Theory of a magnetically controlled quantum-dot spin transistor

We examine transport through a quantum dot coupled to three ferromagnetic leads in the regime of weak tunnel coupling. A finite source-drain voltage generates a nonequilibrium spin on the otherwise nonmagnetic quantum dot. This spin accumulation leads to magnetoresistance. A ferromagnetic but current-free base electrode influences the quantum-dot spin via incoherent spin-flip processes and coherent spin precession. As the dot spin determines the conductance of the device, this allows for a purely magnetic transistorlike operation. We analyze the effect of both types of processes on the electric current in different geometries.

Figure 1

Spin transistor consisting of a quantum dot connected to source and drain leads by tunnel contacts. Source and drain have antiparallel magnetizations so that a nonequilibrium spin is accumulated on the dot, which modifies the conductance of the device. A floating base lead can be used to influence the dot state solely by spin currents, i.e., the source-drain conductance can be modified by the alignment of the magnetization alone.

Figure 2

Angular dependence of the normalized conductance change $\Delta =\left[G\right(\theta )-G_{\Vert }]∕G_{\Vert }$ of the spin transistor (solid line). Comparison to the case where the exchange field was artificially set to zero (dashed) reveals that the transistor effect is significantly enhanced by exchange interaction. The parameters are $\epsilon =0.6U$, $p_L=p_M=p_R=0.6$, ${\Gamma }_L={\Gamma }_M={\Gamma }_R$, and $U=10k_{B}T$.

Figure 3

(a) Gate-voltage dependence of $\Delta =\left[G\right(\theta )-G_{\Vert }]∕G_{\Vert }$ with (solid) and without (dashed) exchange field for $\theta =\pi ∕2$. The level position is at $\epsilon =0$, and charging energy is $U=10k_{B}T$. (b) Absolute value of the exchange field of the middle lead for $p_M=1$. (c) Spin lifetime in the parallel case ${\tau }_{s_{\Vert }}$. The product $B_M{\tau }_{s_{\Vert }}$ determines the conductance change. Other parameters as in Fig. 2.

Figure 4

Two realizations of a system with pairwise orthogonally magnetized leads connected by reversal of the base magnetization. Their different symmetry can be reflected in the symmetry of the conductances.

Figure 5

Rotation shows that the right-handed system is symmetric with the left-handed system with reversed current and voltage.

Figure 6

Current-voltage characteristic for the orthogonal configuration with $p_L=p_R=p_M=0.6$, ${\Gamma }_L={\Gamma }_R={\Gamma }_M=\Gamma$, $\epsilon =10k_{B}T$, $U=30k_{B}T$.