Microscopic model realization of $\boldsymbol{d}$-wave pseudospin current order in Sr$_{\boldsymbol{2}}$IrO$_{\boldsymbol{4}}$

TL;DR

This paper develops a microscopic model for the $d$-wave pseudospin current order in Sr$_2$IrO$_4$, revealing how Coulomb interactions and anisotropy stabilize this hidden order and its coexistence with antiferromagnetism.

Contribution

It introduces a microscopic effective model incorporating Coulomb repulsion and anisotropy to explain the emergence and stability of $d$-wave pseudospin current order in Sr$_2$IrO$_4$.

Findings

$d$PSCO can be stabilized by Coulomb interactions and anisotropy.

Coexistence of $d$PSCO and antiferromagnetism leads to spin bond nematicity.

Doping can tune the coexistence and chirality of the orders.

Abstract

The $d$-wave pseudospin current order ($d$PSCO) with staggered circulating pseudospin current has been proposed as the hidden electronic order to describe the unexpected breaking of spatial symmetries in stoichiometric Sr$_{2}$IrO$_{4}$ and the unconventional pseudogap phenomena in electron doped Sr$_{2}$IrO$_{4}$. However, a microscopic model for the emergence of $d$PSCO is still lacking. The nearest neighbor Coulomb repulsion $V$, which is expected to be significant in Sr$_{2}$IrO$_{4}$ due to the large spatial extension of the Ir $5d$ orbitals, is capable of driving $d$PSCO on the mean-field level, albeit the latter is energetically degenerate to the staggered flux phase with circulating charge current. We find the in-plane anisotropy $\Gamma_2$ in the effective superexchange interaction between $J_\text{eff}={1\over 2}$ pseudospins, originating from the cooperative interplay between Hund's rule coupling and spin-orbit coupling of Ir $5d$ electrons, is able to lift the degeneracy and stabilize the pseudospin currents. The effective single-orbital model of $J_\text{eff}={1\over 2}$ electrons, including onsite Coulomb repulsion $U$, nearest neighbor Coulomb repulsion $V$, and the in-plane anisotropy $\Gamma_2$, is then studied. We obtain the mean-field ground states, analyze their properties, and determine the phase diagram of stoichiometric Sr$_{2}$IrO$_{4}$ in the plane spanned by $U$ and $V$ at a fixed $\Gamma_2$. We demonstrate the realization of $d$PSCO, and its competition and coexistence with antiferromagnetism. Remarkably, we find the coexistence of $d$PSCO and antiferromagnetism naturally leads to spin bond nematicity, with the spin directions of these three orders forming nontrivial chirality. Furthermore, we show that the emergence of the coexistent state and its chirality can be tuned by carrier doping.