Magnons on a dice lattice: Topological features and transport properties

In this paper, we study the topological properties of magnons on a dice lattice, also known as the dual of a more widely studied kagome lattice. This structure has a central atom at the center of the honeycomb lattice, which leads to the formation of a flat band. Magnetic Hamiltonians associated with the magnon bands are scarcely studied in such flat band systems, which motivates us on examining an interplay of different magnetic spin interactions, such as the Heisenberg exchange, Dzyaloshinskii-Moriya interaction (DMI), pseudodipolar interaction (PDI), and magnetocrystalline anisotropies in a dice lattice. In particular, the objective is to ascertain their roles in inducing various topological phases and the phase transitions therein. The magnons are obtained via a Holstein-Primakoff transformation for a ferromagnetic Heisenberg model on a dice lattice, that renders an analog of a pseudospin-1 fermionic Hamiltonian and yields higher Chern numbers, along with larger values of the thermal Hall conductivity. The competing effects of the DMI and the PDI in inducing transitions from either topological to topological or topological to trivial phases are noted and the corresponding results are supported via the magnon band structures, presence (or absence) of edge modes in a nanoribbon geometry, and the transport characteristic, namely, the discontinuities in the thermal Hall conductivities. Meanwhile, the magnetocrystalline anisotropy also plays an intriguing role, where distinct (nonuniform) values at the different sublattice sites result in a richer topological landscape with Chern numbers $C=\ifmmode\pm\else\textpm\fi{}2$, $\ifmmode\pm\else\textpm\fi{}1$, and 0, while a uniform anisotropy yields only $C=\ifmmode\pm\else\textpm\fi{}2$ and 0. This discrepancy arises from the broken valley symmetry in the nonuniform case. Furthermore, we have ascertained the impact of the direction of the spin vectors or the presence of an additional longer-range exchange interaction on magnon band topology. Finally, we have enriched our understanding on the role of the flat band in impacting the topological features by comparing some of the key results with those of a honeycomb structure.