# Two-magnon excitations in resonant inelastic x-ray scattering studied by spin-density-wave formalism

## TL;DR

This paper models two-magnon excitations in RIXS at the transition-metal K-edge using a Hubbard-type model and SDW formalism, providing results that align well with experiments and revealing new spectral features.

## Contribution

It introduces a Hubbard-type $d$-$p$ model combined with SDW formalism for RIXS, offering a more detailed approach than previous Heisenberg models.

## Key findings

- Calculated RIXS spectra match experimental momentum dependence.
- Spectra show large two-magnon weight near the zone center.
- Differences from Heisenberg models suggest new experimental tests.

## Abstract

We study two-magnon excitations in resonant inelastic x-ray scattering (RIXS) at the transition-metal $K$-edge. Instead of working with effective Heisenberg spin models, we work with a Hubbard-type model ($d$-$p$ model) for a typical insulating cuprate La$_2$CuO$_4$. For the antiferromagnetic ground state within the spin-density-wave (SDW) mean-field formalism, we calculate the dynamical correlation function within the random-phase approximation (RPA), and then obtain two-magnon excitation spectra by calculating the convolution of it. Coupling between the $K$-shell hole and the magnons in the intermediate state is calculated by means of diagrammatic perturbation expansion in the Coulomb interaction. Calculated momentum dependence of RIXS spectra agrees well with that of experiments. A notable difference from previous calculations based on the Heisenberg spin models is that RIXS spectra have a large two-magnon weight near the zone center, which may be confirmed by further careful high-resolution experiments.