Angular conductance resonances of quantum dots strongly coupled to noncollinearly oriented ferromagnetic leads

The transport properties of quantum dots coupled to noncollinear magnetic leads is investigated. It is found that the conductance, and current, of the system in the strongly coupled regime is a nonmonotonic function of the angle between the magnetization directions in the two leads. Because of many-body interactions between electrons in the localized states of the quantum dot, induced by the presence of the conduction electrons in the leads, the positions of the quantum dot states are shifted in a spin-dependent way. Thus, the physics of the quantum dot is dynamically dependent on the angle between the magnetization directions of the two leads, which in combination with spin-flip transitions explains the nonmonotonic behavior of the magnetoresistance. The linear response conductance shows a rich complexity ranging from negative to positive magnetoresistance, depending on the positions of the localized states. The nonmonotonic transport characteristics persists for finite bias voltages.

Figure 1

The QD coupled to noncollinearly oriented ferromagnetic leads. The global reference frame and the magnetization $M^L$ of the left reservoir coincide, while the magnetization $M^R$ of the right reservoir is rotated by the angle $\varphi$. In the figure, the bare transition energies, ${\Delta }_{\sigma 0}^0={\epsilon }_0$ and ${\Delta }_{2\sigma }^0={\epsilon }_0+U$ are indicated.

Figure 2

(Color online). The angular dependence of the dressed transition energies in equilibrium (solid) and nonequilibrium (dashed) at the bias voltage $eV∕{\Gamma }_0=5$. The bare transition energies ${\Delta }_{\sigma 0}^0$, ${\Delta }_{2\overline{\sigma }}^0$ are included for reference. Here, $\{{\epsilon }_0,U,\mu \}∕{\Gamma }_0=\{0,2,0\}$, and the spin asymmetry $p_{L∕R}=0.85$ at $T∕{\Gamma }_0=0.08$.

Figure 3

Conductance $G\left(\varphi \right)∕G_0(G_0=e^2∕h)$ as function of the rotation angle $\varphi ∕\pi$ and equilibrium chemical potential $\mu ∕{\Gamma }_0$. Here, $\{{\epsilon }_0,U,k_{B}T\}∕{\Gamma }_0=\{0,2,0.08\}$ and the spin asymmetry $p_{L∕R}=0.85$.

Figure 4

(Color online). Spin-resolved $j_{\sigma }(\omega ,\varphi )$ (a, b) current density and (c, d) density of states ${\rho }_{\sigma }(\omega ,\varphi )$, for a few angles $\varphi ∕\pi ∊\{0,1∕3,2∕3,1\}$ at (a) and (c), $\mu ∕{\Gamma }_0=-0.9$, and (b) and (d), $\mu ∕{\Gamma }_0=0.3$. The positions of the chemical potential (solid), $\mu ∕{\Gamma }_0$, and the bare transition energy (dashed), ${\Delta }_{\sigma 0}^0∕{\Gamma }_0=0$ and ${\Delta }_{2\overline{\sigma }}^0∕{\Gamma }_0=2$, are shown for reference.

Figure 5

(Color online). Magnetoresistance $\mathit{MR}\left(\varphi \right)$ as function of the rotation angle for various values of the correlation strength $U$. Here, $\mu ∕{\Gamma }_0=-0.9$ and other parameters as in Fig. 3

Figure 6

(Color online). (a) $J\text{−}V$ characteristics for various rotation angles, (b) angular dependence of the magnetoresistance for different bias voltages, and (c) detail of the $J\text{−}V$ characteristics. Here, $\mu ∕{\Gamma }_0=0$, whereas $\{{\epsilon }_0,U,k_{B}T\}∕{\Gamma }_0=\{1.5,10,0.08\}$.

Figure 7

(Color online). Differential conductance for various rotation angles, calculated as the numerical derivative of the $J\text{−}V$ characteristics in Fig. 6a.

Figure 8

(Color online). Current for various rotation angles. The current resulting from the HIA at $\varphi ∕\pi =2∕3$ is shown as reference. Inset showing the current over a wider bias voltage interval. Here $\{{\epsilon }_0,U,k_{B}T\}∕{\Gamma }_0=\{5,4,0.08\}$ and $p_L=0.4$ and $p_R=1$.