Unified theory of spiral magnetism in the harmonic-honeycomb iridates {\alpha}, {\beta}, {\gamma} Li2IrO3

TL;DR

This paper presents a unified theoretical framework explaining the spiral magnetic order observed in various Li2IrO3 iridates, based on a specific set of Kitaev-Heisenberg-Ising interactions, and predicts magnetic order in the alpha phase.

Contribution

It introduces a minimal model with Kitaev-Heisenberg-Ising interactions that explains the common spiral magnetic order across different Li2IrO3 polytypes and predicts magnetic behavior in the alpha phase.

Findings

The same triplet of interactions reproduces spiral order in beta and gamma polytypes.

Kitaev interaction stabilizes counter-rotating spiral magnetic order.

Model predicts magnetic order in alpha-Li2IrO3.

Abstract

A family of insulating iridates with chemical formula Li$_2$IrO$_3$ has recently been discovered, featuring three distinct crystal structures $\alpha,\beta,\gamma$ (honeycomb, hyperhoneycomb, stripyhoneycomb). Measurements on the three-dimensional polytypes, $\beta$- and $\gamma$-Li$_2$IrO$_3$, found that they magnetically order into remarkably similar spiral phases, exhibiting a non-coplanar counter-rotating spiral magnetic order with equivalent q=0.57 wavevectors. We examine magnetic Hamiltonians for this family and show that the same triplet of nearest-neighbor Kitaev-Heisenberg-Ising (KJI) interactions reproduces this spiral order on both $\beta,\gamma$-Li$_2$IrO$_3$ structures. We analyze the origin of this phenomenon by studying the model on a 1D zigzag chain, a structural unit common to the three polytypes. The zigzag-chain solution transparently shows how the Kitaev interaction stabilizes the counter-rotating spiral, which is shown to persist on restoring the inter-chain coupling. Our minimal model makes a concrete prediction for the magnetic order in $\alpha$-Li$_2$IrO$_3$.