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

In this work, magnetization dynamics is studied in superconductor-ferromagnet-superconductor three-layered films in a wide frequency, field, and temperature ranges using the broad-band ferromagnetic resonance measurement technique. It is shown that in the presence of both superconducting layers and of superconducting proximity at both superconductor-ferromagnet interfaces a massive shift of the ferromagnetic resonance to higher frequencies emerges. The phenomenon is robust and essentially long-range: it has been observed for a set of samples with the thickness of ferromagnetic layer in the range from tens up to hundreds of nanometers. The resonance frequency shift is characterized by proximity-induced magnetic anisotropies: by the positive in-plane uniaxial anisotropy and by the drop of magnetization. The shift and the corresponding uniaxial anisotropy grow with the thickness of the ferromagnetic layer. For instance, the anisotropy reaches 0.27 T in experiment for a sample with a 350-nm-thick ferromagnetic layer, and about 0.4 T in predictions, which makes it a ferromagnetic film structure with the highest anisotropy and the highest natural resonance frequency ever reported. Various scenarios for the superconductivity-induced magnetic anisotropy are discussed. As a result, the origin of the phenomenon remains unclear. Application of the proximity-induced anisotropies in superconducting magnonics is proposed as a way for manipulations with a spin-wave spectrum.

Figure 1

Schematic illustration of the investigated chip sample. A series of $S$-$F$-$S$ film rectangles is placed directly on top of the central transmission line of the coplanar waveguide. Magnetic field $H$ is applied in-plane along the $x$ axis.

Figure 2

(a),(b) FMR absorption spectra $d{S}_{21}(f,H)/dH$ for S1 sample measured at $T=2\mathrm{K}<T_c$ (a) and $T=9\mathrm{K}\approx T_c$ (b). The grayscale is coded in absolute units. (c) Dependencies of the FMR frequency on magnetic field $f_r(H)$ at different temperatures for S1 sample.

Figure 3

Dependence of the anisotropy field $H_a$ (a) and effective magnetization $M_{\mathrm{eff}}$ (b) on temperature. Black square dots correspond to the S1 $S$-$F$-$S$ sample, red circular dots correspond to the S2 $S$-$F$-${\mathrm{s}}^{\prime }$ sample, and blue diamond dots correspond to the S3 $S$-$F$-$I$-$S$ sample. Green curve in (a) is the fit of $H_a(T)$ with Eq. (2), which yields the following parameters: ${\mu }_0{H}_{a0}=77$ mT, $T_c=9.0$ K, $p=3.7$.

Figure 4

(a) Dependencies of the FMR frequency on magnetic field $f_r(H)$ at different temperatures for the S4 sample. (b),(c) Dependence of the anisotropy field $H_a$ (b) and effective magnetization (c) on temperature. The data in (b),(c) that is shown with black square dots is obtained by fitting $f_r(H)$ in the entire field range from 0 up to 200 mT. The data in (b),(c) that is shown with red circular dots is obtained by fitting $f_r(H)$ in the cutoff field range from 0 up to 90 mT. Error bars in (c) show the 95% confidence interval of the optimized parameter $M_{\mathrm{eff}}$ in Eq. (1). Green curve in (b) shows the fit of $H_a(T)$, which is obtained using the cutoff field range, with Eq. (2), which yields the following parameters: ${\mu }_0{H}_{a0}=196$ mT, $T_c=9.0$ K, $p=7.7$.

Figure 5

(a) Dependencies of the FMR frequency on magnetic field $f_r(H)$ at different temperatures for the S5 sample. (b) Dependence of the anisotropy field $H_a$ on temperature. Green curve in (b) shows the fit of $H_a(T)$ with Eq. (2), which yields the following parameters: ${\mu }_0{H}_{a0}=375$ mT, $T_c=8.74$ K, $p=13.9$.

Figure 6

(a) Dispersion curves for MSSW that propagate in continuous $F$, $S$-$F$, and $S$-$F$-$S$ films. Dispersion curves that are obtained numerically are shown with solid lines. Dispersion curves that are obtained using analytical expression are shown with dashed lines. (b),(c) Spin-wave spectra of $S$-$F$-$S$–based magnonic crystals that are formed in MSSW geometry with the lattice parameter $a=1\mu \mathrm{m}$. Inserts in (b),(c) show schematic illustrations of the considered magnonic crystals.