K. YAMAMOTO(1), G. C. Thiang(2), P. Pirro(3), K.-W. Kim(4), K. Everschor-Sitte(5) and E. Saitoh(6,7,1)
1 Advanced Science Research Center, Japan Atomic Energy Agency
2 School of Mathematical Sciences, University of Adelaide
3 Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern
4 Center for Spintronics, Korea Institute of Science and Technology
5 Institut für Physik, Johannes Gutenberg-Universität Mainz
6 Department of Applied Physics, University of Tokyo
7 Institute for Materials Research, Tohoku University
Magnetostatic surface spin waves (a.k.a Damon-Eshbach mode) have long been known to have the largest decay lengths of all available modes and be robust against surface shapes and disorders [1-3]. Combined with their chiral and unidirectional propagation with respect to the direction of the ground state magnetisation, these features remind one of topologically protected edge states of quantum Hall systems. We present a topological characterisation of the dipolar spin wave Hamiltonian, which predicts, via the bulk-edge correspondence, the presence of robust surface spin wave modes without explicitly calculating eigenmodes of a system with boundaries [4].
While the characterisation is based on the symmetry class CI of electronic topological band theory, it is reformulated for the particular dynamical structure of classical Hamiltonian systems in which symplectic, rather than unitary, structure plays an essential role. By suitably identifying the symplectic structure with the chiral symmetry of class CI, assuming a preferred metric tensor in the space of canonical coordinates, we show that the surface spin waves appear not in a gap of bulk frequency spectrum, consistent with the magnetostatic surface spin waves.
[1] A. V. Chumak et al., Appl. Phys. Lett. 94, 172511 (2009).[2] M. Mohseni et al., Phys. Rev. Lett. 122, 197201 (2019).
[3] T. Yu et al., Phys. Rev. B 99, 174402 (2019).
[4] K. Yamamoto et al., Phys. Rev. Lett. 122, 217201 (2019).