Spin-Orbit Integrated Ground State and Magnetic Anisotropy in Sr${}_2$IrO${}_4$

Abstract

We present a microscopic model for the anisotropic exchange interactions in Sr${}_2$IrO${}_4$. A direct construction of Wannier functions from first-principles calculations proves the $j_{\mathrm{eff}}$=1/2 character of the spin-orbit integrated states at the Fermi level. An effective $j_{\mathrm{eff}}$-spin Hamiltonian explains the observed weak ferromagnetism and anisotropy of antiferromagnetically ordered magnetic state, which arise naturally from the $j_{\mathrm{eff}}$=1/2 state with a rotation of IrO${}_6$ octahedra. It is suggested that Sr${}_2$IrO${}_4$ is a unique class of materials with effective exchange interactions in the spin-orbital Hilbert space.

5 pages, 3 figures