Figure 1

(Color online) Schematics of the precessing magnetic dot coupled to two large reservoirs and the effective spin splittings of the chemical potentials associated with the fictitious Zeeman field of $\hslash \omega$, according to Eqs. (2, 3), in the rotating frame of reference. The long black arrows show magnetization directions.Reuse & Permissions

Figure 2

(Color online) Low-frequency $I=0$ $\left(\hslash \omega ⪡E_c\right)$ numerical curves for $\mu >0$, $\theta =5°$, $P=2/3$, and $k_{B}T/E_c={10}^{-3}$. Here, the increasingly darker gray lines represent $\mu /E_c=\left(1,2,3,4,5\right)\times {10}^{-2}$, respectively, while the dotted-dashed red line corresponds to zero Coulomb blockade, Eq. (1). The $T=0$ small-angle analytic solution, Eq. (8), is shown as a dotted black line superimposed on the corresponding finite-temperature curve in black. Upper inset: high-frequency relief plot of current density for the same parameters as the solid black curve in the main panel with $t_L=t_R=t$ and $I_0=0.02e{k}_{B}T{D}^2{\left|t\right|}^2$. Lower inset: thermal effects for $\mu /E_c=-3\times {10}^{-2}$. The black curve corresponds to $k_{B}T/E_c={10}^{-3}$ and the increasingly long red dashed lines to $k_{B}T/E_c=\left(5,6,7,8\right)\times {10}^{-3}/2$, respectively. The dotted-dashed red line illustrates the zero Coulomb-blockade case, as in the main panel.Reuse & Permissions

Figure 3

(Color online) The solid gray scale curves in the main panel show the differential charge-pumping efficiency ${\mathcal{E}}_{\text{diff}}=\left(e/\hslash \right)\partial V_0/\partial \omega$ for $\mu /E_c=\left(1,2,3,4,5\right)\times {10}^{-2}$ at $\theta =5°$, $P=2/3$, and $k_{B}T/E_c={10}^{-3}$, according to Eq. (9). The dotted lines show sharper efficiency peaks as the temperature is lowered to $k_{B}T/E_c={10}^{-4}$. The dashed red lines show smearing of the peaks as the temperature is increased to $k_{B}T/E_c=\left(5,6,7\right)\times {10}^{-3}$ for $\mu /E_c=5\times {10}^{-2}$. Note that $\mu =0$ efficiency is too small to be seen. Inset: the nominal charge-pumping efficiency $\mathcal{E}=e{V}_0/\hslash \omega$ for the same parameters (omitting the $k_{B}T/E_c={10}^{-4}$ data).Reuse & Permissions

Figure 4

(Color online) Maximum efficiencies ${\mathcal{E}}_{\text{max}}^{+}$ and ${\mathcal{E}}_{\text{max}}^{-}$ for positive and negative gating $\mu$, respectively, at zero temperature and small angles $\theta$, obtained from Eq. (8). ${\mathcal{E}}_{\text{max}}^{+}\left(P\right)=-{\mathcal{E}}_{\text{max}}^{-}\left(-P\right)$. The inset schematics illustrate the difference between the two cases. The short black arrows show the effective spin-up/down chemical potentials in the dot and the leads. $\mu \gtrless 0$ corresponds to the empty/occupied dot $\left(N=0/1\right)$ in equilibrium, which becomes populated/emptied by spin-flipped tunneling (shown by the long red arrows toward/from the dot) when $\hslash \omega >\left|\mu \right|$.Reuse & Permissions