Spin-orbit coupling in three-orbital Kanamori impurity model and its relevance for transition-metal oxides

TL;DR

This paper studies how spin-orbit coupling affects a three-orbital impurity model relevant to transition-metal oxides, revealing three regimes with distinct physical properties and a crossover scale influenced by electronic correlations.

Contribution

It identifies three regimes of impurity behavior under spin-orbit coupling in a three-orbital model and links the crossover scale to the orbital Kondo temperature, highlighting relevance for correlated oxides.

Findings

Three regimes: Hund's impurity, Van Vleck non-magnetic, and J=2 impurity.

Crossover scale (lambda_c) equals the orbital Kondo temperature T_K^orb.

Stronger correlations lower the crossover scale, increasing SOC effects in oxides.

Abstract

We investigate the effects of the spin-orbit coupling (SOC) in a three-orbital impurity model with Kanamori interaction using the numerical renormalization group method. We focus on the impurity occupancy $N_d=2$ relevant to the dynamical mean-field theory studies of Hund's metals. Depending on the strength of SOC $\lambda$ we identify three regimes: usual Hund's impurity for $|\lambda|<\lambda_c$, van-Vleck non-magnetic impurity for $\lambda > \lambda_c$, and a $J=2$ impurity for $\lambda < -\lambda_c$. They all correspond to a Fermi liquid but with very different quasiparticle phase shifts and different physical properties. The crossover between these regimes is controlled by an emergent scale, the orbital Kondo temperature, $\lambda_c =T_K^\mathrm{orb}$ that drops with increasing interaction strength. This implies that oxides with strong electronic correlations are more prone to the effects of the spin-orbit coupling.