Kitaev-Heisenberg model in a magnetic field: order-by-disorder and 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.

10 pages, 8 figures