Dynamics of Spin Transport in Voltage-Biased Josephson Junctions

We investigate spin transport in voltage-biased spin-active Josephson junctions. The interplay of spin filtering, spin mixing, and multiple Andreev reflection leads to nonlinear voltage dependence of the dc and ac spin current. We compute the voltage characteristics of the spin current ($I_S$) for superconductor-ferromagnet-superconductor Josephson junctions. The subharmonic gap structure of $I_S(V)$ is shown to be sensitive to the degree of spin mixing generated by the ferromagnetic interface, and exhibits a pronounced even-odd effect associated with spin transport during multiple Andreev reflection processes. For strong spin mixing both the magnitude and the direction of the dc spin current can be sensitively controlled by the bias voltage.

Figure 1

Diagrammatic representation of Eqs. (2). The solid (dashed) arrows represent electrons (holes), the vertical line indicates the interface. Branch conversion amplitudes (${\gamma }^R$ and ${\tilde{\gamma }}^R$) are shown as semicircles connecting electron and hole lines, interface scattering amplitudes ($S_{ij}$) are shown as circles (○), and the effective reflection and transmission amplitudes ($r_{1l}^R$ and $t_{1l}^R$) are indicated by bullets (●). Only the leading order multiple scattering processes for $r_{1l}^R$ are shown.

Figure 2

The dc spin current (in units of $G_S\Delta /e$) as a function of voltage bias $V$ at zero temperature, for different transmission probabilities, $D_{\uparrow }$ and $D_{\downarrow }$, and spin-mixing angles, $\vartheta =0$ (blue), $\pi /2$ (green), $\pi$ (red).

Figure 3

Left (right): The cosine (sine) components of the ac spin current (in units of $G_S\Delta /e$) at $T=0$ for $\vartheta =0$, $\pi /2$, $\pi$, $D_{\uparrow }=0.5$, and $D_{\downarrow }=0.4$.