Charge and spin pumping in quantum wires by a time-dependent periodic magnetic field

Spin pumping through a quantum wire is considered in the tight binding approximation. With applying time-dependent periodic magnetic field on two sits of the quantum wire and by introducing the Ricatti operator in the Hilbert space of the sideband states (Floquet states), the Ricatti equation for a quantum wire driven by a time-periodic magnetic field is driven. Then, a recursive method is developed for numerical calculation of the Floquet scattering matrix by expressing the right and left transmission and reflection operators in terms of the Ricatti operator for electrons with spin up or down. By using this method, the dependences of the two components of the pumped spin current, i.e., the spin up and down pumped currents, and also the total pumped spin current and the charge pumped current on phase difference are evaluated; we have the equal and opposite directions of spin up and spin down currents for any phase difference, and, as a result, a total amplified spin current and a vanishing charge current. All kinds of the pumped currents for the asymmetric cases are nonzero for phase difference equal zero or pi, while they are zero for the symmetric cases. The dependences of total pumped spin current on driving frequency at zero and nonzero phase differences are investigated, and it is shown that the pumped spin current is quadratic in driving frequency. Finally, we show that all kinds of the pumped currents as a function of the wire-lead coupling show a sign reversal, which, in the viewpoint of theoretical physics, we can build a spintronic rectifier in nanoscale.