Topological Magnon Bands in Ferromagnetic Star Lattice

The experimental observation of topological magnon bands and thermal Hall effect in a kagom\'e lattice ferromagnet Cu(1-3, bdc) has inspired the search for topological magnon effects in various insulating ferromagnets that lack an inversion center allowing a Dzyaloshinskii-Moriya (DM) spin-orbit interaction. The star lattice (also known as the decorated honeycomb lattice) ferromagnets is an ideal candidate for this purpose because it is a variant of the kagom\'e lattice with additional links that connect the up-pointing and down-pointing triangles. This gives rise to twice the unit cell of the kagom\'e lattice, hence a more interesting topological magnon effects. In particular, the triangular bridges on the star lattice can be coupled either ferromagnetically or antiferromagnetically which is not possible on the kagome lattice ferromagnets. Here, we study DM-induced topological magnon bands, chiral edge modes, and thermal magnon Hall effect on the star lattice ferromagnet in different parameter regimes. The star lattice can also be visualized as the parent material from which topological magnon bands can be realized for the kagom\'e and honeycomb lattices in some limiting cases.