Hund's coupling and spin-orbit interaction in the three-band Hubbard model: Anomalous mass renormalization in Sr2RuO4

Abstract

We study electronic correlation effects in the three-band Hubbard model in presence of Hund's and spin-orbit couplings using slave-spin mean-field theory. We consider three different regimes of hopping parameter values for the model on a square lattice. For orbital diagonal and isotropic hopping, we show that spin-orbit coupling (SOC), in general, enhances electronic correlations via the reduction of orbital degeneracy. In presence of Hund's coupling $J$, SOC tends to oppose the effect of $J$ on electronic correlations. Considering symmetry allowed anisotropic hopping, we find that the quasiparticle weights become orbital selective in presence of interaction. The effect of $J$ is particularly interesting for the band filling of two particles per site. Here, the Janus-faced effect of $J$ on correlation is obtained only in the narrower band, whereas electronic correlation in the wider band get reduced by $J$ for all values of Hubbard repulsion $U$. For model parameters corresponding to ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, interestingly, we find that the mass renormalizations in the bands become anomalous in presence of strong $U$ and $J$. The effective mass enhancement in the wider band becomes greater compared to that in the narrower band. We show that it originates in the peculiar electronic band structure of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, in which the spinon Fermi surface topology changes in a particular way in the presence of interactions.