Spin effects in electron tunneling through a quantum dot coupled to noncollinearly polarized ferromagnetic leads

Spin-dependent transport through an interacting single-level quantum dot coupled to ferromagnetic leads with noncollinear magnetizations is analyzed theoretically. The transport properties and average spin of the dot are investigated within the nonequilibrium Green function technique based on the equation of motion in the Hartree-Fock approximation. Numerical results show that Coulomb correlations on the dot and strong spin polarization of the leads significantly enhance precession of the average dot spin around the effective molecular field created by the external electrodes. Moreover, they also show that spin precession may lead to negative differential conductance in the voltage range between the two relevant threshold voltages. Nonmonotonous angular variation of electric current and change in sign of the tunnel magnetoresistance are also found. It is also shown that the diodelike behavior in asymmetrical junctions with one electrode being half-metallic is significantly reduced in noncollinear configurations.

Figure 1

Schematics of the system considered in this paper. The coordinate systems used to describe states of the dot is also shown.

Figure 2

Bias dependence of electric current (a), differential conductance (b), and tunnel magnetoresistance (c), calculated for indicated values of the angle $\phi$. The inset in (a) shows electric current between the lower and higher threshold voltages for $\phi =2\pi ∕3$. The parameters assumed for numerical calculations are: ${\epsilon }_d=0.1\mathrm{eV},U=0.4\mathrm{eV},{\Gamma }_0=0.01\mathrm{eV},p_l=p_r=1,\alpha =1$, and $T=100\mathrm{K}$.

Figure 3

Bias dependence of the average spin components; $⟨S_z⟩$ (a), $⟨S_x⟩$ (b), and $⟨S_y⟩$ (c) for indicated values of the angle $\phi$. The other parameters are as in Fig. 2.

Figure 4

Bias dependence of the average spin component $⟨S_y⟩$ for $\phi =2\pi ∕3$ and for indicated values of the Coulomb correlation parameter $U$ (a) and the lead polarization (b). The other parameters are as in Fig. 2.

Figure 5

Bias dependence of the tunnel magnetoresistance in symmetrical junctions for indicated values of the lead polarization. The curves are plotted for the noncollinear configuration, $\phi =2\pi ∕3$. The other parameters are as in Fig. 2.

Figure 6

Bias dependence of electric current (a), and the average value of the $y$ component of the dot spin (b), calculated for indicated values of the angle $\phi$ and ${\epsilon }_d=-0.1\mathrm{eV}$. The other parameters are as in Fig. 2.

Figure 7

Bias dependence of electric current (a) and magnetoresistance (b), calculated for indicated values of the angle $\phi$. The inset in (a) shows current between the threshold voltages for negative bias. The parameters assumed for numerical calculations are: ${\epsilon }_d=0.1\mathrm{eV},U=0.4\mathrm{eV},{\Gamma }_0=0.01\mathrm{eV},p_l=0.4,p_r=1,\alpha =0.1$, and $T=100\mathrm{K}$.

Figure 8

Angular variation of electric current (a) and TMR (b) for indicated values of the bias voltage. The other parameters are as in Fig. 7

Figure 9

Bias dependence of the average spin components; $⟨S_z⟩$ (a), $⟨S_x⟩$ (b), and $⟨S_y⟩$ (c) for indicated values of the angle $\phi$. The other parameters are as in Fig. 7.

Figure 10

Bias dependence of electric current (a), and the average value of the $y$ component of the dot spin (b), calculated for indicated values of the angle $\phi$ and ${\epsilon }_d=-0.1\mathrm{eV}$. The other parameters are as in Fig. 7.