Spin-Dependent Cooper Pair Phase and Pure Spin Supercurrents in Strongly Polarized Ferromagnets

We study heterostructures of singlet superconductors and strongly spin-polarized ferromagnets and show that a relative phase arises between the superconducting proximity amplitudes in the two ferromagnetic spin bands. We find a tunable pure spin supercurrent in a spin-polarized ferromagnet contacted with only one superconductor electrode. We show that Josephson junctions are most effective for a spin polarization $P\sim 0.3$, and that critical currents for positive and negative bias differ for a high transmission Josephson junction, due to a relative phase between single and double pair transmission.

Figure 1

(a) The coherent transfer of singlet pairs via a SFM (top) is not possible. However, the “crossed” pair transmissions process (bottom) is possible and leads to intriguing effects in high transmission junctions. (b) SC/SFM interface, showing the Fermi surfaces on either side (thick lines). Assuming momentum conservation parallel to the interface (${\overrightarrow{k}}_{\parallel }$), a quasiparticle incident from the SC can either scatter into two (dotted arrows) or into only one (dashed arrows) spin band of the FM.

Figure 2

(a) Josephson junction with spin-active SC/SFM interfaces formed by magnetized layers. (b) Orientation of the interface magnetization described by spherical angles $\alpha$ and $\phi$. (c) The quantities ${\tau }_2^{\pm }$ in Eq. (7) vs ${\overrightarrow{k}}_{\parallel }$ for two polarizations $P$, and vs $P$ for perpendicular impact (inset). (d) Critical current $I_c$ vs temperature $T$ for various polarizations $P$ of the SFM layer. (e) $I_c{R}_n$-product and normal-state resistance $R_{n}A$ as function of $P$ for $T=0.5T_c$, $d={ƛ}_{F1}$, and $(V_I-J_I)/E_F={10}^{-4}$ (dotted line), 0.2 (solid line), 0.5 (dashed line). $R_{n}A$ is in units of $(e^2{N}_{F1}{v}_{F1}{)}^{-1}$, $N_{F1}$ being the normal-state SC density of state. $\Delta =1.76\mathrm{meV}$. In all plots: ${\alpha }_L={\alpha }_R=\pi /2$, ${\phi }_L={\phi }_R$, $L={\xi }_0$, $d=5{ƛ}_{F1}$, $V_I-J_I=0.5E_F$, $p_{F2}=1.18p_{F1}$, unless stated otherwise. $P$ is tuned by $p_{F3}$.

Figure 3

(a) Spin-resolved and total CPR for $\Delta \phi =0$ and $\pi /4$. (b) Coefficients $I_{\mathrm{cp}}$ and $I_{0\sigma }$ of Eq. (8) vs $\Delta \chi$. (c) Critical current in positive ($I_{c+}$)/negative ($I_{c-}$) bias direction vs $\Delta \phi$. (d) The equilibrium phase difference $\Delta {\chi }_{\mathrm{eq}}$ vs $\Delta \phi$ varies from $\pi$ to 0. In all plots $T=0.2T_c$, $d=0.25{ƛ}_{F1}$, $P=0.21$. Other parameters as in Fig. 2.

Figure 4

(a) Setup with only one SC electrode. (b) Spin-supercurrent $I_s$ vs $P$ for various $(V_I-J_I)/E_F={10}^{-4}$ (dotted line), 0.2 (solid line), 0.5 (dashed line). $R_{n}A$ refers to the normal-state resistance of the SC/FM interface. $d={ƛ}_{F1}$; other parameters as in Fig. 2.