Nonreciprocal magnon excitations by the Dzyaloshinskii-Moriya interaction on the basis of bond magnetic toroidal multipoles

The microscopic conditions for the emergence of nonreciprocal magnon excitations in noncentrosymmetric magnets are theoretically investigated. We show that asymmetric magnon excitations appear when a bond magnetic toroidal dipole becomes active, which is defined as a parallel component between the Dzyaloshinskii-Moriya vector and the averaged spin moments at the ends of the bonds. Depending on the magnetic structures accompanying the bond magnetic toroidal dipoles, the higher-rank magnetic toroidal multipoles can also be activated in a magnetic cluster, which describes various angle dependences of asymmetric magnon excitations. We demonstrate a variety of asymmetric magnon excitations for two magnetic systems in the noncentrosymmetric lattice structures: a one-dimensional breathing chain under a uniform crystalline electric field and a three-dimensional layered breathing kagome structure. We show that a bottom shift of magnon bands occurs by the cluster magnetic toroidal dipole and a valley splitting occurs by the cluster magnetic toroidal octupole under magnetic orderings. Our result provides a way to identify the important Dzyaloshinskii-Moriya interaction for nonreciprocal magnon excitations at the microscopic level beyond the symmetry argument, which will be useful not only to understand the origin of asymmetric band modulations observed in experiments but also to give an insight with which to explore further spintronics materials.