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Recent optical second-harmonic generation experiments observed unexpectedbroken spatial symmetries in the undoped spin-orbit Mott insulatorSr$_2$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 ofcirculating staggered pseudospin current. Symmetry analysis shows that a proper$c$-axis stacking of the canted antiferromagnetism and the pseudospin currentlead to a magnetoelectric coexistence state that breaks the two-fold rotation,inversion, and time-reversal symmetries, consistent with experimentalobservations. We construct a three-dimensional Hubbard model with spin-orbitcoupling for the five localized 5$d$ Wannier orbitals centered at Ir sites, anddemonstrate the microscopic realization of the desired coexistence state in awide range of band parameters via a combination of self-consistent Hartree-Fockand variational calculations.

physical review. b./physical review. b

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