Kitaev-Heisenberg model in a magnetic field: order-by-disorder and commensurate-incommensurate transitions

TL;DR

This study explores the magnetic phases of the honeycomb Kitaev-Heisenberg model under magnetic fields, revealing complex phase transitions and the role of thermal fluctuations in stabilizing specific magnetic orders.

Contribution

It provides the first comprehensive phase diagram combining Monte Carlo simulations and analytical methods for the model under magnetic fields.

Findings

Zeeman coupling favors non-coplanar magnetic order

Thermal fluctuations stabilize collinear zigzag phase

Discovery of commensurate-incommensurate transitions

Abstract

We present a theoretical study of field-induced magnetic phases in the honeycomb Kitaev-Heisenberg model, which is believed to describe the essential physics of Mott insulators with strong spin-orbit coupling such as $A_2$IrO$_3$ and $\alpha$-RuCl$_3$. We obtain a finite temperature phase diagram based on extensive Monte Carlo simulations and analytical calculations. We show that, while Zeeman coupling favors a symmetric non-coplanar magnetic order, thermal fluctuations enhances the stability of a collinear zigzag phase that breaks the rotational symmetry of the lattice. Our large-scale simulations also uncover intriguing commensurate-incommensurate transitions and multiple-$\mathbf Q$ incommensurate phases at high field. Experimental implications are also discussed.