Spin-motive force and orbital-motive force: from magnon Bose–Einstein condensation to chiral Weyl superfluids

Spin-motive geometric force acting on electrons in metallic ferromagnets is extended to spin-motive force in magnon BEC, which is represented by phase-coherent precession of magnetization, and to the orbital-motive force in superfluid $^3$He–A. In $^3$He–A there are two contributions to the orbital-motive force. One of them comes from the chiral nature of this liquid. Another one originates from chiral Weyl fermions living in the vicinity of the topologically protected Weyl points, and is related to the phenomenon of chiral anomaly.