Tunable topological magnon-polaron states and intrinsic anomalous Hall phenomena in two-dimensional ferromagnetic insulators

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 intrinsic anomalous Hall responses of the system, namely, the intrinsic thermal Hall and intrinsic spin Nernst 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 topology and magnetic ordering, offering compelling avenues for on-demand control over emergent nontrivial topological states and quantum transport phenomena in condensed matter systems by potential applications in both classical and quantum information technology.