Topological valley transport of gapped Dirac magnons in bilayer ferromagnetic insulators

Bilayer Heisenberg ferromagnetic insulators hold degenerate terahertz Dirac magnon modes associated with two opposite valleys of the hexagonal Brillouin zone. We show that this energy degeneracy can be removed by breaking of the inversion symmetry ($\mathcal{I}$), leading to a topological magnon valley current. We show furthermore that this current leads to valley Seebeck effect for magnons and is thereby detectable. We perform calculations in the specific example of bilayer ${\mathrm{CrBr}}_{3}$, where $\mathcal{I}$ can be broken by electrostatic doping.