Effect of lattice geometry on magnon Hall effect in ferromagnetic insulators

TL;DR

This study explores how lattice geometry influences the magnon Hall effect in various ferromagnetic insulators, revealing that the effect depends on the crystal structure and topological properties of the material.

Contribution

It demonstrates the relationship between lattice geometry and magnon Hall effect, extending the understanding to different crystal structures and highlighting the role of Berry curvature and Dzyaloshinskii-Moriya interaction.

Findings

Finite thermal Hall conductivities observed in pyrochlore ferromagnets.

Thermal Hall effect correlates with Berry curvature induced by DM interaction.

Absence or reduction of effect in distorted perovskites.

Abstract

We have investigated the thermal Hall effect of magnons for various ferromagnetic insulators. For pyrochlore ferromagnetic insulators Lu$_2$V$_2$O$_7$, Ho$_2$V$_2$O$_7$, and In$_2$Mn$_2$O$_7$, finite thermal Hall conductivities have been observed below the Curie temperature $T_C$ . From the temperature and magnetic field dependences, it is concluded that magnons are responsible for the thermal Hall effect. The Hall effect of magnons can be well explained by the theory based on the Berry curvature in momentum space induced by the Dzyaloshinskii-Moriya (DM) interaction. The analysis has been extended to the transition metal (TM) oxides with perovskite structure. The thermal Hall signal was absent or far smaller in La$_2$NiMnO$_6$ and YTiO$_3$, which have the distorted perovskite structure with four TM ions in the unit cell. On the other hand, a finite thermal Hall response is discernible below $T_C$ in another ferromagentic perovskite oxide BiMnO$_3$, which shows orbital ordering with a larger unit cell. The presence or absence of the thermal Hall effect in insulating pyrochlore and perovskite systems reflect the geometric and topological aspect of DM-induced magnon Hall effect.