Large off diagonal exchange couplings and spin liquid states in $\mathbf{C_3}$ symmetric iridates

TL;DR

This study reveals that high symmetry in honeycomb iridates leads to large off-diagonal exchange couplings, resulting in magnetic frustration and quantum spin liquid states, supported by ab-initio calculations and exact diagonalization.

Contribution

It demonstrates the role of $C_3$ symmetry in enhancing off-diagonal exchange couplings, providing a new pathway to realize spin liquid states in iridates.

Findings

High symmetry causes strong magnetic frustration.

Large off-diagonal exchange couplings drive spin liquid behavior.

Quantum fluctuations prevent magnetic ordering, consistent with experiments.

Abstract

Iridate oxides on a honeycomb lattice are considered promising candidates for realization of quantum spin liquid states. We investigate the magnetic couplings in a structural model for a honeycomb iridate K$_2$IrO$_3$, with $C_3$ point group symmetry at the Ir sites, which is an end member of the recently synthesized iridate family K$_x$Ir$_y$O$_2$. Using \textit{ab-initio} quantum chemical methods, we elucidate the subtle relationship between the real space symmetry and magnetic anisotropy and show that the higher point group symmetry leads to high frustration with strong magnetic anisotropy driven by the unusually large off-diagonal exchange couplings ($\Gamma$'s) as opposed to other spin-liquid candidates considered so far. Consequently, large quantum fluctuations imply lack of magnetic ordering consistent with the experiments. Exact diagonalization calculations for the fully anisotropic $K$-$J$-$\Gamma$ Hamiltonian reveal the importance of the off-diagonal anisotropic exchange couplings in stabilizing a spin liquid state and highlight an alternative route to stabilize spin liquid states for ferromagnetic $K$.