Effect of intrinsic spin relaxation on the spin-dependent cotunneling transport through quantum dots

Spin-polarized transport through quantum dots is analyzed theoretically in the cotunneling regime. It is shown that the zero-bias anomaly, found recently in the antiparallel configuration, can also exist in the case when one electrode is magnetic while the other one is nonmagnetic. The physical mechanism of the anomaly is also discussed. It is demonstrated that intrinsic spin relaxation in the dot has a significant influence on the zero-bias maximum in the differential conductance—the anomaly becomes enhanced by weak spin-flip scattering in the dot and then disappears in the limit of fast spin relaxation. Apart from this, inverse tunnel magnetoresistance has been found in the limit of fast intrinsic spin relaxation in the dot. The diode-like behavior of transport characteristics in the cotunneling regime has been found in the case of quantum dots asymmetrically coupled to the leads. This behavior may be enhanced by spin-flip relaxation processes.

Figure 1

The differential conductance in the parallel and antiparallel configurations (a,b) and tunnel magnetoresistance (c) as a function of the bias voltage for different spin relaxation $r=h∕\left({\tau }_{\mathrm{sf}}\Gamma \right)$. The parameters are $k_{\mathrm{B}}T=0.2\Gamma$, $\epsilon =-15\Gamma$, $U=30\Gamma$, and $p_{\mathrm{L}}=p_{\mathrm{R}}=0.5$.

Figure 2

The spin accumulation in the antiparallel configuration as a function of the bias voltage for different spin relaxation $r=h∕\left({\tau }_{\mathrm{sf}}\Gamma \right)$. The parameters are the same as in Fig. 1.

Figure 3

The spin relaxation time dependence of the linear conductance in the antiparallel configuration (a) and the relative height of the zero-bias anomaly in differential conductance (b), as well as the linear-response TMR (c). The parameters are the same as in Fig. 1.

Figure 4

The differential conductance in the nonlinear response regime for different spin relaxation in the parallel (a) and antiparallel (b) configurations. The parameters are $k_{\mathrm{B}}T=0.2\Gamma$, ${\epsilon }_{\uparrow }=-16\Gamma$, ${\epsilon }_{\downarrow }=-14\Gamma$, $U=30\Gamma$, and $p=0.5$.

Figure 5

The differential conductance in the nonlinear response regime for the asymmetric (a,c) and symmetric (b) Anderson model for different spin relaxation. The parameters are $k_{\mathrm{B}}T=0.2\Gamma$, $U=60\Gamma$, $p_{\mathrm{L}}=0.95$, and $p_{\mathrm{R}}=0$.

Figure 6

The differential conductance in the nonlinear response regime for different spin relaxation. The parameters are $k_{\mathrm{B}}T=0.2\Gamma$, ${\epsilon }_{\uparrow }=\epsilon -\Delta ∕2$, ${\epsilon }_{\downarrow }=\epsilon +\Delta ∕2$, $\Delta =2\Gamma$, $U=60\Gamma$, $p_{\mathrm{L}}=0.95$, and $p_{\mathrm{R}}=0$.