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arXiv · 1905.07909

Topological characterization of classical waves: the topological origin of magnetostatic surface spin waves

Kei Yamamoto·Guo Chuan Thiang·Philipp Pirro·Kyoung-Whan Kim·Karin Everschor-Sitte·Eiji Saitoh
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Abstract

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.

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Kei Yamamoto, Guo Chuan Thiang, Philipp Pirro, Kyoung-Whan Kim, Karin Everschor-Sitte, Eiji Saitoh. 2019-05-20. Topological characterization of classical waves: the topological origin of magnetostatic surface spin waves. https://doi.org/10.1103/physrevlett.122.217201

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