Scanning tunneling microscope operating as a spin diode

We theoretically investigate spin-polarized transport in a system composed of a ferromagnetic scanning-tunneling-microscope (STM) tip coupled to an adsorbed atom (adatom) on a host surface. Electrons can tunnel directly from the tip to the surface or via the adatom. Since the tip is ferromagnetic and the host surface (metal or semiconductor) is nonmagnetic we obtain a spin-diode effect when the adatom is in the regime of single occupancy. This effect leads to an unpolarized current for direct bias ($V>0$) and polarized current for reverse ($V<0$) bias voltages, if the tip is nearby the adatom. Within the nonequilibrium Keldysh technique we analyze the interplay between the lateral displacement of the tip and the intra adatom Coulomb interaction on the spin-diode effect. As the tip moves away from the adatom the spin-diode effect vanishes and the currents become polarized for both $V>0$ and $V<0$. We also find an imbalance between the up and down spin populations in the adatom, which can be tuned by the tip position and the bias. Finally, due to the presence of the adsorbate on the surface, we observe spin-resolved Friedel oscillations in the current, which reflects the oscillations in the calculated local density of states (LDOS) of the subsystem surface $+$ adatom.

Figure 1

Ferromagnetic scanning-tunneling-microscope (FM-STM) tip coupled to a host surface with an adatom. The matrix elements $t_{12}$, $t_{13}$, and $t_{23}$ represent tip-adatom, tip-surface, and adatom-surface couplings, respectively. The tip-adatom lateral distance is denoted by $R$.

Figure 2

(a) Adatom occupations and magnetization and (b) spin-resolved currents against the tip position $R$. Both negative (grey line) and positive (black line) bias voltages are shown. For $\left|eV\right|=30{\Gamma }_0$, only single occupancy (i.e., ${\epsilon }_{\sigma }+U$ is much higher than the emitter chemical potential) is allowed. This results in the spin-diode effect: for negative bias voltages the current is polarized for all $R$ values while for positive biases the current polarization goes to zero when the tip is close to the adatom. Panel (c)–(f): zoom of each spin component of the current in the range where the tip-adatom coupling is negligible. In (c) we also show the LDOS (thick solid black line) evaluated at ${\epsilon }_F$. The LDOS displays Friedel oscillations which show up in the polarized current. The vertical scale for the LDOS is not shown.

Figure 3

Similar to Fig. 2 except that $\left|eV\right|=150{\Gamma }_0$ here. This bias allows double occupancy of the adatom. In this regime no spin-diode effect is observed. The spin polarized currents are the same (in modulus) for both positive and negative $eV$. For forward voltages (black curves), the adatom becomes doubly occupied for large $R$ values ($n_{\uparrow }+n_{\downarrow }=2$).

Figure 4

Current polarization against $R$. In the single-occupancy regime ($eV=\pm 30{\Gamma }_0$) the current polarization is approximately constant for reverse bias ($V<0$) and goes down to zero for direct bias ($V>0$) when the tip is close to the adatom. In the case of double occupancy ($eV=\pm 150{\Gamma }_0$), the current polarization is suppressed for small $R$, however, it does not vanish; notice that the dotted lines lie essentially on top of each other. For large $R$'s, the polarization for both single and double occupancies tends to a plateau and presents tiny oscillations (inset).