Disordered Kondo nanoclusters: Effect of energy spacing

Exact-diagonalization results for Kondo nanoclusters alloyed with mixed-valence impurities show that tuning the energy spacing $\Delta$ drives the system from the Kondo to the Ruderman-Kittel-Kasuya-Yosida (RKKY) regime. The interplay of $\Delta$ and disorder gives rise to a $\Delta$ versus concentration $T=0$ phase diagram very rich in structure. The parity of the total number of electrons alters the competition between the Kondo and RKKY correlations. The local Kondo temperatures $T_K$ and RKKY interactions depend strongly on the local environment and overall are enhanced by disorder, in contrast to the hypothesis of “Kondo disorder” single-impurity models.

Figure 1

Left panel: Alloy configurations for various concentrations $x⩽3$ along with the value of the spin $S_g$ in the ground state for $t=1$. Right panel: Energy difference (in units of ${10}^{-4}t$) between the lowest eigenstates and the ground state as a function of ${ϵ}_f^B$.

Figure 2

Temperature dependence of the average $f$ susceptibility for different alloy concentrations. The inset shows the low-temperature behavior.

Figure 3

$A$ atoms: Local Kondo temperatures (in K) vs the local $f\text{−}c$ SCF for different configurations and two values of $t$. The closed circles refer to the $x=0$ case and the lines are a guide to the eye.

Figure 4

Left panel: Configuration-averaged local $f\text{−}c$ (top) and NN $f\text{−}f$ SCF’s (bottom) for the A atoms as a function of $t$. The solid line denotes the $x=0$ case. Right panel: Zero-temperature $t$ vs $x$ phase diagram for the nanocluster. Black (gray) circles denote the Kondo (RKKY) regime. The white circles and the dashed contour delimit the FM region. The horizontal gray stripes denote qualitatively regions of NM, MV, and LM behavior of the $B$ atoms.