Pumping of magnons in a Dzyaloshinskii-Moriya ferromagnet

We formulate a microscopic linear response theory of magnon pumping applicable to multiple-magnonic-band uniform ferromagnets with Dzyaloshinskii-Moriya interactions. From the linear response theory, we identify the extrinsic and intrinsic contributions where the latter is expressed via the Berry curvature of magnonic bands. We observe that in the presence of a time-dependent magnetization Dzyaloshinskii-Moriya interactions can act as fictitious electric fields acting on magnons. We study various current responses to this fictitious field and analyze the role of Berry curvature. In particular, we obtain an analog of the Hall-like response in systems with nontrivial Berry curvature of magnon bands. After identifying the magnon-mediated contribution to the equilibrium Dzyaloshinskii-Moriya interaction, we also establish the Onsager reciprocity between the magnon mediated thermal torques and heat pumping. We apply our theory to the magnonic heat pumping and torque responses in honeycomb and kagome lattice ferromagnets.