Spin Current through a Quantum Dot in the Presence of an Oscillating Magnetic Field

Nonequilibrium spin transport through an interacting quantum dot is analyzed. The coherent spin oscillations in the dot provide a generating source for spin current. In the interacting regime, the Kondo effect is influenced in a significant way by the presence of the processing magnetic field. In particular, when the precession frequency is tuned to resonance between spin-up and spin-down states of the dot, Kondo singularity for each spin splits into a superposition of two resonance peaks. The Kondo-type cotunneling contribution is manifested by a large enhancement of the pumped spin current in the strong coupling low temperature regime.

Figure 1

Model setup for spin transport through a QD. Because of the imbalance between spin-up and spin-down chemical potentials (see text), the electron may tunnel from the spin-down channel, through the QD, to the spin-up channel.

Figure 2

(a) Noninteracting spin current at different temperatures with the undressed spin levels set ${\epsilon }_{d\uparrow }=-2.5$, ${\epsilon }_{d\downarrow }=-1.5$; (b) Contour plot of spin current as a function of gate voltage and rotating frequency. The spin levels in the dot are modulated by the gate voltage as ${\epsilon }_{d\sigma }(V_g)={\epsilon }_{d\sigma }+e{V}_g$ with ${\epsilon }_{d\uparrow }=1$, ${\epsilon }_{d\downarrow }=2$. Other parameters are $\Gamma =0.1$ and $g{\mu }_B{B}_1=0.2$.

Figure 3

Spin current versus gate voltage for different rotating frequencies with $U=2$. Other parameters are the same as in Fig. 2b.

Figure 4

The spin-up (solid state) and spin-down (dashed line) spectral densities at different rotating frequency. Parameters are ${\epsilon }_{d\uparrow }=-2.5\Gamma$, ${\epsilon }_{d\downarrow }=-1.5\Gamma$, $T=0.001\Gamma$, and $g{\mu }_B{B}_1=0.2\Gamma$.

Figure 5

Spin current in the Kondo-type cotunneling regime (solid line). The noninteracting spin current is also shown (dotted line) for comparison. Other parameters are the same as in Fig. 4.