Quantum Hall-like transitions in the thermal Hall behavior of multilayer topological magnon insulators

Two-dimensional magnetic insulators can be promising hosts for topological magnons. In this study, we show that ABC-stacked honeycomb lattice multilayers with alternating Dzyaloshinskii-Moriya interaction (DMI) reveal a rich topological magnon phase diagram. Based on our bandstructure and Berry curvature calculations, we demonstrate jumps in the thermal Hall behavior that corroborate with topological phase transitions triggered by adjusting the DMI and interlayer coupling. We connect the phase diagram of generic multilayers to a bilayer and a trilayer system. We find an even-odd effect amongst the multilayers where the even layers show no jump in thermal Hall conductivity, but the odd layers do. We also observe the presence of topological proximity effect in our trilayer. Multilayer characterized by ferro- and anti-ferromangetic interlayer coupling are considered in addition to rhombohedral and monoclinic stacking arrangements. Our results offer new schemes to manipulate Chern numbers and their measurable effects in topological magnonic systems.