Importance of anisotropic exchange interactions in honeycomb iridates. Minimal model for zigzag antiferromagnetic order in Na$_2$IrO$_3$

TL;DR

This paper explores the microscopic magnetic interactions in honeycomb iridates, emphasizing the importance of anisotropic Kitaev interactions, and demonstrates how these interactions can stabilize zigzag antiferromagnetic order in Na$_2$IrO$_3$.

Contribution

It introduces a minimal model including both isotropic and anisotropic interactions, highlighting the role of next-nearest neighbor Kitaev interactions in magnetic ordering.

Findings

Kitaev interactions are significant between next-nearest neighbors.

Zigzag antiferromagnetic order can be stabilized without third neighbor coupling.

The model explains the experimentally observed zigzag phase in Na$_2$IrO$_3$.

Abstract

In this work, we investigate the microscopic nature of the magnetism in honeycomb iridium-based systems by performing a systematic study of how the effective magnetic interactions in these compounds depend on various electronic microscopic parameters. We show that the minimal model describing the magnetism in A$_2$IrO$_3$ includes both isotropic and anisotropic Kitaev-type spin-exchange interactions between nearest and next-nearest neighbor Ir ions, and that the magnitude of the Kitaev interaction between next-nearest neighbor Ir magnetic moments is comparable with nearest neighbor interactions. We also find that, while the Heisenberg and the Kitaev interactions between nearest neighbors are correspondingly antiferro- and ferromagnetic, they both change sign for the next-nearest neighbors. Using classical Monte Carlo simulations we examine the magnetic phase diagram of the derived super-exchange model. Zigzag-type antiferromagnetic order is found to occupy a large part of the phase diagram of the model and, for ferromagnetic next-nearest neighbor Heisenberg interaction relevant for Na$_2$IrO$_3$, it can be stabilized even in the absence of third nearest neighbor coupling. Our results suggest that a natural physical origin of the zigzag phase experimentally observed in Na$_2$IrO$_3$ is due to the interplay of the Kitaev anisotropic interactions between nearest and next-nearest neighbors.