Single-atom gating and magnetic interactions in quantum corrals

Single-atom gating, achieved by manipulation of adatoms on a surface, has been shown in experiments to allow precise control over superposition of electronic states in quantum corrals. Using a Green's function approach, we demonstrate theoretically that such atom gating can also be used to control the coupling between magnetic degrees of freedom in these systems. Atomic gating enables control not only on the direct interaction between magnetic adatoms, but also over superpositions of many-body states which can then control long distance interactions. We illustrate this effect by considering the competition between direct exchange between magnetic impurities and the Kondo screening mediated by the host electrons, and how this is affected by gating. These results suggest that both magnetic and nonmagnetic single-atom gating may be used to investigate magnetic impurity systems with tailored interactions, and may allow the control of entanglement of different spin states.

Figure 1

RKKY interaction between magnetic adatoms in a QC and nonmagnetic atom gating. (a) One of the magnetic atoms is moved along the $x$ direction, while the other is kept fixed at the left focus, $x_c\approx 64\AA$ (red curve). The QC phase shifts and reduces the interaction in comparison with the free 2DEG (blue curve). (b) Two magnetic atoms are fixed at 1-nm separation, while a third nonmagnetic atom moves along the line $y=1\mathrm{nm}$. The RKKY interaction is strongly modulated when near the two magnetic adatoms. (c) RKKY for magnetic adatoms at 2.1-nm separation; the nonmagnetic atom gating greatly enhances as it sits a few nanometers away from the magnetic pair. Notice different vertical scales in all panels. We have set $J=0.2$ eV in all these plots.

Figure 2

Spatial scan of the LDOS at the Fermi energy. (a) Empty QC with no magnetic impurities. (b) QC with two magnetic impurities, one at the left focus, and the other one 2 nm away.

Figure 3

Magnetic adatom gating of quantum mirage signal: RKKY vs Kondo competition. Spectral function $A$ (LDOS) at the empty focus in the QC, $\vec{r}=(c,0)$, as function of energy near the Fermi energy for different configurations. One adatom is held at left focus, ${\vec{r}}_1=(-c,0)$, while second is placed at ${\vec{r}}_2$ as labeled (10, 21, and 50 Å away). Inset shows corresponding ${\widehat{T}}_{11}$ vs energy. When close to each other, adatoms form a local singlet as RKKY dominates (red curves), while Kondo prevails at large separation (blue).

Figure 4

Nonmagnetic atom gating regulates RKKY vs Kondo states. LDOS at the empty right focus, $\vec{r}=(c,0)$, as a function of energy, for different configuration of three adatoms. Two magnetic impurites are 2.1 nm apart, with one at the left focus. The third nonmagnetic adatom is placed at different locations, as indicated by ${\vec{r}}_3$. When gating adatom is close to magnetic pair, the RKKY interaction dominates, causing only small features in LDOS and weak ${\widehat{T}}_{11}$ (pink curves). At larger separations, the RKKY nearly vanishes (see Fig. 1), and the Kondo screening of each impurity dominates, as seen clearly in the green curves.