Unraveling Orbital Correlations with Magnetic Resonant Inelastic X-Ray Scattering

Abstract

Although orbital degrees of freedom are a factor of fundamental importance in strongly correlated transition metal compounds, orbital correlations and dynamics remain very difficult to access, in particular by neutron scattering. Via a direct calculation of scattering amplitudes we show that instead magnetic resonant inelastic x-ray scattering (RIXS) does reveal orbital correlations. In contrast to neutron scattering, the intensity of the magnetic excitations in RIXS depends very sensitively on the symmetry of the orbitals that spins occupy and on photon polarizations. We show in detail how this effect allows magnetic RIXS to distinguish between alternating orbital ordered and ferro-orbital (or orbital liquid) states.

Using RIXS to Uncover Elementary Charge and Spin Excitations

“…In the cross-polarized channel, we have shown that on a qualitative level, Cu L-edge RIXS line shapes correspond to the spin dynamical structure factor Sðq; ωÞ, consistent with lowest-order approximations as postulated by the fast collision approximation (or the effective operator approach) [24,27,31,32] (see Appendix E). As a consequence, we expect that the line shapes reported from cross-polarized RIXS experiments can be reproduced to some extent by theoretical modeling of the spin dynamical structure factors (or empirically through inelastic neutron scattering experiments when also considering differences in the effective matrix elements between the two techniques).…”

“…However, this semiempirical connection to the spin dynamical structure factor has been based primarily on approximate theoretical and numerical treatments for the full RIXS cross section. The fast collision approximation [28][29][30] and the effective operator approach [31] suggested that only single magnon excitations or Sðq; ωÞ should be measured by RIXS at the Cu L edge [27,31,32]. More sophisticated treatments-the ultrashort core-hole lifetime (UCL) expansion [33][34][35] and the UCL-inspired ansatz [36]-highlighted that RIXS should also be sensitive to bimagnon excitations.…”

“…First, the fast collision approximation (or the effective operator approach) [27,31,32] relies on an estimation of the dynamics only at the site where the core hole has been created in the intermediate state. However, the intermediate state is drawn from a manifold of states, which differ from the ground state not only locally, at the site where a core hole is created, but also on neighboring sites due to hopping or spin exchange associated with the dynamical screening process.…”

Directly Characterizing the Relative Strength and Momentum Dependence of Electron-Phonon Coupling Using Resonant Inelastic X-Ray Scattering

“…One can show that such a resonance approximation for the 2p propagator (which neglects the contributions from other edges) works well for RIXS at either the Cu L 2 or L 3 edge [31,32]. As shown in these references and by a number of other recent works, the effect of the core hole does make qualitative changes to the overall resonance profile of RIXS.…”

“…Moreover, we are solely interested in the RIXS transitions for which the spin of the 3d electrons is conserved: This is possible when choosing a particular combination of the polarization vectors e i and e f [31,[34][35][36][37]. Thus, assuming that the latter indeed takes place, we can neglect the spin quantum number carried by the 3d electron, and we are left with the dipole matrix elements that depend solely on the 2p orbital quantum number: d 2pα;3dβ ≡ d 2pα;3d , where α ¼ x, y.…”