Dirac cones and valley topological states of classical spin waves in artificial magnonic crystals with two-dimensional honeycomb lattice

A model of artificial magnonic crystals (AMCs) with a two-dimensional honeycomb lattice of cylindrical ferromagnetic rods embedded in another ferromagnetic material is proposed. Topological properties including Dirac cones, Dirac-like point and valley states of classical spin waves in the above AMCs are theoretically investigated by numerically solving the Landau-Lifshitz equation. It is shown that Dirac cones and valley states at the boundary of the first Brillouin zone can be generated in the dispersion relation. Furthermore, Dirac-like point can also be obtained at the center of the first Brillouin zone due to the accidental degeneracy of the magnonic bands. These discoveries of Dirac cones, Dirac-like point and valley topological states in artificial magnonic crystals not only open a new field in topological condensed matter, but also provide a novel platform for fabricating topological classical spin-wave devices.