Dirac points and flat bands in a hexagonal magnonic crystal

Spin waves (magnons) in 2D ferromagnets can have band structures similar to 2D electronic band structures, and can exhibit, e.g., linear-dispersion Dirac cones near Brillouin zone edges in graphene-analog systems [1]. These modes, however, appear in the THz range, making interesting graphene-analog physics often difficult to access. We investigated a 2D hexagonal magnonic crystal through micromagnetic simulations. Thin films imitating the properties of yttrium-iron garnet were patterned with arrays of holes, following prior work on similar systems [2]. The resulting band structure transitions from weakly-scattered spin waves to a lattice of coupled macrospins as the hole diameter is increased. Large-hole lattices are found to host multiple Dirac points and flat bands in the few-GHz range. The resulting band structure can be modeled by mapping these macrospin interactions in linear spin wave theory to a tight binding model, which may provide predictions for 2D-analog physics in this system. Given the freedom associated with the patterning of such lattices via electron beam lithography, we hope for this simulation work to lead to experimental realizations of theoretically proposed 2D magnon physics like edge states, pseudomagnetic fields, and magnon valley-Hall effects in accessible frequency ranges and length scales [3].