Magnetic Resonant X-Ray Scattering in KCuF3

TL;DR

This study uses ab initio calculations to analyze magnetic resonant x-ray scattering in KCuF3, revealing the importance of spin-orbit interaction and lattice distortion in the observed spectra.

Contribution

It demonstrates that the RXS intensity arises from orbital polarization in 4p states due to spin-orbit interaction and shows the dominant role of lattice distortion over 3d orbital order.

Findings

Finite RXS intensity on magnetic superlattice spots due to SOI.

RXS intensity on orbital spots increases with Jahn-Teller distortion.

Orbital spot intensity mainly controlled by lattice distortion, not 3d orbital order.

Abstract

We study the magnetic resonant x-ray scattering (RXS) spectra around the $K$ edge of Cu in KCuF$_3$ on the basis of an {\em ab initio} calculation. We use the full-potential linearlized augmented plane wave method in the LDA$+U$ scheme, and introduce the lattice distortion as inputs of the calculation. We obtain finite intensity on magnetic superlattice spots, about three orders of magnitude smaller than on orbital superlattice spots, by taking account of the spin-orbit interaction (SOI). No intensity appears without the SOI, indicating that the intensity arises not from the spin polarization but from the orbital polarization in $4p$ states. The present calculation reproduces well the experimental spectra as functions of photon energy and of azimuthal angle. We also calculate the RXS intensity on orbital superlattice spots. It is found that the intensity increases with increasing Jahn-Teller distortion. The spectra remain nearly the same in the nonmagnetic state given by the simple LDA, in which the orbital polarization in the 3d states is much smaller. This strongly suggests that the intensity on orbital spots is mainly controlled by the lattice distortion, not by the 3d orbital order itself.