Figure 1

Current-voltage characteristic of a quantum dot connected to three ferromagnetic leads $i\in \{1,2,3\}$, with respective polarizations $P_i$, through tunnel junctions with capacitances $C_i$ and net tunneling rates ${\gamma }_i$ (circuit shown in the inset). A bias voltage $V$ is applied to leads 1 and 3; lead 2 is connected to ground. The average current $I_2$ through lead 2 is shown as a function of voltage, for $C_1=C_2=C_3$, ${\gamma }_1={\gamma }_2/50={\gamma }_3/10$, $k_{B}T/E_0=0.1$, and different values of lead polarizations. The current is plotted in units of $e{\gamma }_{\mathrm{tot}}=e{\gamma }_2({\gamma }_1+{\gamma }_3)/({\gamma }_1+{\gamma }_2+{\gamma }_3)$; the voltage in units of $V_0=E_{0}C/(C_1+C_3)e$; $E_0$ is the position of the dot level. For $P_1=P_2=P_3$, $I_2$ coincides with the paramagnetic case (diamonds). In the other cases, the high-voltage limit of $I_2$ can be larger or smaller than the paramagnetic value, depending on the lead polarizations. For $P_1=-P_2=P_3=0.6$ (circles), the effect of spin-flip scattering is shown. Spin-flip scattering makes the $I_2-V$ curve tend to the paramagnetic one.Reuse & Permissions

Figure 2

Fano factor $F=S_{22}/2e{I}_2$ of lead 2 as a function of voltage, for the same circuit parameters as in Fig. 1. In all curves ${\gamma }_{sf}=0$. For $P_1=P_2=P_3$, the Fano factor is different from that of the paramagnetic case (diamonds) in contrast to what happens for the average currents. The inset shows the typical time dependence of the spin on the dot, in the high-voltage limit $V\gg V_0$ for the case $P_1=P_2=P_3=0.6$.Reuse & Permissions

Figure 3

Current cross correlations between leads 1 and 3 as a function of voltage. The curves are shown for the same circuit parameters as in Fig. 2. The cross correlations can be positive in the cases $P_1=-P_2=P_3=0.6$ (circles) and $P_1=P_2=P_3=0.6$ (squares). Note that the sign of cross correlations can be reversed by changing the sign of $P_1$. In all curves ${\gamma }_{sf}=0$. The inset shows the influence of spin-flip scattering on the cross correlations in the high-voltage limit $V\gg V_0$. In the paramagnetic case (diamonds), spin-flip scattering has no effect. In the limit ${\gamma }_{sf}\gg {\gamma }_{\mathrm{tot}}$, the cross correlations tend to the paramagnetic value.Reuse & Permissions

Figure 4

Influence of the asymmetry between ${\gamma }_2$ and ${\gamma }_1+{\gamma }_3$ on the high-voltage limit of the cross correlations, for $P_1=P_2=P_3=0.6$ (squares) and $-P_1=P_3=0.9$, $P_2=0$ (hexagons), for ${\gamma }_3/{\gamma }_1=10$ (full symbols) and ${\gamma }_3/{\gamma }_1=1$ (empty symbols). Large values of ${\gamma }_2/({\gamma }_1+{\gamma }_3)$ favor positive cross correlations. For $-P_1=P_3=0.9$, $P_2=0$, an asymmetry between ${\gamma }_1$ and ${\gamma }_3$ is also necessary. The vertical dotted line indicates the ratio ${\gamma }_2/({\gamma }_1+{\gamma }_3)$ corresponding to Figs. 1, 2. The two insets show the high-voltage limit of the cross correlations as a function of $P_3$, for ${\gamma }_1={\gamma }_2/50={\gamma }_3/10$, $P_1=P_3$ (left inset), $P_1=-P_3$ (right inset), and $P_2=0$ (dashed lines) or $P_2=0.6$ (full lines). For all curves ${\gamma }_{sf}=0$.Reuse & Permissions