Magnetic order and anisotropic interactions induced by mixing between the $J=1/2$ and $3/2$ sectors in spin-orbit coupled honeycomb-lattice compounds

TL;DR

This paper investigates how mixing between different electronic sectors in spin-orbit coupled honeycomb compounds induces weak anisotropic magnetic interactions, leading to novel magnetic orders and excitations that explain experimental observations.

Contribution

It introduces a three-orbital model showing emergent anisotropic interactions from sector mixing, revealing new magnetic orders and excitation features in honeycomb-lattice materials.

Findings

Emergent anisotropic interactions induce Nél and zigzag magnetic orders.

Magnon energies are extremely small compared to hopping energies.

Anisotropy effects are enhanced at smaller spin-orbit coupling.

Abstract

Novel magnetic ordering on the honeycomb lattice due to emergent weak anisotropic interactions generated by the mixing between the $J=1/2$ sector and the magnetically inactive 3/2 sector is investigated in a three-orbital interacting electron model in the absence of Hund's coupling. Self-consistent determination of magnetic order yields anisotropic N\'{e}el and zigzag orders for different parameter regimes, highlighting the effect of the emergent single-ion anisotropy. Study of magnon excitations shows extremely small magnon energy scale compared to the hopping energy scale, and enhancement of anisotropy effects for smaller spin-orbit coupling. These results account for several features of the honeycomb lattice compounds such as $\rm Na_2 Ir O_3$ and $\rm Ru Cl_3$, where the leading order anisotropic interactions within the magnetically active $J=1/2$ sector are completely quenched due to the edge-sharing octahedra.