Controlling the Kondo Effect in ${\mathrm{CoCu}}_n$ Clusters Atom by Atom

Clusters containing a single magnetic impurity were investigated by scanning tunneling microscopy, spectroscopy, and ab initio electronic structure calculations. The Kondo temperature of a Co atom embedded in Cu clusters on Cu(111) exhibits a nonmonotonic variation with the cluster size. Calculations model the experimental observations and demonstrate the importance of the local and anisotropic electronic structure for correlation effects in small clusters.

Figure 1

(a) STM image of Co and Cu atoms on Cu(111) prior to fabricating ${\mathrm{CoCu}}_n$ clusters. (b)–(e) Sequence of STM images showing ${\mathrm{CoCu}}_n$ clusters. The same lateral and height scale was used for all images. Images were acquired at a sample voltage of 100 mV and a tunneling current of 0.1 nA. (f) Ball-and-stick models of fully relaxed adsorption structures of ${\mathrm{CoCu}}_n$ on Cu(111). (g) Experimental energy of unoccupied cluster state versus cluster size. The size of the symbols (squares) corresponds to the uncertainty of the energies. Calculated energies are depicted as dots.

Figure 2

Spectroscopy of $dI/dV$ of ${\mathrm{CoCu}}_n$ clusters around the Fermi level. The spectroscopic feature is the Abrikosov-Suhl resonance induced by the Kondo effect. Lines depict fits of Fano lines [Eq. (1)] to experimental data. Prior to spectroscopy the tunneling gap was set at 30 mV and 1 nA. Spectra for $n=1,\dots ,4$ are vertically offset by 5, 10, 20, 25 nS, respectively.

Figure 3

Kondo temperatures (a) and asymmetry parameters (b) as a function of cluster size from experiments (squares) and calculations (dots).

Figure 4

Calculated LDOS at the Co site for ${\mathrm{CoCu}}_n$ assemblies. (a) $sp$ LDOS, $N(E)$, plotted for energies between $-1.9$ and 1.9 eV with respect to the Fermi energy. (b) Close-up view of (a) showing the energy range of the Kondo resonance. The number of Cu atoms in the cluster is indicated. (c) $p_z$ LDOS, $N_{p_z}(E)$, with indicated energies of unoccupied cluster resonances shown in Fig. 1g.