Exotic Kondo Effect from Magnetic Trimers

Motivated by the recent experiments of Jamneala et al. [Phys. Rev. Lett. 87, 256804 (2001)] by combining ab initio and renormalization group methods, we study the strongly correlated state of a Cr trimer deposited on gold. Internal orbital fluctuations of the trimer lead to a huge increase of $T_K$ compared to the single ion Kondo temperature explaining the experimental observation of a zero-bias anomaly for the trimers. The strongly correlated state seems to belong to a new yet hardly explored class of non-Fermi-liquid fixed points.

Figure 1

(a) Top view of the equilateral Cr cluster on the Au(111) surface. Au and Cr atoms are indicated by gray and black circles, respectively. (b) Eigenstate structure of $H_{\mathrm{spin}}$ of the Cr cluster (1) in the absence and (2) in the presence of spin-orbit coupling.

Figure 2

Kondo temperature as a function of the overlap parameter $\alpha$ for a cluster formed of atoms with spin $\tilde{S}=5/2$ and spin $\tilde{S}=1/2$. We used ${\tilde{D}}_0=5000\mathrm{K}\approx 3J$ and a dimensionless coupling $G=0.09$. The inset shows in a log-log plot the Kondo temperature of the trimer as a function of the single Cr’s Kondo temperature for two overlap parameters $\alpha =0.33$ and $\alpha =0.6$.

Figure 3

Energy of the Cr trimer as a function of the direction of magnetization computed using a relativistic ab initio method (full line) and the effective model, Eq. (6) (dotted line), for the particular configurations sketched in the inset. In this example only the angle $\vartheta$ with respect to the $z$ axis is varied (upper inset). The lower inset shows the projections of the magnetization onto the surface ($xy$ plane).