Ab initio modeling of resonant inelastic x-ray scattering from Ca2RuO4

TL;DR

This work develops and applies an ab initio, fully relativistic DFT-based framework (GGA+$U$ with SOC in a Dirac LMTO basis) to model RIXS at the Ru $L_3$ and O $K$ edges in Ca$_{2}$RuO$_{4}$. It reveals a SOC-induced $t_{2g}$ split into $J_{ m eff}=3/2$ and $J_{ m eff}=1/2$ manifolds, with a gap that emerges upon electronic correlations, consistent with a mixed Slater–Mott insulating character. The RIXS spectra, including intra-$t_{2g}$ and higher-energy transitions, are best reproduced with $U_{ m eff}=0.5$ eV, and the calculations capture polarization and incident-energy dependences, while indicating possible excitonic contributions not captured by one-particle theory. Overall, the study provides a rigorous, first-principles pathway to model and interpret RIXS in complex 4$d$ oxides and lays the groundwork for extending this approach to other correlated materials.

Abstract

The single-layered perovskite Ca$_2$RuO$_4$, characterized by a 4$d^4$ electron configuration, has been studied from first principles using density functional theory (DFT) using the generalized gradient approximation, with inclusion of strong on-site Coulomb interactions and spin-orbit coupling (GGA+SO+$U$), in the framework of the fully relativistic, spin-polarized Dirac linear muffin-tin orbital (LMTO) band-structure method. This approach enabled a comprehensive investigation of the electronic structure of Ca$_2$RuO$_4$ through the modeling of relevant spectra obtained from synchrotron-based techniques widely used to probe electronic properties, with a primary focus on resonant inelastic X-ray scattering (RIXS) at the Ru $L_3$ and O $K$ edges. The calculated spectra were thoroughly analyzed with available experimental data reported in the literature. The good agreement between our results and experimental observations for Ca$_2$RuO$_4$ enables a conclusive interpretation of key features in the spectra obtained from the aforementioned techniques. Consequently, this enables us to describe its electronic properties and to establish a solid theoretical approach suitable for routine modeling of spectra, particularly from RIXS, aimed at characterizing the electronic structure and properties of similar or more complex strongly correlated, technologically relevant materials.

Figures (14)

• Figure 1: (Color online) Schematic representation of the AFM structure of Ru ions (red arrows) in Ca$_2$RuO$_4$ (space group $pbca$, number 61). Grey spheres represent Ca atoms, blue and green spheres show oxygen atoms.
• Figure 2: (Color online) The $t_{2g}$ energy band structure of Ca$_2$RuO$_4$ calculated in the GGA approach without SOC for the FM ordering for the spin up (a) and spin down (b) states. The panel (c) shows the energy bands for the AFM ordering in the GGA approach. The panel (d) presents the fully relativistic Dirac GGA+SO approximation. The bands crossing the Fermi level which have almost pure $d_{5/2}$ character (open red circles) are formed by $t_{2g}$ states with $J_{\rm{eff}}$ = 1/2. The lower panel (e) presents the $t_{2g}$ energy bands calculated in the GGA+SO+$U$ approximation with $U_{\rm{eff}}$ = 0.5 eV for the canted noncollinear AFM ordering AFM$^{\rm{NC}}_{010}$.
• Figure 3: (Color online) The phase diagram in the $U_{\rm{eff}}-$SOC plane for Ca$_2$RuO$_4$ in comparison with Sr$_2$IrO$_4$AKB24a. The solid-circled lines separates metal and Mott insulator states connected via a first-order phase transition.
• Figure 4: (Color online) The ab initio energy band structure of Ca$_2$RuO$_4$ calculated in the GGA+SO+$U$ with $U_{\rm{eff}}$ = 0.5 eV approximation.
• Figure 5: (Color online) The partial density of states DOS [in states/(atom eV)] in Ca$_2$RuO$_4$ calculated in the GGA+SO+$U$ approximation ($U_{\rm{eff}}$ = 0.5 eV).