P. Wahl, L. Diekh¨oner, M.A. Schneider and K. Kern; P. Simon (Universit´e Joseph Fourier and CNRS, France); V.S. Stepanyuk and P. Bruno (MPl f¨ur Mikrostrukturphysik, Weinberg) It is a vision of information technology to store
data in the smallest available units – single atoms – thus enabling the development of novel mass storage devices with huge capacities but compact dimensions. At the same time this vi-sion poses the physical limit on the informa-tion density of magnetic recording media. Both, for a realization of such a visionary device as well as to explore the limits of conventional mass storage media, it is crucial to understand the mutual interaction and dynamics of individ-ual spins. This interaction can be due to direct coupling or indirect coupling mediated via a supporting substrate or host. Depending on the strength and sign of the exchange interaction, a nanostructure can be driven into ferromagnetic or antiferromagnetic behavior. However, until recently it was impossible to measure experi-mentally the magnetic interaction between indi-vidual atoms. We have exploited the Kondo ef-fect as a local probe to determine the exchange interaction between individual cobalt adatoms on a metallic substrate as a function of their dis-tance [1,2].
The Kondo effect originates from the screening of the spin of a magnetic impurity by the sur-rounding conduction band electrons and is char-acterized by a strong peak in the impurity’s den-sity of states near the Fermi level. In scanning tunneling spectroscopy (STS) spectra, it shows up as a feature which can be described by a Fano line shape. From afit, the peak widthΓis obtained which is proportional to the character-istic energy scale – the Kondo temperatureTK– of the impurity system.
As a second impurity is brought into proxim-ity, magnetic interactions between the impuri-ties become important and may considerably modify the Kondo resonance. Here, we demon-strate that it is possible to determine the mag-netic interaction between single magmag-netic atoms adsorbed on a noble metal surface by deter-mining its influence on the Kondo spectrum.
The results are compared to theoretical predic-tions of the magnetic interacpredic-tions between sin-gle atoms [3]. The evolution of the Kondo line shape obtained by STS upon varying the inter-atomic distance between Co adatoms in dimer
and trimer configurations on a Cu(100) sin-gle crystal surface is compared to many body theory, which allows us to determine the mag-netic coupling as function of the interatomic spacing. Dimers with well-defined interatomic separation have been fabricated byfirst forming cobalt carbonyl complexes. The CO ligands in-hibit nucleation and island formation and facil-itate the growth of one-dimensional structures.
Once these structures are grown, the CO ligands can be removed by tip-induced dissociation of the molecules leaving only the cobalt atoms be-hind on the surface. The panels in Fig. 12(a) show different cobalt dimer configurations pre-pared as described above with interatomic dis-tances between the neighboring cobalt atoms
ranging from 2.56A to 8.1˚ A together with the˚ corresponding STS spectra. For the compact dimer the interaction between the spins is much stronger than the coupling to the substrate and the Kondo effect (at 6 K) is suppressed. For the next-nearest neighbor distance, however, a onance is found at the Fermi energy. The res-onance is considerably broader than that of a single cobalt adatom. Byfitting the STS signal with a single Fano line shape, we extract that the energy width of the feature would correspond to a Kondo temperatureTK= 181±13 K. For dis-tances larger than 5A the Kondo resonance has˚ almost recovered the width and line shape of the resonance of a single cobalt adatom. The widths of the resonances are summarized in Fig. 12(b).
Figure 12: Kondo resonance of cobalt dimers on Cu(100) measured by scanning tunnelling spectroscopy at 6 K. As a consistency check, spectra taken on both ends of the dimers are shown (green and black dots) to be equivalent. (a) Model, topography and spectra for (from top to bottom) a compact dimer (2.56A), a dimer˚ at 5.12A, at 5.72˚ A, at 7.24˚ A, at 7.68˚ A, at 8.10˚ A and for a single adatom at infinite distance (>˚ 20A) are˚ depicted. The spectra are shown together withfits of a Fano function (red solid line), for the dimer at 5.12A˚ also a simulated curve withJ= 15 meV andΓ= 1.2TK0 is plotted (blue solid line). For the dimer at 5.12A, a˚ linear background had to be taken into account to obtain a reasonablefit for a Fano function. (spectra shifted vertically for clarity) (b) shows the width of the resonance as a function of distance and (c) KKR calculations for the exchange interaction between cobalt adatoms on Cu(100) [3]. The three distinct regimes discussed in the text are shaded in different greys.
