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Real-Space Imaging of Kondo Screening in a Two-Dimensional O2 Lattice

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Science  15 Jul 2011:
Vol. 333, Issue 6040, pp. 324-328
DOI: 10.1126/science.1205785

Abstract

Kondo lattice systems can exhibit unusual many-body behaviors that result from the interplay between onsite Kondo screening and intersite coupling. We used scanning tunneling microscopy to image the Kondo resonance in a nonconventional Kondo lattice formed by self-assembled oxygen (O2) molecules, which are paramagnetic, on the gold reconstructed surface [Au(110)-1×2]. The interplay between the intermolecular coupling for molecules adsorbed along chains and the onsite Kondo effect leads to the coexistence of both local and nonlocal Kondo screening at the atomic level. The latter provides evidence for collective deconfinement of magnetization induced in Au, whereas the former shows local “hybridization” between the Kondo clouds of nearest-neighbor O2 molecules.

The Kondo effect arises from spin-flip scattering processes of itinerant electrons around localized spins of magnetic impurities (15). When individual local spins are brought into a spatially ordered lattice, remarkably rich many-body behaviors of the Kondo systems can appear and require an understanding of how the intersite coupling affects the Kondo screening (69). Below a characteristic temperature T*, a collective local-moment deconfinement develops and leads to nonlocal Kondo screening (10, 11). The coherence temperature T* defines an energy scale different from the single-impurity Kondo temperature TK (12, 13) and is believed to be controlled by the nearest-neighbor intersite coupling (11, 14). There is no cohesive understanding for the Kondo lattice systems due to the complex interplay between single-site Kondo screening and intersite coupling, but this interplay can be enhanced in systems with reduced spatial dimensions through quantum confinement effects (15, 16).

Here, we illustrate the intersite coupling effect in a two-dimensional (2D) Kondo lattice formed by a self-assembled monolayer of oxygen molecules on the Au(110)-1×2 reconstructed surface at 10 K (17). The weak interaction between O2 and gold preserves the magnetic ground state of gas-phase O2 molecules and leads to a Kondo resonance around the Fermi energy (2). We visualized the interplay between the onsite Kondo screening and intersite coupling with a scanning tunneling microscope (STM) and achieved high spatial resolution by using the Kondo resonance as a local probe (18). The observation of delocalized Kondo screening over the entire surface and the intermolecular distance–dependent coherence temperatures in different O2 lattices provide evidence for the intersite coupling in the O2 lattice. In addition, the Kondo resonance exhibits periodic enhancements in regions between O2 molecules analogous to the hybridization between atomic orbitals.

The O2 molecules at low coverage were highly mobile along the rows of Au(110)-1×2 surface even at 10 K (fig. S1A); some O2 molecules were occasionally trapped in single-atom defects. With increasing coverage, O2 molecules formed monolayer islands (fig. S1B) and eventually a complete O2 monolayer (fig. S1C). The well-ordered O2 monolayer consists of two different O2 chains, both on the rows of the Au(110)-1×2 surface (marked as a and b in Fig. 1A). Chain a is composed of O2 molecules that pair with each other as dimers, whereas chain b shows a pronounced “zig-zag” feature. It is striking that chains a and b alternate, which results in a 3×4 supercell. With the underlying Au(110)-1×2 lattice superimposed, the adsorption sites of O2 molecules were determined (Fig. 1B). Both O2 molecules in chain a are bonded nearly on top of gold atoms, whereas in chain b, one O2 is bonded nearly on top of a gold atom but the other one is adsorbed in the nearby bridge site.

Fig. 1

(A) Constant-current STM topography of the O2 monolayer (34 × 34 Å2). The 3×4 unit cell is highlighted by a dashed rectangle. The two different kinds of O2 chains, a and b, are distinguishable. (B) Zoom-in image (10 × 17 Å2) of chains a and b with Au(110)-1×2 lattice superimposed to show the adsorption sites of the O2 molecules. All the STM topographic images were acquired with V = 0.5 V, I = 0.1 nA. (C) DFT calculations for the configuration of the O2 monolayer corresponding to the area in (B). Oxygen and gold atoms are denoted by red and golden spheres, respectively. (D) dI/dV and d2I/dV2 spectra taken on (at point marked × in B, black curves) and off (gray curves) the O2 monolayer. Set point: V = 0.1 V and I = 0.1 nA. The dashed white curve shows a fit to the dI/dV with the Fano equation described in the text.

The adsorption configurations were confirmed by ab initio calculations based on the spin-polarized density functional theory (SP-DFT) at the level of generalized gradient approximation (Fig. 1C). In addition to O2 chains observed in STM images, we found that additional O2 molecules were needed in the troughs of the Au(110)-1×2 surface for energy optimization (17). These molecules are absent in STM topography because they are about 1.8 Å lower than those on the rows. The O2 molecules in the top monolayer are weakly bound to the Au(110)-1×2 surface, with an average binding energy of 53 meV/molecule and O-Au bond lengths longer than 2.71 Å. These values correlate well with our experimental observation that the entire monolayer of O2 molecules desorbed when the STM junction was illuminated by a 532-nm continuous wave laser with power density greater than 15 W/cm2.

