Interplay of the Kondo Effect and Spin-Polarized Transport in Magnetic Molecules, Adatoms, and Quantum Dots

We study the interplay of the Kondo effect and spin-polarized tunneling in a class of systems exhibiting uniaxial magnetic anisotropy. Using the numerical renormalization group method we calculate the spectral functions and linear conductance in the Kondo regime. We show that the exchange coupling between conducting electrons and localized magnetic core generally leads to suppression of the Kondo effect. We also predict a nontrivial dependence of the tunnel magnetoresistance on the strength of exchange coupling and on the anisotropy constant.

Figure 1

(a) Schematic of a molecular quantum dot (magnetic molecule, magnetic adatom, or quantum dot exchange coupled to a magnetic moment) coupled to two ferromagnetic electrodes. (b)–(e) Normalized spin-resolved orbital level (OL) spectral functions $\pi {\Gamma }_{\sigma }{A}_{\sigma }(\omega )$ in the antiparallel (left) and parallel (right part of each figure) magnetic configuration of electrodes for two different values of the exchange parameter $J$. The bottom curves (black) in each plot correspond to $J=0$, with the solid line referring to $\sigma =\uparrow$ and the dashed one to $\sigma =\downarrow$. To increase readability, for $J\ne 0$ the curves for $\sigma =\uparrow$ ($\sigma =\downarrow$) are shifted up and right by 0.2 (0.4). The parameters are $S=2$, $U=1\mathrm{meV}$, $\epsilon /U=-0.5$, $\Gamma /U\approx 0.075$, $D/U\approx 1.7\times {10}^{-4}$, and $p=0.5$.

Figure 2

(a)–(f) Dependence of the linear conductance $g_{\sigma }$ on the OL energy $\epsilon$ for indicated values of the exchange parameter $J$ in the antiparallel (a),(b) and parallel (c)–(f) magnetic configuration. Panels (g) and (h) show the corresponding TMR. Top panel represents the case of ferromagnetic ($J>0$) coupling between electrons in the OL and MQD’s magnetic core, whereas the bottom one corresponds to the antiferromagnetic ($J<0$) coupling. Parameters as in Fig. 1.

Figure 3

Conductance $g=\sum _{\sigma }{g}_{\sigma }$ (a),(b) and TMR (c),(d) in the parallel (P) and antiparallel (AP) configurations as a function of the exchange parameter $J$ for indicated values of the OL energy $\epsilon$. The dashed vertical line indicates the Kondo temperature. Other parameters as in Fig. 1.

Figure 4

Influence of the molecule’s magnetic anisotropy $D$ on TMR for the ferromagnetic (a) and antiferromagnetic (b) exchange coupling $J$. Parameters are the same as in Fig. 1 with $|J|=2T_K$.