Our data can be theoretically interpreted as a realization of a two-impurity Kondo problem.
Depending on the relative strength of the ex-change interaction compared to the single im-purity Kondo temperature TK0, the dimers en-ter different regimes. For a strong ferromag-netic exchange interaction|J| TK0 (marked as regime I in Fig. 12(c)) a correlated state with a new Kondo temperatureTKdimer≈(TK0)2/|J|will occur. This new Kondo scale is much lower than the temperature of the experiment and can therefore not be detected in our measure-ments. For intermediate exchange interaction J (regime II in Fig. 12(c)), the single impurity Kondo resonance is recovered.
Finally, for a sufficiently strong antiferromag-netic exchange interaction J>J≈2TK0 (marked as regime III in Fig. 12(c)) between neighboring magnetic atoms, the Kondo res-onance is split and a singlet state is formed between the impurities. This singlet state is characterized in the impurity density of states by peaks located at energies±J/2 [4]. We can show that the splitting can be described by a sum of two Fano resonances at ±J/2 with a widthΓwhich is of the same order as the single impurity one. The resonances appear in the tun-neling spectrum as only one broadened feature due to the width of the resonances, which is of the same size as the splitting. Thus the width of the resonance in this case provides a mea-sure for the magnetic interaction between the adatoms.
Experimentally, we find that for the compact dimer (2.56A) the Kondo resonance disappears.˚ This is consistent with previous experiments on Co dimers on Au(111) by Chenet al. [2] and the strong ferromagnetic coupling predicted by ab initio calculations [3]. The coupling intro-duces a Kondo scaleTKdimer≈2 K for the near-est neighbor dimer, which is smaller than the temperature of the experiment. The spectrum on the next-nearest neighbor dimer (5.12A) shows˚ a distinct Kondo resonance at the Fermi level, which is broadened compared to the spectrum of the isolated Co adatom. From the width of
the resonance we can extract an antiferromag-netic coupling J of about 16 meV. The broad-ened spectrum can be rationalized by an an-tiferromagnetic coupling between the two Co adatoms. The relevant Kondo energy scale is kBTK= 7.58 meV for a Co atom on Cu(100).
The magnetic interactions are thus large enough to induce a singlet-triplet splitting but still small enough to prevent complete quenching of the Kondo effect as observed for the com-pact dimer. At larger interatomic distances the spectrum and TK transforms back to the sgle adatom value, with the exception of an in-teratomic distance of 7.68A, where the reso-˚ nance width has a local maximum as a func-tion of distance. According to ab initio calcu-lations [3], the interaction between two cobalt adatoms on Cu(100) is mainly due to RKKY interactions. When the adatoms are on next-nearest neighbor sites, Stepanuyk et al. pre-dict an antiferromagnetic interaction of about 17 meV (Fig. 12(c)). This is in excellent agree-ment with the estimation we obtain assuming a split Kondo resonance. When the adatoms are further apart (5.72A), the calculations predict˚ that the RKKY interaction is reduced to 8 meV, which is not large enough to split the Kondo resonance and therefore explains why the usual single impurity Kondo resonance is almost re-covered.
Next to the cobalt dimers, we have studied linear trimers. The trimers have the adatoms on next-nearest neighbor sites as shown in Fig. 13(a) and (b) and have been prepared in a similar way as the dimers. The tunneling spec-tra change qualitatively on a trimer. As can be seen from Fig. 13(c), the spectra show a super-position of features – resulting in two maxima and a dip in between them.
A theoretical analysis within a slave boson meanfield theory [5] reveals that the two zero-bias resonances are collective features putting the trimer in the correlated Kondo regime. The nearest neighbor spin interaction of the trimer is found to be comparable to that of the dimer.
Figure 13: Kondo resonance of the Cobalt trimer on Cu(100) measured by scanning tunneling spec-troscopy at 6 K. (a) Model of the trimer investi-gated, (b) STM topography (same scale as model).
(c) Spectra taken on the left, right and center atom, the spectra are shifted vertically. The solid line is a fit to a double Fano resonance.
In conclusion, we have shown how the magnetic interaction between single magnetic atoms cou-pled to a substrate can be determined via the Kondo effect. Understanding and being able to
measure the magnetic coupling on the single atom level is expected to play a key role in the design of magnetoelectronic devices. Magnetic nanostructures with specific properties can be tailored by controlling and manipulating the ex-change interaction.
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