Stability of the Antiferromagnetic State in the Electron Doped Iridates

TL;DR

This paper investigates why the antiferromagnetic state remains stable in electron-doped iridates despite expectations of destruction from doping, using a Hubbard model with third-neighbor interactions to explain experimental observations.

Contribution

It introduces a phase diagram based on a Hubbard model that accounts for third-neighbor interactions, explaining the stability of AFM in doped iridates.

Findings

AFM state persists beyond half-filling in doped iridates.

Third-neighbor interactions are crucial for Fermi surface description.

Phase diagram predicts stability regions matching experiments.

Abstract

Iridates such as Sr$_2$IrO$_4$ are of considerable interest owing to the formation of the Mott insulating state driven by a large spin-orbit coupling. However, in contrast to the expectation from the Nagaoka Theorem that a single doped hole or electron destroys the anti-ferromagnetic (AFM) state of the half-filled Hubbard model in the large U limit, the anti-ferromagnetism persists in the doped Iridates for a large dopant concentration beyond half-filling. With a tight-binding description of the relevant J$_{\rm eff}$ = 1/2 states by the third-neighbor ($t_1$, $t_2$, $t_3$, $U$) Hubbard model on the square lattice, we examine the stability of the AFM state to the formation of a spin spiral state in the strong coupling limit. The third-neighbor interaction $t_3$ is important for the description of the Fermi surface of the electron doped system. A phase diagram in the parameter space is obtained for the regions of stability of the AFM state. Our results qualitatively explain the robustness of the AFM state in the electron doped iridate (such as Sr$_{2-x}$La$_x$IrO$_4$), observed in many experiments, where the AFM state continues to be stable until a critical dopant concentration.