Magnon quantum anomalies in Weyl ferromagnets

When subjected to parallel electric field $\mathbit{E}$ and magnetic field $\mathbit{B}$, Weyl semimetals exhibit the exotic transport property known as the chiral anomaly due to the pumping of electrons between Weyl cones of opposite chiralities. When one or both electromagnetic (EM) fields are replaced by strain-induced chiral pseudoelectromagnetic (pseudo-EM) fields, other types of quantum anomalies occur. In the present paper, we will show that such quantum anomalies can be reproduced in a completely different system---a Weyl ferromagnet whose magnonic structure remarkably encodes Weyl physics. By analytical and numerical calculations, we will show that the magnon bands can be Landau-quantized by either an inhomogeneous electric field $\mathbit{E}$ or a chiral pseudoelectric field $\mathbit{e}$ induced by a torsional strain, and magnons can be pumped along bands by either an inhomogeneous magnetic field $\mathbit{B}$ or a chiral pseudomagnetic field $\mathbit{b}$ due to a dynamic uniaxial strain. We list the magnon quantum anomalies and the associated anomalous spin and heat currents in the Weyl ferromagnet, and show they are distinct from their Weyl semimetal counterparts.