Magnetic structure and excitation spectrum of the hyperhoneycomb Kitaev magnet $\beta$-Li$_2$IrO$_3$

TL;DR

This paper provides a theoretical analysis of the magnetic structure and excitation spectrum of the hyperhoneycomb Kitaev magnet $eta$-Li$_2$IrO$_3$, identifying signatures of dominant interactions through neutron-scattering predictions.

Contribution

It introduces a minimal $J$-$K$-$ extGamma$ model to explain the incommensurate magnetic order and computes distinctive excitation spectra for different interaction regimes.

Findings

Distinct neutron-scattering fingerprints for $K$- and $ extGamma$-dominant states.

Qualitative understanding of incommensurate order via a long-wavelength twist of a period-3 state.

Different structures emerge depending on whether $K$ or $ extGamma$ dominates.

Abstract

We present a theoretical study of the static and dynamical properties of the Kitaev magnet $\beta$-Li$_2$IrO$_3$ based on the minimal $J$-$K$-$\Gamma$ model. We argue that the incommensurate magnetic order of $\beta$-Li$_2$IrO$_3$ can be qualitatively understood in terms of a long-wavelength twisting of a nearby commensurate, period-3 state, that shares the same symmetry, propagation vector, counter-rotation of the two spin sublattices, and non-coplanarity. This period-3 state shows very different structure when either the Kitaev interaction $K$ or the off-diagonal exchange anisotropy $\Gamma$ is dominant, featuring in particular ferromagnetic or antiferromagnetic spin dimers, respectively. We compute the magnon excitation spectra and the dynamical spin structure factor for both structures. The results for the momentum and energy dependence of the neutron-scattering intensity provide distinctive qualitative and quantitative fingerprints of the $K$-dominant or $\Gamma$-dominant states and thus gives additional information on the relative strength of these interactions in $\beta$-Li$_2$IrO$_3$.