  Berry curvature of Bloch bands arising in lattice systems can induce a Hall
response even in the absence of topology due to the so-called Berry-curvature
dipole (BCD). Such a response is universal and, in principle, should occur as a
thermal-Hall effect in magnon systems under the application of a temperature
gradient. However, this effect intrinsically appears as a non-linear
(second-order) response to the temperature gradient making experimental
detection difficult. Here, we propose an alternate route to access BCD in
magnons. By utilizing the process of spin-injection in conjunction with a
temperature gradient, we uncover two previously unreported contributions to the
BCD-induced Hall response for magnons -- one that is linear in temperature
gradient, and the other is non-linear in the magnon-chemical potential gradient
arising from spin injection. As an added benefit of our approach, both these
responses extract distinct moments of the genuine BCD distribution over the
magnon bands, as opposed to the recently reported extended BCD in magnons. We
use Boltzmann transport theory to derive the expression for the magnon-Hall
response in the presence of a thermal gradient and spin injection. Furthermore,
using this expression, we offer predictions for the BCD-induced magnon-Hall
effect to be observed in experiments for ferro, anti-ferro and ferri
magnetically-ordered models on various lattices, including the honeycomb
lattice, the kagome lattice, and the dice lattice.
