Supercurrent Pumping in Josephson Junctions with a Half-Metallic Ferromagnet

A Josephson current through a half-metallic ferromagnet between two conventional superconductors is theoretically studied. The spin dynamics such as magnon excitation plays a crucial role not only for the conversion between spin-singlet and spin-triplet pairs but also for the formation of the composite state of a triplet Cooper pair and magnon, by which the Josephson current flows between the superconductors. We propose the supercurrent pumping driven by the coherent precession of the magnetization by tuning the microwave frequency to the ferromagnetic resonance frequency in a ferromagnetic Josephson junction.

Figure 1

Josephson junction with HM of thickness $d_F$ between two $s$-wave spin-singlet $S1$ and $S2$. A tunnel barrier is inserted at the interface. A microwave radiation $h_{\mathrm{ac}}$ onto HM causes the precession of the magnetization $\mathbf{M}$.

Figure 2

Feynman diagrams, (a) and (b), describing the correlated tunneling of a Cooper pair from $S1$, through HM, to $S2$. The wavy lines represent the propagation of magnon, and $T_{\sigma {\sigma }^{\prime }}$ is the spin-dependent tunnel matrix element.

Figure 3

(a) Normalized critical current $I_c$ vs microwave frequency $\Omega$. (b) Normalized critical current $I_c$ vs temperature $T$ for different values of thickness $d_F$ of HM and ${\xi }_0={\xi }_T(T_c)$.