Pumping $ac$ Josephson current in the Single Molecular Magnets by spin nutation

We demonstrate that an {\it ac} Josephson current is pumped through the Single Molecular Magnets (SMM) by the spin nutation. The spin nutation is generated by applying a time dependent magnetic field to the SMM. We obtain the flowing charge current through the junction by working in the tunneling limit and employing Green’s function technique. At the resonance conditions some discontinuities and divergencies are appeared in the normal and Josephson currents, respectively. Such discontinuities and divergencies reveal themselves when the absorbed/emitted energy, owing to the interaction of the quasiparticles with the spin dynamics are in the range of the superconducting gap.