Supercurrent-induced magnetization dynamics in a Josephson junction with two misaligned ferromagnetic layers

We investigate supercurrent-induced magnetization dynamics in a Josephson junction with two misaligned ferromagnetic layers and demonstrate a variety of effects by solving numerically the Landau-Lifshitz-Gilbert equation. In particular, we demonstrate the possibility of obtaining supercurrent-induced magnetization switching for an experimentally feasible set of parameters, and we clarify the favorable condition for the realization of magnetization reversal. These results constitute a superconducting analog to conventional current-induced magnetization dynamics and indicate how spin-triplet supercurrents may be utilized for practical purposes in spintronics.

Figure 1

The proposed experimental structure. Two ferromagnetic layers separated by a normal spacer are sandwiched between two $s$-wave superconductors. The magnetization directions may be nonaligned and tuned by means of an external field, as long as the exchange coupling between the ferromagnets is sufficiently reduced by the normal spacer. By current-biasing this system one may generate a supercurrent which induces magnetization dynamics.

Figure 2

The time evolution of the normalized magnetization components $m_j$. Here, we have set $\zeta =290$ with an initial angle misalignment ${\theta }_0/\pi =0.1$. We have considered the weak-damping regime $\alpha \ll 1$ in the upper row, setting (a) $\omega =0.5$ and $\alpha =0.05$ while in (b) $\omega =1.5$ and $\alpha =0.05$. In the lower row, we have considered stronger Gilbert damping and set (c) $\omega =0.5$ and $\alpha =0.5$ while in (d) $\omega =1.5$ and $\alpha =0.5$. The insets display a parametric plot of the $\mathit{ŷ}$ and $\mathit{ẑ}$ components of the magnetization, with the red circles indicating the point $\tau =0$ (the initial magnetization configuration). The time span in the insets is $\tau \in [0,50]$. Note that the magnetization traverses back and forth along the black line in the insets; i.e., the point farthest away from the red circle does not necessarily correspond to $\tau =50$.

Figure 3

(a) The time evolution of the normalized magnetization component $m_y$. Here, we have set $\omega =1.1$ and $\alpha =0.4$ with an initial angle misalignment ${\theta }_0/\pi =0.1$. Above a critical value of $\zeta$, permanent switching occurs from ${\mathit{m}}_L\parallel \mathit{ŷ}$ to ${\mathit{m}}_L\parallel (-\mathit{ŷ})$. Inset: Magnetization reversal can also occur for smaller Gilbert damping, here illustrated by $\alpha =0.09$, $\zeta =360$, $\omega =0.6$. The phase diagram for magnetization reversal [from the parallel (P) configuration ${\mathit{m}}_L\parallel {\mathit{m}}_R$ to the antiparallel (AP) configuration ${\mathit{m}}_L\parallel (-{\mathit{m}}_R)$] is shown in (b)–(d). A contour-plot is given for $m_y(t\to \infty )$ with (b) $\omega =0.5$, (c) $\alpha =0.1$, and (d) $\zeta =200$.