Spin waves in two-dimensional placoid-like ferromagnetic lattices

The topology of placoid scales is explored as a model of a two-dimensional ferromagnetic lattice. We start from Heisenberg's Hamiltonian, adopting in low temperature regime and performing the study of free modes of the magnetic excitations. The Holstein-Primakoff approximation was employed, restricting our attention to the bilinear terms in the quantized second operators. The dispersion relation was obtained and the properties of the magnetic modes were studied in terms of the physical fit parameter J2, which reveals the energy dynamics for different regions of the Brillouin Zone. A comparison was made with the energy maps from the square and triangular lattices in order to verify the equivalence of the effects from the placoid geometry. We concluded that this topology imprints a significant energy growing in the regime of low wave vectors with more effective rates than those observed in the triangular lattice, a fact that can be explained by the presence of 4 sites in the unit cell.