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

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.

5 pages, four figures,references and acknowledgement added