Results

1
Theory of resonant inelastic X-ray scattering
L.J.P. Ament, F. Forte, J. van den Brink
Instituut-Lorentz, Universiteit Leiden, P.O. Box
9506, 2300 RA Leiden, The Netherlands
Abstract
The cross section for indirect resonant inelastic
X-ray scattering (RIXS) on the K-edge of
transition metal ions is derived. It turns out to
be a linear combination of the charge response
function and the dynamic longitudinal spin
density function. This result is asymptotically
exact for both strong and weak local core-hole
potentials and constitutes a smooth interpolation
in between these limits. The relative charge and
spin contribution to the inelastic spectral
weight can be changed by varying the incident
photon energy.
cond-mat/0609767
Results
RIXS
Core electron is excited Core-hole excited
electron induce potential Fermi-surface
electrons interact with this potential After a
short time relaxation
Spinless fermions
(T 0 K)
See below!
Density correlation function,
Spin-1/2 fermions
Dynamic longitudinal spin correlation function
Simplest case spinless fermions
They interact with the core-hole
P1,2 practically T-independent! T-dependence in
structure factors.
No monopole due to local exciton interaction
drops off rapidly. Approximate
Cross section is given by Kramers-Heisenberg
formula1
Adjust detuning ?in to see either spin or charge
correlation!
Multi-band systems. Example transition metal
with 3d and 4s band.
with
Scattering amplitude
Energy conservation

• Various scattering cross sections are expressed
  in terms of the dynamical charge and spin
  correlation functions. These are exact for strong
  and weak core-hole potentials U.
• The resonant prefactors are weakly temperature
  dependent.
• On the basis of our results, the charge and spin
  structure factor of e.g. Hubbard-like model
  Hamiltonians can be directly compared to the
  experimental RIXS spectra.

Intermediate states are short-lived energy
broadening ? is large, thus many intermediate
states can be reached. Use spectral
decomposition (after some manipulations) to
obtain an exact solution for both strong and weak
U.
1 H.A. Kramers and W. Heisenberg, Z. Phys. 31,
681 (1925)