27 May 2025 Tue 4 pm

Over the past few decades, topology has become recognised as a guiding principle in understanding robust macroscopic behaviours of many-body condensed matter systems. While genuinely novel phenomena such as quantised Hall conductivity [1] and appearance of anyons [2] seem to be scarce and limited to specific realisations in low dimensions, a universal feature of topologically non-trivial phases turns out to be something more commonly observed; presence of oscillator modes localised on the boundary or defects. Although not every localised mode is necessarily topological, it is tempting to speculate that those that are prevalent across different samples of a class of materials may have a topological mechanism underlying their robustness.

In this talk, I outline how such a topological interpretation can be given to a very well-known instance of surface localised waves. Magnetostatic surface spin waves are a type of propagating spin fluctuations in ferro- and ferri-magnetic materials originating from magnetic dipole-dipole interactions [3]. They are chiral with respect to the direction of ordered magnetic moments and known to be robust against disorders of all spatial scales [4]. I show that there is an unremovable vortex-like singularity in the dispersion relation of bulk magnetostatic spin waves and demonstrate that it gives rise to the magnetostatic surface spin wave modes via topological bulk-edge correspondence of 1D chains [5]. This result highlights not only the universal nature of topological phases in wave phenomena but also the limitation of presently established theoretical framework.

References

[1] D. J. Thouless et al., Phys. Rev. Lett. 49, 405 (1982).

[2] A. Kitaev, Ann. Phys. 321, 2-111 (2006).

[3] R. Damon and J. Eshbach, J. Phys. Chem. Solids 19, 308 (1961).
[4] A. V. Chumak et al., Appl. Phys. Lett. 94, 172511 (2009).

[5] K. Yamamoto et al., Phys. Rev. Lett. 122, 217201 (2019).

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