Doping-dependent bandwidth renormalization and spin-orbit coupling in (Sr$_{1-x}$La$_x$)$_2$RhO$_4$

TL;DR

This study uses advanced computational methods to analyze how doping affects bandwidth and spin-orbit coupling in (Sr$_{1-x}$La$_x$)$_2$RhO$_4$, revealing that correlations weaken with doping and influence magnetic properties.

Contribution

It demonstrates that electronic correlations do not enhance spin-orbit splitting as previously thought, and clarifies the doping-dependent electronic and magnetic behavior of the material.

Findings

Electronic correlations do not significantly enhance spin-orbit splitting.

Doping increases quasiparticle bandwidth, reducing correlation effects.

The material transitions from a weakly correlated metal to an itinerant ferromagnet around x=0.2.

Abstract

We investigate the electronic structure of (Sr$_{1-x}$La$_x$)$_2$RhO$_4$ using a combination of the density functional and dynamical mean-field theories. Unlike the earlier local density approximation plus Hubbard $U$ (LDA+U) studies, we find no sizable enhancement of the spin-orbit splitting due to electronic correlations and show that such an enhancement is a spurious effect of the static mean-field approximation of the LDA+U method. The electron doping suppresses the importance of electronic correlations, which is reflected in quasi-particle bandwidth increasing with $x$. (Sr$_{1-x}$La$_x$)$_2$RhO$_4$ can be classified as weakly correlated metal, which becomes an itinerant in-plane ferromagnet (but possibly A-type antiferromagnet) due to Stoner instability around $x=0.2$.