  With spin-layer locking, the manipulation of spin degree of freedom via
perpendicular electric field can be realized in a typical antiferromagnetically
coupled bilayer. In analogy to the electric control of the anomalous layer Hall
effect of electron within such bilayer system, we propose here its magnon
counterpart i.e., thermal Hall effect controlled by a perpendicular electric
field. Unlike electrons, magnon is charged neutral and its transport in solids
can be driven by a thermal gradient. It also exhibits Hall response due to the
intrinsic Berry curvature of magnon, analogous to the achievement in electron
system. Taking bilayer 2H-VSe2 with both H-type stacking and interlayer
antiferromagnetic coupling as a platform, we perform first-principles
calculations towards the magnetic exchange coupling parameters under applied
electric field perpendicular to the plane. Based on linear spin wave
approximation, we then fit the magnon band structures accordingly and calculate
the corresponding Berry curvature. The thermal Hall coefficient dependence on
the temperature under thermal gradient can be calculated correspondingly in
linear response regime. It is shown that electric field reversal is able to
reverse the sign of the coefficient. These findings provide a platform for the
realization of all-electric magnon spintronics.
