Spin-orbit coupling in three-orbital Kanamori impurity model and its relevance for transition-metal 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 $λ$ we identify three regimes: usual Hund's impurity for $|λ|<λ_c$, van-Vleck non-magnetic impurity for $λ> λ_c$, and a $J=2$ impurity for $λ< -λ_c$. 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, $λ_c =T_K^\mathrm{orb}$ 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.