Modified dispersion law for spin waves coupled to a superconductor

Abstract

In this work, we consider dispersion laws of spin waves that propagate in a ferromagnet/superconductor bilayer, specifically in a ferromagnetic film coupled inductively to a superconductor. The coupling is viewed as an interaction of a spin wave in a ferromagnetic film with its mirrored image generated by the superconductor. We show that, in general, the coupling enhances substantially the phase velocity of magnons in in-plane spin wave geometries. In addition, a heavy nonreciprocity of the dispersion law is observed in the magnetostatic surface spin wave geometry where the phase velocity depends on the direction of the wave propagation.

Magnetization Dynamics in Proximity-Coupled Superconductor-Ferromagnet-Superconductor Multilayers

“…Blue solid curves show a typical dispersion curve for MSSW in the plain F film that is obtained with simulations in the absence of any contribution from S subsystem. Simulation results are well confirmed by the analytical dispersion relation [53], shown with blue dashed curves. Red solid and dashed lines show the dispersion curve of MSSW in the S-F bilayer in the presence of magnetostatic interaction between the S and F subsystems.…”

“…The excitation field pulse has the maximum frequency f max = 30 GHz, the Gaussian spatial profile with the width at half-maximum of 200 nm, and the amplitude of 0.001 Ms. In simulations, the diamagnetic (Meissner) contribution of S subsystem on magnetization dynamics is accounted via the method of images [17,53] in the case of continuous S layers and via the diamagnetic representation of superconductors [18,19] in the case of finite-size S elements. The effect of the superconducting proximity in S-F-S is represented by a local uniaxial anisotropy field μ 0 H s = 0.07 T that corresponds to the S1 sample [see Fig.…”

“…Red solid and dashed lines show the dispersion curve of MSSW in the S-F bilayer in the presence of magnetostatic interaction between the S and F subsystems. The magnetostatic interaction is accounted for using the method of images [17,53]. It shows that in the presence of magnetostatic interaction the dispersion is nonreciprocal: the frequency pass band for positive wave numbers is approximately doubled as compared to the pass band for negative wave numbers.…”

“…The nonreciprocity is a known property of MSSWs, which emerges due to asymmetry of the ferromagnetic film across its thickness or due to asymmetry of its surrounding (see Ref. [53] for details). Purple solid and dashed lines show the dispersion curve of MSSW in the S-F-S three layer in the presence of the proximity-induced uniaxial anisotropy H s but the absence of magnetostatic interaction between the S and F subsystems.…”

“…For this structure similar geometrical parameters are considered: the lattice period a = 1 μm, the width of F-S section 0.5 μm, and the thickness of the upper S layers 120 nm. Calculating this spectrum the diamagnetic representation of S stripes [18,19], the image method [17,53] is used for finite-size and continuous superconducting elements, respectively. The effect of the proximity in S-F-S sections is represented by the same local anisotropy H s .…”