  We study magnon-polaron hybrid states, mediated by Dzyaloshinskii-Moriya and
magnetoelastic interactions, in a two-dimensional ferromagnetic insulator. The
magnetic system consists of both in-plane and flexural acoustic and optical
phonon bands, as well as acoustic and optical magnon bands. Through
manipulation of the ground-state magnetization direction using a magnetic
field, we demonstrate the tunability of Chern numbers and (spin) Berry
curvatures of magnon-polaron hybrid bands. This adjustment subsequently
modifies two anomalous Hall responses of the system, namely, thermal Hall and
spin Nernset signals. Notably, we find that by changing the magnetic field
direction in particular directions, it is possible to completely suppress the
thermal Hall signal while maintaining a finite spin Nernst signal. Our finding
reveals the intricate interplay between topological and quantum geometrical
phenomena and magnetic ordering, offering compelling avenues for on-demand
control over emergent quantum states in condensed matter systems.
