Niedzielski B., Jia C., Berakdar J.

We study the magnon propagation in a micrometer-size ferromagnetic waveguide affected by the proximity to a superconductor that hosts a vortex formation. By solving the time-dependent Ginzburg-Landau equations of superconductivity, we obtain the equilibrium state of the vortex configuration and the associated stray fields that act on the magnetic dynamics. Spin wave dynamics in the presence of the superconductors are inferred from the Landau-Lifschitz equation. For a quantitative comparison, the simulations are performed under the experimental conditions as reported by Dobrovolskiy et al. (Nature Physics, 15, 477 (2019)). We found that the presence of the vortex lattice leads to the formation of a Bloch-like band structure in the magnon spectrum. The width and the number of allowed bands are found to depend mainly on the in-plane component of the vortex field along the waveguide. A shift to lower energies of the lowest-order-allowed bands occurs due to the confinement of the magnonic modes above the locations of the superconductor vortices. We also studied the role of the films thickness. At least two GHz-frequency backward-volume magnetostatic spin waves modes are observed at the top and bottom surfaces (in addition to these magnetostatic surface modes, the vertical confinement can also give rise to longer-wavelength and low-frequency perpendicular standing spin waves). Effects of the vortex fields are found to depend strongly on the type of the magnon modes. It is found that the effect of the superconducting vortices of the spin waves can be emulated well by the stray fields of air-separated magnetic nanocubes of appropriate dimensions.

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