Topological characterization of classical waves; The Topological origin of magnetostatic surface spin waves

山本 慧; Thiang, G. C.*; Pirro, P.*; Kim, K.-W.*; Everschor-Sitte, K.*; 齊藤 英治*

Physical Review Letters, 122(21), p.217201_1 - 217201_5, 2019/05

AA2018-0627.pdf:0.98MB

https://doi.org/10.1103/PhysRevLett.122.217201

We propose a topological characterization of Hamiltonians describing classical waves. Applying it to the magnetostatic surface spin waves that are important in spintronics applications, we settle the speculation over their topological origin. For a class of classical systems that includes spin waves driven by dipole-dipole interactions, we show that the topology is characterized by vortex lines in the Brillouin zone in such a way that the symplectic structure of Hamiltonian mechanics plays an essential role. We define winding numbers around these vortex lines and identify them to be the bulk topological invariants for a class of semimetals. Exploiting the bulk-edge correspondence appropriately reformulated for these classical waves, we predict that surface modes appear but not in a gap of the bulk frequency spectrum. This feature, consistent with the magnetostatic surface spin waves, indicates a broader realm of topological phases of matter beyond spectrally gapped ones.