Proximate ferromagnetic state in the Kitaev model material $\alpha$-RuCl$_{3}$

TL;DR

This study reveals that $ ext{α}$-RuCl$_{3}$ is close to a ferromagnetic state and that its zigzag magnetic order is fragile, with quantum fluctuations stabilizing the zigzag phase amid competing ferromagnetic and Kitaev spin liquid states.

Contribution

The paper quantifies the spin Hamiltonian of $ ext{α}$-RuCl$_{3}$ and shows that its classical ground state is ferromagnetic, with zigzag order stabilized by quantum fluctuations, highlighting the proximity of multiple magnetic states.

Findings

The paramagnetic state shows broad magnetic excitation maxima at the zone center.

The classical Hamiltonian predicts a ferromagnetic ground state.

Zigzag order is stabilized by quantum 'order by disorder' mechanisms.

Abstract

$\alpha$-RuCl$_{3}$ is a major candidate for the realization of the Kitaev quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures indicates deviations from the Kitaev model. We have quantified the spin Hamiltonian of $\alpha$-RuCl$_{3}$ by a resonant inelastic x-ray scattering study at the Ru $L_{3}$ absorption edge. In the paramagnetic state, the quasi-elastic intensity of magnetic excitations has a broad maximum around the zone center without any local maxima at the zigzag magnetic Bragg wavevectors. This finding implies that the zigzag order is fragile and readily destabilized by competing ferromagnetic correlations. The classical ground state of the experimentally determined Hamiltonian is actually ferromagnetic. The zigzag state is stabilized via a quantum "order by disorder" mechanism, leaving ferromagnetism -- along with the Kitaev spin liquid -- as energetically proximate metastable states. The three closely competing states and their collective excitations hold the key to the theoretical understanding of the unusual properties of $\alpha$-RuCl$_{3}$ in magnetic fields.