Investigating the Magnon Hall effect in Lu₂V₂O₇

Over the last decade, there has been immense interest in magnetic materials which host topologically non-trivial excitations. In ordered magnetic insulators, features analogous to those of topological insulators and semimetals can arise in the magnon band structure, and the associated Berry phases can manifest to observable heat and spin transport phenomena. This was unambiguously observed in the ferromagnetic pyrochlore Lu₂V₂O₇ in the form of a magnon thermal Hall signal, and proposed to arise from the antisymmetric Dzyaloshinskii-Moriya (DM) interaction. A precise value of the DM interaction is not known, as the values obtained from fitting both thermal transport and inelastic neutron scattering data, as well as from density functional theory, are all mutually inconsistent. Motivated by this, we investigate the effect of additional symmetry allowed perturbations to the spin Hamiltonian of Lu₂V₂O₇ in an attempt to reconcile the different experimental probes of this material. Our calculations provide an upper bound on the achievable thermal Hall conductivity that is consistent with available neutron scattering data. Building on these calculations, we extend our results to the family of rare-earth pyrochlores, motivating future thermal transport experiments of these materials.