Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals

TL;DR

This paper explores the complex magnetic phases of the honeycomb-lattice Heisenberg-Kitaev model under an external magnetic field, revealing vortex-crystal phases and metamagnetic transitions through simulations and theory.

Contribution

It provides a detailed classical phase diagram of the model in magnetic fields, identifying novel vortex-crystal and multi-Q phases not previously characterized.

Findings

Identification of vortex-crystal phase in [111] magnetic field direction

Complex sequences of phases and metamagnetic transitions

Quantum corrections analyzed in high-field phase

Abstract

The Heisenberg-Kitaev model is a paradigmatic model to describe the magnetism in honeycomb-lattice Mott insulators with strong spin-orbit coupling, such as A$_2$IrO$_3$ (A = Na, Li) and $\alpha$-RuCl$_3$. Here we study in detail the physics of the Heisenberg-Kitaev model in an external magnetic field. Using a combination of Monte-Carlo simulations and spin-wave theory we map out the classical phase diagram for different directions of the magnetic field. Broken SU(2) spin symmetry renders the magnetization process rather complex, with sequences of phases and metamagnetic transitions. In particular, we find various large-unit-cell and multi-Q phases including a vortex-crystal phase for a field in the [111] direction. We also discuss quantum corrections in the high-field phase.