Motivated by recent experiments of a novel $5d$ Mott insulator in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, 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 an on-site Coulomb interaction $U$ as well as $\lambda$. It is found that the transition from a paramagnetic metal to an antiferromagnetic insulator occurs at a finite $U=U_{\mathrm{MI}}$, which is greatly reduced by a large $\lambda$, characteristic of $5d$ 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 antiferromagnetic order. We have further studied the one-particle excitations by 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 ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$.

• Received 9 September 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.216410