Figure 1

(Color online) (a) SEM photo of the ferromagnetic Josephson junction used in the experiment. Junction area is $500\times 500{\text{nm}}^2$. (b) Schematic cross section of the Josephson junction. The ac Josephson current $I\left(t\right)$ flows through the junction creating an rf magnetic field $\mathbf{H}\left(t\right)$, causing the magnetization precession $\mathbf{M}\left(t\right)$, which in turn resonantly couples with the Josephson phase at frequency ${\omega }_J$. Layers are, respectively, from the bottom: Nb (50 nm), ${\text{Pd}}_{0.9}{\text{Ni}}_{0.1}$ (20 nm), and Nb (50 nm). (c) The equivalent RSJ model and the sketch of the effect of the FMR on the current-voltage characteristics. The ferromagnetic layer is modeled as a series LCR oscillator, in parallel with the Josephson junction. Resistance $R_0$ is proportional to the imaginary part of the susceptibility ${\chi }^{″}$.Reuse & Permissions

Figure 2

(Color online) Dependence of the Josephson critical current on the external magnetic field in plane. The solid curve represents the normalized experimental data taken at 35 mK and the dotted curve is the Fraunhofer pattern expected for our junction parameters including the magnetization. Left insert: the magnetic hysteresis taken at 10 K on a millimetric trilayer with the same cross section as the junction, with field applied in plane (dotted curve) and perpendicular to the plane (solid curve). Right insert: current-voltage curves for different field values, measured at 35 mK.Reuse & Permissions

Figure 3

(Color online) Dynamical resistance of the ferromagnetic Josephson junction (solid curve, SFS, bottom and left axis) shows resonances compared to a similar nonferromagnetic junction (solid curve, SNS, top and right axis). Dotted curve is a fit to theory [Eq. (6)]. The mode at $23\mu \text{V}$ is the FMR. Bottom insert: conventional cavity ferromagnetic resonance on a macroscopic trilayer. Top insert: comparison between the field dependence of the FMR ${\nu }_s={\omega }_s/2\pi$ in the Josephson junction (solid square) with the cavity measurement on a macroscopic trilayer (open square). Dotted curve is a parameter free fit of the FMR using the Kittel formula [Eq. (7)].Reuse & Permissions

Figure 4

(Color online) (a) The dynamical resistance of the ferromagnetic Josephson junction with applied external microwaves. Pronounced dip is the Shapiro resonance, and arrows indicate sideband resonances at the same frequency as the $m=2$ mode at $10\mu \text{V}$ from Fig. 3. The external microwave frequency is 17.35 GHz and the temperature 35 mK. Insert: typical $IV$ curve with applied external microwaves of 2 GHz at 35 mK, showing Shapiro steps. (b) Dependence of the $m=2$ FMR mode on the in plane magnetic field. Solid curves are the measured derivative of the dynamical resistance from Fig. 3, and dotted curves are a fit [Eq. (6)]. The spin-wave frequency increases with field. Insert: the field dispersion relation of the modes. The solid line is Eq. (7) when the spatial dependence of the FMR modes is taken into account.Reuse & Permissions