Three-dimensional Stacking of Canted Antiferromagnetism and Pseudospin Current in Undoped Sr$_2$IrO$_4$: Symmetry Analysis and Microscopic Model Realization

TL;DR

This paper proposes a new magnetic and pseudospin current order in Sr$_2$IrO$_4$, explaining broken symmetries observed experimentally through symmetry analysis and a microscopic Hubbard model.

Contribution

It introduces a three-dimensional model showing how canted antiferromagnetism and pseudospin currents coexist, providing a microscopic basis for experimental symmetry-breaking observations.

Findings

Symmetry analysis reveals a magnetoelectric coexistence state.

Microscopic Hubbard model demonstrates realization of the state.

The model explains broken symmetries in Sr$_2$IrO$_4$.

Abstract

Recent optical second-harmonic generation experiments observed unexpected broken spatial symmetries in the undoped spin-orbit Mott insulator Sr$_2$IrO$_4$, leading to intensive debates on the nature of its ground state. We propose that it is a canted antiferromagnetism with a hidden order of circulating staggered pseudospin current. Symmetry analysis shows that a proper $c$-axis stacking of the canted antiferromagnetism and the pseudospin current lead to a magnetoelectric coexistence state that breaks the two-fold rotation, inversion, and time-reversal symmetries, consistent with experimental observations. We construct a three-dimensional Hubbard model with spin-orbit coupling for the five localized 5$d$ Wannier orbitals centered at Ir sites, and demonstrate the microscopic realization of the desired coexistence state in a wide range of band parameters via a combination of self-consistent Hartree-Fock and variational calculations.