Effect of broken symmetry on resonant inelastic x-ray scattering from undoped cuprates

TL;DR

This paper investigates how broken symmetry in undoped cuprates affects resonant inelastic x-ray scattering spectra, revealing anisotropic contributions that enhance spectral intensities near zero momentum transfer, supported by theoretical and numerical analysis.

Contribution

It introduces a new theoretical framework accounting for anisotropic effects in RIXS spectra due to symmetry breaking, extending previous models beyond the fast collision approximation.

Findings

Anisotropic terms significantly enhance spectral intensity at zero momentum transfer.

Derived explicit expressions for RIXS scattering amplitudes including anisotropic contributions.

Numerical calculations support the presence of anisotropic effects in two-dimensional spin systems.

Abstract

We study the magnetic excitation spectra of resonant inelastic x-ray scattering (RIXS) at the $L$-edge from undoped cuprates beyond the fast collision approximation. We analyse the effect of the symmetry breaking ground state on the RIXS process of the Heisenberg model by using a projection procedure. We derive the expressions of the scattering amplitude in both one-magnon and two-magnon excitation channels. Each of them consists of the isotropic and anisotropic contributions. The latter is a new finding and attributed to the long range order of the ground state. The presence of anisotropic terms is supported by numerical calculations on a two-dimensional spin cluster. We express the RIXS spectra in the form of spin-correlation functions with the coefficients evaluated on the cluster, and calculate the function in a two dimensional system within the $1/S$ expansion. Due to the anisotropic terms, the spectral intensities are considerably enhanced around momentum transfer $\textbf{q}=0$ in both one-magnon and two-magnon excitation channels. This finding may be experimentally confirmed by examining carefully the $\textbf{q}$-dependence of the spectra.