N. Knorr, M.A. Schneider, L. Diekh¨oner, P. Wahl, L. Vitali, and K. Kern The Kondo problem is one of the most widely
studied many-body phenomena in physics which deals with the electronic interaction of magnetic impurities with the electron system of a non-magnetic host. Although the ‘Kondo effect’, i.e., the resistance minimum of met-als with magnetic impurities at low tempera-ture is known since the 1930s and theoreti-cally understood since the work of J. Kondo in the 1960s it remains to be an appealing sys-tem to theorists and experimentalists alike due to its relevance to other many-body phenom-ena like high-Tc superconductivity. Recently a new class of experiments has emerged that use the Scanning Tunneling Microscope (STM) to probe the Kondo state of single magnetic atoms adsorbed on metallic surfaces or even carbon nanotubes [J. Li et al., Physical Review Letters 80, 2893 (1998); V. Madhavan et al., Science 280, 567 (1998); T.W. Odom et al., Science 290, 1549 (2000)].
The STM offers an unparalleled insight into the morphological and electronic structure of sur-faces and adsorbates on sursur-faces on the atomic scale. By Scanning Tunneling Spectroscopy (STS), i.e., measuring the differential conduc-tance of the tunneling junction as function of bias voltage and tip position, the local density of states (LDOS) of a molecule or atom ad-sorbed on a surface can be measured. However, for a correct interpretation of the spectra thus obtained a clear experimental and theoretical understanding of the electronic states involved in the tunneling process has to be achieved.
We have demonstrated by local spectroscopy of Co atoms on Cu substrates that the interaction between the magnetic impurities and different electronic states of the substrate can be individ-ually identified.
Figure 52: Principle of probing a (magnetic) adatom with STM. The tip coordinates are given by (r, z). The electron transmission via the direct chan-neltaand via the indirect channeltscontribute to the STM current.
Our experimental approach is sketched in Fig. 52: the tip of an STM is positioned with sub-pm precision on or near the adsorbate atom and the differential conductance dI/dV of the tunneling junction is recorded as function of tunneling bias. In this situation there are a num-ber of possible channels contributing to the
tun-neling current that can be classified as the di-rect channel ta, i.e., tunneling ‘through’ the ad-sorbate, and indirect channels ts, i.e., tunneling into the electron system of the substrate.
To determine the relative weight of the tunnel-ing channel via the adsorbate resonance and the substrate electronic states we performed tunnel-ing spectroscopy on stunnel-ingle Co atoms adsorbed on Cu(111) and Cu(100). STM topographies of these two systems are shown in Fig. 53. In both systems the Co adatoms appear as protrusions (white). Characteristic of the Cu(111) system is the appearance of Friedel oscillations in the sur-face state electron density which are imaged as circular waves around the adsorbate scatterer.
The tunneling spectra taken directly on the Co atom on the two substrates is shown in Fig. 54(a). The energetically narrow feature at the Fermi energy results from the formation of a Kondo resonance at low temperatures. Al-though the spectra of Co on Cu(100) and Co on Cu(111) look quite different they belong to the Fano family of line shapes.
Figure 53: Constant current STM images (–50 mV bias, I = 2 nA) of Co atoms (bright) on the Cu(100) and the Cu(111) surface. The Friedel oscillations of the surface state electrons on the Cu(111) surface can be seen to extend up to 10 nm. The inset compares the apparent height of the adsorbates for typical STM conditions.
Figure 54: (a) On atom differential conductance (dI/dV) spectra for Co/Cu(100) and Co/Cu(111).
The solid lines are fits of a Fano line to the exper-imental data. (b) The Fano line shape parameter q as a function of lateral distance r between tip and adatom. The solid line is a fit to the Co/Cu(100) data taking into account the r-dependence of the di-rect channelta. The dashed lines are obtained from calculations withta= 0.
This type of line shape was found to be char-acteristic of all single atom Kondo resonance spectra and was successfully explained by the-ory[M. Plihal et al., Physical Review B 63, 085404 (2001)]. The detailed spectral information con-tained allows to determine some of the underly-ing physics. Only two parameter determine the actual shape, one is the Kondo temperature TK,
i.e., the width of the resonance and the other is a parameter q that contains information on the weight of contributing tunneling channels.
Both parameters reveal interesting physics. The Kondo temperature of Co adsorbed on Cu(111) (54 K) is lower than that for Co on Cu(100) (96K) and both are lower than that found for a diluted alloy of Co in bulk Cu (500 K). The TKof a magnetic impurity system depends ex-ponentionally on the product of exchange cou-pling constant and density of states:
TKe12Jρe1n
where J is the exchange coupling integral and ρ is the density of states at the Fermi energy.
The observed behavior of TKcan be explained by assuming the product (Jρ) to be propor-tional to the number of nearest neighbors n of the Co atom which is n = 3 in the case of Co on Cu(111), n = 4 in the case of Cu(100), and n = 12 for a bulk alloy.
The symmetry of the line shapes is governed by the Fano parameter q. A q-value close to zero results from a symmetric line shape and signifies a small contribution from the direct tunneling channel via the adsorbate resonance.
For Co on Cu(111) this q-value is close to zero (q0.2) resulting in a slightly asymmetric curve, whereas Co on Cu(100) has the highest value (q1.1) signifying a higher contribution of the direct tunneling channel. This is experi-mentally proven by determining the q-value as function of lateral distance r between tip and adatom (Fig. 54(b)). For Co on Cu(111) there is hardly a change in the q-value as function of distance showing that the direct tunneling chan-nel which has to decay with increasing distance plays a minor role indeed. On the other hand there is a clear decrease of the q-value at r6 ˚A for Co on Cu(100) showing the decay of the di-rect tunneling channel.