Finite-temperature spintronic transport through Kondo quantum dots: Numerical renormalization group study

We study the temperature dependence of the linear conductance and tunnel magnetoresistance of quantum dots coupled to ferromagnetic leads. Using the numerical renormalization group method, we determine transport properties for a wide range of temperatures $T$, ranging from zero through the Kondo temperature $T_K$ up to the high-temperature regime. We show that tunnel magnetoresistance in the local moment regime displays a nonmonotonic dependence on $T$ and vanishes when $T~T_K$. In addition, we also analyze the spin polarization $\mathcal{P}$ of the linear conductance in the parallel configuration and show that $\mathcal{P}$ is suppressed in the odd electron Coulomb blockade valley and can be enhanced above the spin polarization of the leads in the even Coulomb valley.

Figure 1

(a) Schematic of a quantum dot coupled to ferromagnetic leads. The leads’ magnetizations can form either parallel or antiparallel configurations. The normalized spectral function ${\mathcal{A}}^{\mathrm{AP}/\mathrm{P}}$ in the (b) antiparallel (AP) and (c) parallel (P) configuration as a function of energy $\omega$ and the position of the dot level $\varepsilon$. For parameters, we assumed that $U=1.2$ meV, $\Gamma =0.1$ meV, $p=0.5,$ and $T=0$.

Figure 2

The linear conductance in the (a) antiparallel and the (b) parallel configurations, $G^{\mathrm{AP}/\mathrm{P}}={\sum }_{\sigma }{G}_{\sigma }^{\mathrm{AP}/\mathrm{P}}$; the spin-resolved conductance in the parallel configuration for (d) spin-up $G_{\uparrow }^{\mathrm{P}}$ and (e) spin-down $G_{\downarrow }^{\mathrm{P}}$; as well as (c) the TMR and (f) spin polarization $\mathcal{P}=(G_{\uparrow }^{\mathrm{P}}-G_{\downarrow }^{\mathrm{P}})/G^{\mathrm{P}}$ as a function of the temperature $T$ and the position of the dot level $\varepsilon$. The other parameters are the same as in Fig. 1.

Figure 3

The temperature dependence of the linear conductance $G^{\mathrm{AP}/\mathrm{P}}$ in the (a) antiparallel and (b) parallel configurations as well as (c) the TMR and (d) spin polarization $\mathcal{P}$ for different values of the level position $\varepsilon$, as indicated. The vertical dashed line indicates the Kondo temperature $T_K$, $T_K/\Gamma \simeq 0.022$. Parameters are as in Fig. 1.