O. V. Dobrovolskiy, R. Sachser, T. Brächer, T. Böttcher, V. V. Kruglyak, R. V. Vovk, V. A. Shklovskij, M. Huth, B. Hillebrands, and A. V. Chumak
Nature Physics (2019)
Ferromagnetism and superconductivity are most fundamental phenomena in condensed-matter physics. Entailing opposite spin orders, they share an important conceptual similarity: disturbances in magnetic ordering in magnetic materials can propagate in the form of spin waves (magnons) while magnetic fields penetrate superconductors as a lattice of magnetic flux quanta (fluxons). Despite a rich choice of wave and quantum phenomena predicted, magnon–fluxon coupling has not been observed experimentally so far. Here, we clearly evidence the interaction of spin waves with a flux lattice in ferromagnet/superconductor Py/Nb bilayers. We demonstrate that, in this system, the magnon frequency spectrum exhibits a Bloch-like band structure that can be tuned by the biasing magnetic field. Furthermore, we observe Doppler shifts in the frequency spectra of spin waves scattered on a flux lattice moving under the action of a transport current in the superconductor.

Fig.1. (a,b), Sketch (a) and false-colour scanning electron micrograph (b) of the Nb and Au layout. The Py/Nb bilayer is in an inclined magnetic field μ₀H_ext with a constant in-plane component μ₀H_|| = 59.5 mT and an out-of-plane component μ₀H_⊥ varying between 3 and 11 mT. BVMSWs are excited by antenna 1, propagate through the Py waveguide, whose arrangement is indicated by the dashed lines in b, and are detected by antenna 2. The vortex lattice induces a spatially periodic magnetic field h(x, y) in Py, which becomes alternating in time when the vortices move.