Two-Site Kondo Effect in Atomic Chains

Linear ${\mathrm{CoCu}}_n\mathrm{Co}$ clusters on Cu(111) fabricated by atomic manipulation represent a two-site Kondo system with tunable interaction. Scanning tunneling spectroscopy reveals oscillations of the Kondo temperature $T_K$ with the number $n$ of Cu atoms for $n\ge 3$. Density functional calculations show that the Ruderman-Kittel-Kasuya-Yosida interaction mediated by the Cu chains causes the oscillations. Calculations find ferromagnetic and antiferromagnetic interaction for $n=1$ and 2, respectively. Both interactions lead to a decrease of $T_K$ as experimentally observed.

Figure 1

Left: Pseudo-three-dimensional representations of constant-current STM images ($38\AA \times 21\AA$) of linear ${\mathrm{CoCu}}_n\mathrm{Co}$ clusters ($n=1\dots 6$). Right: $dI/dV$ spectra recorded above a Co atom of the chains. Green dots are experimental data, solid lines indicate Fano line shapes fit to the data. The dashed lines are Fano lines for $T_K=110\mathrm{K}$.

Figure 2

$T_K$ of Co atoms in ${\mathrm{CoCu}}_n\mathrm{Co}$ chains as a function of $n$ (squares). A dashed line indicates ${\tilde{T}}_K=110\mathrm{K}$ of a single Co adatom attached to the end of a ${\mathrm{Cu}}_3$ or ${\mathrm{Cu}}_4$ chain. Circles (red) indicate calculated single-impurity Kondo temperatures, which would be expected for ${\mathrm{CoCu}}_n\mathrm{Co}$ chains in the absence of magnetic Co-Co interactions. The sinusoidal line is a fit to data in the RKKY interaction regime with calculated periodicity.

Figure 3

(a) Local density of states (LDOS) of Cu $4s$ and $4p$ orbitals in a ${\mathrm{CoCu}}_5\mathrm{Co}$ chain and in an infinitely long Cu chain (${\mathrm{Cu}}_{\infty }$) on Cu(111). Cu sites at which the LDOS was evaluated are indicated by dots. (b) LDOS of ${\mathrm{Cu}}_{\infty }$ on Cu(111) versus energy and wave vector along the chain direction. (c) Cross section of (b) at $E=0\mathrm{eV}$. (d) Relaxed ${\mathrm{CoCu}}_n\mathrm{Co}$ ($3\le n\le 5$) chains with calculated magnetization density for ferromagnetically aligned Co spins. Light (red) and dark (blue) colors indicate up and down orientations, respectively. Away from the Co impurity the induced magnetization density is largest around the chain atoms. Therefore, the major contribution to the RKKY interaction between the Co atoms is mediated by the Cu chains.