Coulomb Promotion of Spin-Dependent Tunneling

We study transport of spin-polarized electrons through a magnetic single-electron transistor (SET) in the presence of an external magnetic field. Assuming the SET to have a nanometer size central island with a single-electron level we find that the interplay on the island between coherent spin-flip dynamics and Coulomb interactions can make the Coulomb correlations promote rather than suppress the current through the device. We find the criteria for this new phenomenon—Coulomb promotion of spin-dependent tunneling—to occur.

Figure 1

Sketch of the nanomagnetic SET device discussed in the text: a quantum dot, modeled as a single spin-degenerate electron level, is coupled to two leads with antiparallel magnetization. $T_{L,R}$ are probability amplitudes for tunneling from the dot to the left and right leads, and $U$ is the Coulomb interaction energy of a doubly occupied dot. The potential difference ${\mu }_L-{\mu }_R=eV$ between the leads is due to a bias voltage $V$. An external magnetic field $h$ induces flips between the spin-up and spin-down states (dotted arrows) on the dot.

Figure 2

Drop of the magnetic-field promoted current $\Delta J$, due to the lifting of the Coulomb blockade at $V=U$, as a function of the asymmetry parameter $\alpha$ for different lead polarizations $\beta$ (see text). The inset shows a domain in the $\alpha ,\beta$ plane, where a negative differential conductance (NDC) may be observed (dark). The drop in the total current associated with a NDC is of order $I_{\parallel }$ and peaks at $\beta =1$, $\alpha \simeq +1$.

Figure 3

Current $I$ through an asymmetric $(\alpha =0.9)$ magnetic SET structure as a function of transverse magnetic field $h$ and bias voltage $V$. The magnetization of source and drain is antiparallel; the polarization parameter $\beta =0.98$. For fixed magnetic field the current changes abruptly at the CB threshold, where $V=U$. The background current at $h=0$ and the large-field current $h\gg \Gamma /\mu$ increase as expected when the CB is lifted. In contrast, in some interval of intermediate magnetic fields (controlled by the polarization parameter $\beta$), the current drops when the CB is lifted. This is one signature of the Coulomb promotion phenomenon described in the text.