Studying magnon band topology through low-energy magnon excitations: role of anisotropic Dzyaloshinskii-Moriya interaction.

Abstract

In this work, we study topological properties of magnons via creating spin excitations in both ferromagnets (FMs) and antiferromagnets (AFMs) in presence of an external magnetic field on a two-dimensional square lattice. It is known that Dzyaloshinskii-Moriya interaction (DMI) plays an important role in coupling between different particle (spin excitation) sectors, here we consider an anisotropic DMI and ascertain the role of the anisotropy parameter in inducing topological phase transitions. While the scenario, for dealing with FMs, albeit with isotropic DMI is established in literature, we have developed the formalism for studying magnon band topology for the AFM case. The calculations for the FM case are included to facilitate a comparison between the two magnetically ordered systems. Owing to the presence of a two-sublattice structure of an AFM, a larger number of magnon bands participate in deciding upon the topological properties. However, in both the cases, an extended trivial region is observed even with the DMI to be non-zero, which is surprising since the DMI is the origin of the finite Berry curvature in presence of external magnetic field. The nature of the phases in both the cases and the phase transitions therein are characterized via computing the band structure, ascertaining the presence (or absence) of the chiral edge modes observed in a semi-infinite nano-ribbon geometry, and investigation of the thermal Hall effect. Moreover, the strength of the magnetic field is found to play a decisive role in controlling the critical point that demarcates various topological phases.