEL . . . 186
8.2 X-ray scattering with an XFEL . . . 186
Appendices 191 A QED 191 A.1 HΨ to second order . . . 191
A.2 HΨ to third order . . . 192
B YTiO3 197 B.1 RIXS – Single site processes . . . 197
B.2 Multiplet factors . . . 198
B.3 The operators ˆΓ in terms of orbitons . . . 199
B.4 RIXS – two-site processes with superexchange model . . . 201
C Phonon RIXS 203 D Magnetic spectral weight at the Γ point in 2D cuprates 205 D.1 H¯eff(4) to fourth order in t/U . . . 205
D.2 Scattering amplitude to fourth order in t/U . . . 210
Bibliography 213
Samenvatting 227
Publications 231
CONTENTS vii
Curriculum vitae 233
viii CONTENTS
