Tuning into the Kitaev spin liquid phase:A spin model on the honeycomb lattice with two types of Heisenberg exchange couplings

TL;DR

This paper introduces a spin model on the honeycomb lattice with two types of Heisenberg couplings, demonstrating how tuning these parameters can realize the Kitaev spin liquid phase, relevant for layered iridates.

Contribution

The study proposes a tunable spin model on the honeycomb lattice that can access the Kitaev spin liquid phase through parameter adjustments, including Rashba spin-orbital coupling.

Findings

Kitaev spin liquid phase occurs at equal Heisenberg couplings ($J= ilde J$).

Layered A$_2$IrO$_3$ materials can be tuned into this phase.

Link-dependent Rashba coupling enables control over the phase.

Abstract

We study a spin model on honeycomb lattice with two types of Heisenberg exchange couplings, $J$ and $\tilde J$, where $J$ is for the conventional spin and and $\tilde J$ for rotated spin. When $\tilde J=0$, this is the conventional Heisenberg model. When J=0, the system is either in a stripy antiferromagnetic order($\tilde J<0$, ferromagnetic for rotated spin) or a zig-zag antiferromagnetic order ($\tilde J>0$, antiferromagnetic for rotated spin). The competition between two ferromagnetic orders or two antiferromagnetic orders induces Kitaev's spin liquid phase characterized by the exactly solvable Kitaev model ($J=\tilde J$). Our model can be applied to layered Mott insulators A$_2$IrO$_3$ (A=Li, Na). For a monolayer of Li$_2$IrO$_3$, we show that it is possible to tune the controlling parameter into the Kitaev spin liquid regime by a link-dependent Rashba spin-orbital coupling.