Effect of lattice geometry on magnon Hall effect in ferromagnetic insulators

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 dependencies, 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.