Phase Dynamics of Ferromagnetic Josephson Junctions

We have investigated the classical phase dynamics of underdamped ferromagnetic Josephson junctions by measuring the switching probability in both the stationary and nonstationary regimes down to 350 mK. We found the escape temperature to be the bath temperature, with no evidence of additional spin noise. In the nonstationary regime, we have performed a pump-probe experiment on the Josephson phase by increasing the frequency of the junction current bias. We show that an incomplete energy relaxation leads to dynamical phase bifurcation. Bifurcation manifests itself as premature switching, resulting in a bimodal switching distribution. We directly measure the phase relaxation time ${\tau }_{\phi }$ by following the evolution of the bimodal switching distribution when varying the bias frequency. Numerical simulations account for the experimental values of ${\tau }_{\phi }$.

Figure 1

(a) The switching mechanism in the nonstationary regime, where the phase can either relax to the bottom of the potential well and then escape (solid circle) or stay near the top and escape early (open circle). (b) The calculated voltage $V(t)$ across the junction (solid curve), with the imposed current sawtooth ramp (dotted curve). Either the switching takes place as in equilibrium, around $I_s$, or around the retrapping current $I_r$. (c) The phase diagram, calculated for $\beta =0.01{\omega }_0$, ${\omega }_b=0.001{\omega }_0$, and ${\eta }_b=1.2$. The attractor (solid curve) corresponds to the locked state, while the dotted curves correspond to the running state. In the case of the early escape, the phase trajectory is near the separatrix (dashed curve). (d) Numerically obtained distribution of the initial phase speed at the start of each cycle $⟨\dot{\phi }(0)⟩$, as a function of the ramp frequency. The error bars are augmented 5 times. The solid line is a linear fit, and the dashed line is the bifurcation threshold corresponding to the separatrix.

Figure 2

(a) Typical $IV$ curve at 350 mK. (b) Distribution width as a function of temperature for junctions with 70, 80, and 85 Å of PdNi (triangles, circles, and squares, respectively). The solid curve is a fit for the junction with 80 Å in the low damping regime. (c) The measured histograms $P(I)$ (dotted curves) for $T=0.5$, 0.8, 1.1, 2.0, 3.0, and 4.2 K, respectively, from the right, and a fit (solid curves), for a junction with 80 Å of PdNi. The effective temperature, obtained as a fitting parameter, is almost equal to the bath temperature.

Figure 3

(a) Switching histogram of the junction with 85 Å of PdNi taken at 350 mK with the sweep frequency of 4 (solid curve), 6 (dotted curve), and 12 kHz (dashed-dotted curve). (b) Early switching probability $N_1$ as a function of ramp frequency, measured at 350 mK for the junctions with 85 (open circles), 100 (solid squares), and 90 Å (crossed squares) of PdNi. The dotted lines are a theoretical prediction [Eq. (2)]. The solid curves are obtained from the same equation, when keeping ${\tau }_{\phi }$ as the fitting parameter. Inset: The dependence of the bifurcation onset frequency ${\nu }^{*}$ of temperature, measured on a junction with 85 Å. The solid line is a fit taking into account the measured quasiparticle resistance $R$.