Microscopic study of spin-orbit-induced Mott insulator in Ir oxides

TL;DR

This paper investigates how strong spin-orbit coupling in 5d iridates leads to a novel Mott insulating state, using a three-orbital Hubbard model and variational methods to match experimental findings.

Contribution

It provides a detailed theoretical analysis of the spin-orbit-induced Mott insulator in Sr$_2$IrO$_4$, highlighting the role of spin-orbit coupling and Hund's coupling in stabilizing the phase.

Findings

Transition from paramagnetic metal to AF insulator at finite U

Large spin-orbit coupling reduces the critical U for insulating behavior

Electronic structure analysis aligns with experimental observations

Abstract

Motivated by recent experiments of a novel 5$d$ Mott insulator in Sr$_2$IrO$_4$, we have studied the two-dimensional three-orbital Hubbard model with a spin-orbit coupling $\lambda$. The variational Monte Carlo method is used to obtain the ground state phase diagram with varying a on-site Coulomb interaction $U$ as well as $\lambda$. It is found that the transition from a paramagnetic metal to an antiferromagnetic (AF) insulator occurs at a finite $U=U_{\mathrm{MI}}$, which is greatly reduced by a large $\lambda$, characteristic of 5$d$ electrons, and leads to the "spin-orbit-induced" Mott insulator. It is also found that the Hund's coupling induces the anisotropic spin exchange and stabilizes the in-plane AF order. We have further studied the one-particle excitations using the variational cluster approximation, and revealed the internal electronic structure of this novel Mott insulator. These findings are in agreement with experimental observations on Sr$_2$IrO$_4$, and qualitatively different from those of extensively studied 3$d$ Mott insulators.