  We formulate a phenomenological description of thin ferromagnetic layers with
inversion asymmetry where the single-domain magnetic dynamics experiences
magnon current-induced torques and leads to magnon-motive forces. We first
construct a phenomenological theory based on irreversible thermodynamics,
taking into account the symmetries of the system. Furthermore, we confirm that
these effects originate from Dzyaloshinskii-Moriya interactions from the
analysis based on the stochastic Landau-Lifshitz-Gilbert equation. Our
phenomenological results generalize to a general form of Dzyaloshinskii-Moriya
interactions and to other systems, such as pyrochlore crystals and chiral
magnets. Possible applications include spin current generation, magnetization
reversal and magnonic cooling.
