Adiabatic charge and spin pumping through quantum dots with ferromagnetic leads

We study the adiabatic pumping of electrons through quantum dots attached to ferromagnetic leads. Hereby, we make use of a real-time diagrammatic technique in the adiabatic limit that takes the strong Coulomb interaction in the dot into account. We analyze the degree of spin polarization of electrons pumped from a ferromagnet through the dot to a nonmagnetic lead (N-dot-F) as well as the dependence of the pumped charge on the relative leads’ magnetization orientations for a spin-valve (F-dot-F) structure. For the former case, we find that, depending on the relative coupling strength to the leads, spin and charge can, on average, be pumped in opposite directions. For the latter case, we find an angular dependence of the pumped charge, which becomes more and more anharmonic for large spin polarization in the leads.

Figure 1

Schematic illustration of the N-dot-F or F-dot-F setup. The magnetization directions and the polarization strengths of the left and right leads can, in general, differ from each other (left). Sketch of the coordinate system and the magnetization directions of the leads (right).

Figure 2

(a) Ratio of the pumped spin per period (in units of $\hslash /2$) to the pumped charge per period (in units of $-e$) as a function of the relative tunnel-coupling strength ${\overline{\Gamma }}_R/\overline{\Gamma }$ for different polarizations of the right lead. (b) Ratio between the linear dc spin conductance and the linear dc conductance as a function of the relative tunnel-coupling strength ${\overline{\Gamma }}_R/\overline{\Gamma }$ for different polarizations of the right lead.

Figure 3

Time-resolved spin and charge currents as a function of time. The values of the parameters used for this plot are $p_R=0.99$, ${\overline{\Gamma }}_L={\overline{\Gamma }}_R$, $\overline{ϵ}=-\overline{\Gamma }$, $U=10\overline{\Gamma }$, $\left|\delta {\Gamma }_L\right|/\overline{\Gamma }=\left|\delta ϵ\right|/\overline{\Gamma }=0.1$, and $k_{B}T=\overline{\Gamma }$.

Figure 4

Pumped charge as a function of the average level position $\overline{ϵ}$ for different values of the angle between the magnetizations. The polarizations in the leads are $p_L=p_R=0.8$.

Figure 5

Pumped charge as a function of the angle between the magnetizations of the leads $\varphi$ for different polarization strengths $p_L=p_R=p$. This result does not depend on the level position and the interaction strength.

Figure 6

Pumped charge as a function of the polarization strength $p=p_L=p_R$ for different values of the angle between the magnetizations. This result does not depend on the level position and the interaction strength.