# Observation of spin-orbit excitations and Hund's multiplets in Ca$_2$RuO$_4$

## TL;DR

This study uses Ru L3-edge RIXS to analyze the electronic structure of Ca$_2$RuO$_4$, revealing spin-orbit excitations and Hund's multiplets, and providing key interaction parameters for modeling its magnetic properties.

## Contribution

First direct measurement of spin-orbit and Hund's interactions in Ca$_2$RuO$_4$ using RIXS, linking spectral features to fundamental electronic interactions.

## Key findings

- Identification of a 320 meV spin-orbit excitation
- Observation of Hund's-rule driven spin-state transitions at 750 and 1000 meV
- Quantitative determination of spin-orbit coupling, crystal-field, and Hund's interaction parameters

## Abstract

We use Ru $L_3$-edge (2838.5 eV) resonant inelastic x-ray scattering (RIXS) to quantify the electronic structure of Ca$_2$RuO$_4$, a layered $4d$-electron compound that exhibits a correlation-driven metal-insulator transition and unconventional antiferromagnetism. We observe a series of Ru intra-ionic transitions whose energies and intensities are well described by model calculations. In particular, we find a $\rm{J}=0\rightarrow 2$ spin-orbit excitation at 320 meV, as well as Hund's-rule driven $\rm{S}=1\rightarrow 0$ spin-state transitions at 750 and 1000 meV. The energy of these three features uniquely determines the spin-orbit coupling, tetragonal crystal-field energy, and Hund's rule interaction. The parameters inferred from the RIXS spectra are in excellent agreement with the picture of excitonic magnetism that has been devised to explain the collective modes of the antiferromagnetic state. $L_3$-edge RIXS of Ru compounds and other $4d$-electron materials thus enables direct measurements of interactions parameters that are essential for realistic model calculations.