Time-dependent single electron tunneling through a shuttling nanoisland

We offer a general approach to the calculation of single electron tunneling spectra and conductance of a shuttle oscillating between two half-metallic leads with fully spin-polarized carriers. In this case the spin-flip processes are completely suppressed and the problem may be solved by means of canonical transformation, where the adiabatic component of the tunnel transparency is found exactly, whereas the nonadiabatic corrections can be taken into account perturbatively. Time-dependent corrections to the tunnel conductance of moving shuttle become noticeable at finite bias in the vicinity of the even/odd occupation boundary at the Coulomb diamond diagram.