Orbital Ordering and Resonant X-ray Scattering in Layered Manganites

TL;DR

This paper develops a theoretical framework for resonant x-ray scattering in layered manganites, elucidating how orbital and charge orderings influence scattering intensities through local and itinerant electron behaviors.

Contribution

It introduces a formulation of the atomic scattering factor considering both local Coulomb interactions and band effects, explaining polarization dependences in manganites.

Findings

Polarization dependence explained by local and itinerant 4p electron characters.

Formulation of scattering factor incorporating Coulomb and band effects.

Analysis of orbital ordered states in layered manganites.

Abstract

In layered manganites with orbital and charge orderings, the degeneracy of the Mn $4p$ orbitals as well as the $3d$ ones is lifted by the effects of the $4p$ bands and the local Coulomb interactions. We formulate the atomic scattering factor for the resonant x-ray scattering in the memory function method by taking into account these effects on an equal footing. It is shown that the polarization dependences of the scattering intensities at the orbital and charge superlattice reflections observed in LaSr$_{2}$Mn$_2$O$_7$ are caused by the local and itinerant characters of $4p$ electrons, respectively. We examine the type of the orbital ordered state.