On the mechanism of ferromagnetic resonance in ferromagnet-superconductor trilayers

TL;DR

The paper investigates how superconducting proximity in Nb/Py/Nb trilayers alters ferromagnetic resonance (FMR) as a function of temperature and layer thickness. It combines 12 GHz FMR experiments across varying Nb and Py thicknesses with a simple analytical model in which screening currents in the SC layers, driven by the precessing FM magnetization, generate an alternating back-action field that shifts the FMR frequency, yielding a modified Kittel relation $f=\frac{\gamma}{2\pi}\sqrt{(H_0-H^{\rm sc})(H_0+4\pi M_s+H_a)}$ with $H^{\rm sc}$ given by $-4\pi M_s\frac{d_f[1-e^{-d_s/\lambda}]}{2\lambda+d_f[1-e^{-d_s/\lambda}]}$. The key finding is a large SC-induced shift that grows with both SC and FM thickness and saturates at large thickness, and that insulating spacers suppress the effect while conducting spacers do not; this dynamic mechanism is further supported by hysteresis measurements showing no static Meissner contribution. The work clarifies magnetization dynamics in SC/FM/SC systems and suggests a route to increase GHz operating frequencies for magnonic devices by exploiting screening currents in the superconducting layers.

Abstract

Temperature dependent magnetic properties of superconductor-ferromagnet-superconductor (SC/FM/SC) trilayers are studied both experimentally and theoretically, with a focus on ferromagnetic resonance (FMR). The influence of the SC and FM layer thicknesses on the FMR field is examined. To differentiate the mechanisms involved, we additionally investigate structures containing nonmagnetic metallic (M) or insulating (I) spacers (SC/FM/M/SC or SC/FM/I/SC). All the studied multilayers show large reductions in the FMR field below the critical temperature of the SC, except the system containing an insulating spacer (SC/FM/I/SC). This SC-induced FMR-shift (resonance field/frequency) is larger for thicker SC as well as FM layers, reaching a saturation value for very large thicknesses. To explain the measured results, an analytical model is developed, in which the FM-magnetization precession modulates the magnetic flux in the system, thereby inducing an alternating supercurrent in the SC, which in turn produces a dynamic back-action magnetic field on the FM that shifts its resonance frequency. The model considers closed current loops, where the FM layer conductively links the supercurrents flowing in the opposite directions in the two outer SC layers. Our results provide a practical route for increasing the operating frequency of magnonic devices.

Figures (4)

• Figure 1: Schematic of the multilayer structure of length $L$, consisting of a ferromagnetic Py layer of thickness $d_\mathrm{f}$, an optional spacer layer of thickness $d_{\mathrm{sp}}$, enclosed by two superconducting Nb layers of thickness $d_\mathrm{s}$.
• Figure 2: Temperature dependence of the resonance field for the samples with: (a) $d_{\rm s} = 50$ nm and different values of $d_{\rm f}$; (b) $d_{\rm f} = 50$ nm and different values of $d_{\rm s}$; and (c) $d_{\rm f} = 50$ nm, $d_{\rm s} = 50$ nm, with different spacers (conductive: Ag and insulating: $\rm Al_2O_3$) between SC and FM. The resonance frequency is 12 GHz. Points and solid lines correspond to experimental data and theoretical calculations, respectively.
• Figure 3: Hysteresis loop measured for the sample S4 with $d_{\rm f}=100$ nm, $d_{\rm s}=50$ nm (a) and for the sample S5 with $d_{\rm f}=200$ nm, $d_{\rm s}=50$ nm (b).
• Figure 4: (a) Resonance frequency as a function of FM layer thickness $d_{\rm f}$ for $d_{\rm s}=50$ nm. (b) Resonance frequency as a function of SC layer thickness $d_{\rm s}$ for $d_{\rm f}=50$ nm. Both dependencies are plotted at $H_0=0$ and $T=0$. Black and red lines correspond to theoretical calculations based on our model and that of Silaev, respectively.