Tunable Doniach phase diagram for strongly-correlated nanoclusters

Exact diagonalization calculations reveal that the energy spacing $\Delta$ in the conduction band tunes the interplay between the local Kondo and nonlocal Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, giving rise to a Doniach phase diagram for a nanocluster with regions of prevailing Kondo or RKKY correlations. The parity of the total number of electrons alters the competition between the Kondo and RKKY correlations. This interplay may be relevant to experimental realizations of small rings or quantum dots with tunable magnetic properties. Below a critical value $V_c$ of the hybridization the susceptibility exhibits a low-$T$ exponential activation behavior determined by the interplay of the spin gap and $\Delta$.

Figure 1

Nearest-neighbor $f\text{‐}f$ SCF (circles) and on-site $f\text{‐}c$ SCF (squares) as a function of $V$ for $t=0.2$ (closed symbols) and $t=1.2$ (open symbols), respectively.

Figure 2

Energy spacing $\Delta$ vs hybridization zero-temperature phase diagram. The solid curve denotes the crossover point of the spin-spin correlation function in Fig. 1; the dashed curve denotes the set of points where the on-site total moment squared $⟨{({\mu }_f+{\mu }_c)}^2⟩=0.0\pm 0.05$.

Figure 3

Nearest-neighbor $f\text{‐}f$ and on-site $f\text{‐}c$ SCF vs temperature for $t=0.2$ and $V=0.2<V_c$ and $V=0.4>V_c$, where $V_c=0.25$.

Figure 4

Effect of energy spacing, $\Delta =4t∕(N-1)$ on the exact Doniach phase diagram for a strongly correlated electron nanochain. The curve represents the crossover temperature $T_{\mathit{TRKKY}}^{\mathit{cl}}$, where the nonlocal short-range AF spin correlations become equal to the local on-site Kondo spin correlations.

Figure 5

Local $f$ magnetic susceptibility as a function of temperature for $t=0.2$ and $V=0.2<V_c$, $V=V_c=0.25$, and $V=0.4>V_c$. The inset shows the linear fit for $\ln \left({\chi }^f\right)$ vs $1∕T$ at low T.