Spin waves and stability of zigzag order in the Hubbard model with spin-dependent hopping terms - Application to the honeycomb lattice compounds ${\rm Na_2 Ir O_3}$ and ${\rm \alpha - Ru Cl_3}$

TL;DR

This paper models spin waves in honeycomb lattice compounds using a Hubbard model with spin-dependent hopping, revealing how various interactions influence zigzag order stability and matching experimental neutron scattering data.

Contribution

It introduces a comprehensive Hubbard model with spin-dependent hopping terms to explain zigzag order stability and spin wave properties in honeycomb lattice materials.

Findings

DM interactions destabilize zigzag order

Secondary spin-dependent hopping stabilizes zigzag order

Model results agree with neutron scattering experiments

Abstract

Spin waves in the zigzag ordered state on a honeycomb lattice are investigated within a Hubbard model with spin-dependent hopping terms. Roles of the emergent Kitaev, Heisenberg, Dzyaloshinskii-Moriya, and symmetric-off-diagonal spin interactions are investigated on the stability of the zigzag order. While the DM interactions are found to destabilize the zigzag order, the secondary spin-dependent hopping terms (associated with structural distortions) are shown to strongly stabilize the zigzag order and account for magnetocrystalline anisotropy, easy axis, and spin wave gap. The calculated spin wave dispersion and energy scale are in good agreement with inelastic neutron scattering measurements on $\rm \alpha - RuCl_3$ and $\rm Na_2 Ir O_3$.