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The microscopic conditions for the emergence of nonreciprocal magnonexcitations in noncentrosymmetric magnets are theoretically investigated. Weshow that asymmetric magnon excitations appear when a bond magnetic toroidaldipole becomes active, which is defined as a parallel component between theDzyaloshinskii-Moriya vector and the averaged spin moments at the ends of thebonds. Depending on magnetic structures accompanying the bond magnetic toroidaldipoles, the higher-rank magnetic toroidal multipoles can also be activated ina magnetic cluster, which describes various angle dependences of asymmetricmagnon excitations. We demonstrate a variety of asymmetric magnon excitationsfor two magnetic systems in the noncentrosymmetric lattice structures; aone-dimensional breathing chain under a uniform crystalline electric field anda three-dimensional layered breathing kagome structure. We show that a bottomshift of magnon bands occurs by the magnetic toroidal dipole and a valleysplitting occurs by the magnetic toroidal octupole under magnetic orderings.

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