Nonreciprocal magnon propagation in a noncentrosymmetric ferromagnet

Relativistic spin-orbit interaction drastically modifies electronic band and endows emergent functionalities. One of the example is the Rashba effect. In noncentrosymmetric systems such as interface and polar materials, the electronic band is spin-splitted depending on the momentum direction owing to the spin-orbit interaction, which is useful for the electric manipulation of spin current. Similar relativistic band-modification is also emergent for spin wave (magnon) in magnetic materials. The asymmetric magnon band dispersion induced by the Dzyaloshinskii-Moriya interaction, which is antisymmetric exchange interaction originating from the spin-orbit interaction, is theoretically expected, and experimentally observed recently in noncentrosymmetric ferromagnets. Here, we demonstrate that the nonreciprocal microwave response can be induced by the asymmetric magnon band in a noncentrosymmetric ferrimagnet LiFe$_5$O$_8$. This result may pave a new path to designing magnonic device based on the relativistic band engineering.