  We formulate a microscopic linear response theory of nonequilibrium magnonic
torques and 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. After identifying the magnon-mediated contribution to the
equilibrium Dzyaloshinskii-Moriya interaction, we also establish the Onsager
reciprocity between the magnon-mediated torques and heat pumping. We apply our
theory to the magnonic heat pumping and torque responses in honeycomb and
kagome lattice ferromagnets.
