Tunable magnetism of a hexagonal Anderson droplet on the triangular lattice

Motivated by recent progress on quantum engineered Kondo lattices, we numerically investigated the local magnetic properties of a hexagonal Anderson droplet consisting of multiple rings of magnetic atoms periodically arrayed on a triangular lattice. We demonstrated the tunability of the magnetic properties via their evolution with the droplet geometry for two types of systems with distinct local orbital occupancy profiles. We found that the local susceptibility of the droplet center of some types of droplets can be remarkably enhanced, in contrast to the conventionally rapid decrease due to spin correlations of surrounding droplet rings. The tunability of the magnetic properties is attributed to the charge redistribution with varying the droplet geometry enforced by the confined lattice with an open boundary. Our simulations complement the exploration of the novel artificial tunability of engineered lattice systems.

Figure 1

Lattice structure of two types of Anderson droplets consisting of multiplet rings of Anderson impurities with distance (a) $n{a}_0$ and (b) $\sqrt{3}n{a}_0$, with $a_0\equiv 1$ being the lattice constant. $n$ is an integer, and only the $n=1$ case is shown here. The red line denotes the direction adopted to examine the evolution of local properties.

Figure 2

Local $f$-electron susceptibility ${\chi }_{ff}\left(\mathbf{r}\right)$ for various A and B droplet geometries in systems with both $\rho =1$ and $\mu =0$, where we have simplified the label as $A/Bn\equiv A/B\{n:N_r\}$ for various cases of $N_r$. $T=t/10$ is chosen to access large enough droplets (especially for $A1$ droplets).

Figure 3

Comparison of ${\chi }_{ff}(\mathbf{r}=0)$ at the central impurity as a function of the number of impurity rings $N_r$ for various A and B droplets.

Figure 4

(a) and (b) Comparison of ${\chi }_{ff}(\mathbf{r}=0)$ for droplets with a single impurity ring $N_r=1$ but varying distance $n$ to the central impurity at $T=t/20$. (c) and (d) The local orbital-dependent occupancy at the central impurity anticorrelates with ${\chi }_{ff}(\mathbf{r}=0)$.

Figure 5

Local orbital-resolved occupancy of droplet site ${\rho }_f\left(\mathbf{r}\right)$ (solid lines) and conduction electrons ${\rho }_c\left(\mathbf{r}\right)$ (dashed lines) in various systems at $T=t/10$. The general anticorrelation to ${\chi }_{ff}\left(\mathbf{r}\right)$ shown in Fig. 2 is visible.

Figure 6

Local interorbital susceptibility $|{\chi }_{cf}\left(\mathbf{r}\right)|$ for various systems at $T=t/10$. The general weaker dependence on $N_r$ and its anticorrelation to ${\chi }_{ff}\left(\mathbf{r}\right)$ shown in Fig. 2 are visible.

Figure 7

Comparison of ${\chi }_{ff}(\mathbf{r}=0)$ at the central impurity (a) and (b) as a function of the number of droplet rings $N_r$ for various droplets and (c) and (d) as a function of ring distance $n$ for droplets with a single droplet ring $N_r=1$ in $L=12$ lattices at $T=t/10$.

Figure 8

${\chi }_{ff}(\mathbf{r}=0)$ at the central impurity (a) as a function of $N_r$ for various droplets and (b) as a function of $n$ for droplets with a single droplet ring $N_r=1$ for $c-f$ hybridization strength $V/t=2.0$ at $T=t/10$.

Figure 9

(a) ${\chi }_{ff}(\mathbf{r}=0)$ and (b) the local orbital occupancy $\rho (\mathbf{r}=0)$ at the central impurity (solid lines for the droplet $f$ orbital and dashed lines for conduction electrons) vs the chemical potential $\mu$ for $V/t=1.0$ in $L=10$ lattices at $T=t/10$.

Figure 10

(a) The local magnetic moment $\langle m^2{}_f(\mathbf{r}=0)\rangle$ of the droplet center and (b) the local orbital occupancy $\rho (\mathbf{r}=0)$ at the central impurity (solid lines for the droplet $f$ orbital and dashed lines for conduction electrons) vs $U$ for $V/t=1.0$ in $L=10$ lattices of $\mu =0$ systems at $T=t/10$.