Kondo Effect in Quantum Dots Coupled to Ferromagnetic Leads

We study the Kondo effect in a quantum dot coupled to ferromagnetic leads and analyze its properties as a function of the spin polarization of the leads. Based on a scaling approach, we predict that for parallel alignment of the magnetizations in the leads the strong-coupling limit of the Kondo effect is reached at a finite value of the magnetic field. Using an equation of motion technique, we study nonlinear transport through the dot. For parallel alignment, the zero-bias anomaly may be split even in the absence of an external magnetic field. For antiparallel spin alignment and symmetric coupling, the peak is split only in the presence of a magnetic field, but shows a characteristic asymmetry in amplitude and position.

Figure 1

Spin-dependent DOS for spin-up (solid line) and spin-down (dashed line), calculated for P and AP alignment (as indicated), for a spin polarization of the leads $P=0.2$. The parts (d),(e) include the effect of an applied magnetic field $B$ and (b),(e) of an applied bias voltage $V$. The other parameters are $T/\Gamma =0.005$ and $ϵ/\Gamma =-2$.

Figure 2

Total differential conductance (solid lines) as well as the contributions for spin-up (dashed lines) and spin-down (dot-dashed lines) vs the applied bias voltage $V$ at zero magnetic field $B=0$ (a),(c),(e) and at finite magnetic field (b),(d),(f),(h) for normal (a),(b) and ferromagnetic leads with parallel (c),(d) and antiparallel (e),(f),(h) alignment of the lead magnetizations. (g) The tunnel magnetoresistance, $\mathrm{T}\mathrm{M}\mathrm{R}=(G_{\mathrm{P}}-G_{\mathrm{A}\mathrm{P}})/G_{\mathrm{A}\mathrm{P}}$, for the cases (c) and (e). (h) The conductance $G_{\mathrm{A}\mathrm{P}}/(1-P^2)$ for several values of $P$ as indicated. Other parameters are as in Fig. 1