The calculated magnetic moment of each O2 in the monolayer is 1.997 μB, which is near that of the gas phase O2, 2.0 μB in its triplet ground state. The O2 monolayer forms a ferromagnetic (FM) ground state with a rather weak exchange interaction because the intermolecular distances are as large as 4.2 Å. If we selectively flip the magnetic moment of any O2 molecule in the lattice, the energy change is less than 1.5 meV, almost within the error range of typical DFT calculations (17). Each molecule can flip its magnetic moment almost freely at 10 K, uninhibited by exchange coupling to adjacent molecules. The lack of traditional Ruderman-Kittel-Kasuya-Yoshida interactions makes the O2 lattice different from heavy fermion materials because the intersite coupling arises from the long-range coherence in the periodic lattice.

A symmetric Lorentzian-like dip was observed around the Fermi level (V = 0) in the dI/dV curve, in sharp contrast to the flat spectrum taken over the clean Au surface (Fig. 1D). No other spectroscopic features were observed throughout the bias range from –250 to 250 mV (fig. S1D). The spectroscopic dip has very large magnitude, reaching about 65% of the zero-bias conductance (17, 19). By fitting the dI/dV curves with the Fano equation dI(V)dV=A(ε+q)21+ε2+B [with ε=(eVε0)Γ], where A is the magnitude, B is the background dI/dV signal, q is the Fano parameter, ε0 is the energetic position, and Γ is the half-width at half-minimum (2022), we obtained Γ = 13.5 ± 0.2 meV, which corresponds to a coherence temperature T* of 130 ± 2 K (23). The Fano parameter q obtained in the fit is only about 0.013 ± 0.004, which implies that almost all electrons from the tip tunnel into the conduction states of the Au substrate modified by the Kondo resonance (22). If Γ has negligible spatial dependence, as discussed below, it is more accurate and convenient to extract the value of A from the d2I/dV2 extrema than from the dI/dV amplitude, especially when the Kondo signal is weak (24).

The dI/dV spectra recorded over the points in Fig. 2A along the rows and troughs on the Au(110)-1×2 surface are displayed in Fig. 2B. The spatial dependences of ε0, q, and Γ of the Kondo resonance extracted from these curves are negligible (Fig. 2C). Similar spatial invariance of q observed for Co adatoms on the Cu(111) surface was ascribed to the dominance of tunneling into the substrate conduction band (25, 26).

Fig. 2

(A) STM topography of an O2 monolayer, in which the positions of the tip for recording dI/dV spectra in (B) are depicted. Set point: 0.1 V and 0.1 nA. Each dI/dV spectrum in (B) is fitted with the Fano equation. (C) Spatial dependence of the energetic position ε0, Fano parameter q, half-width at half-minimum Γ, and the magnitude A of the Kondo resonance at different positions shown in (A). The horizontal dotted lines in the upper three panels of (C) denote the average values: ε0 = 0.7 ± 0.5 meV, q = 0.021 ± 0.027, and Γ = 13.7 ± 0.7 meV. The horizontal dotted line in the bottom panel of (C) highlights the existence of a uniform background signal level of 0.16 nA/V.

The Kondo magnitude, A, however, exhibits pronounced periodic enhancements along the rows and troughs (Fig. 2C, bottom), with variations up to 0.25 nA/V. Notably, A does not go to zero; its minimum approaches a constant of 0.15 nA/V (dotted line in Fig. 2C, bottom). The larger enhancements for trough positions cannot be simply attributed to the lower tip position. For example, the tip heights at points 2 and 3 are smaller by 0.1 Å than that at point 1, but the signals there are close to the minimum level.

We obtained more comprehensive information on the spatial distribution of the Kondo resonance by constructing Kondo images of the d2I/dV2 signals that were simultaneously acquired with the topography (Fig. 3A). The Kondo image of an ordered O2 lattice (Fig. 3B) was obtained by fixing the bias at the positive peak position (7 mV) in the d2I/dV2 spectra. The image obtained at the negative dip (–7 mV) is basically the same, except for the change in sign. The Kondo image shows a delocalized uniform background signal (7.8 nA/V2, equivalent to 0.16 nA/V in dI/dV) superimposed with a periodic enhancement of localized Kondo signal (up to 18.2 nA/V2, equivalent to 0.38 nA/V in dI/dV), in agreement with the mapping data in Fig. 2C. The same (3×4) periodicity in Fig. 3, A and B, implies that the Kondo signal is intimately correlated with the geometric structure of the O2 monolayer.

Fig. 3

Topographic images: (A) 100×100 pixels, 34×34 Å2 and (C) 85×85 pixels, 14 × 14 Å2. (B) and (D) Simultaneously acquired Kondo images by recording the intensity of the positive peak (V = +7 mV) in d2I/dV2 spectrum. Set point: V = 0.1 V and I = 0.1 nA. The black arrows in (C) highlight the fuzzy features associated with the weakly bonded O2 molecules in the trough. The black dashed ellipses in (D) highlight the periodic enhancements. The position of the trough in (C) is denoted by the black dashed line in (D). The big and small circles denote the big and small lobes of each O2 molecule in chain a, whereas the two circles are similar in size for chain b. (E) dI/dV spectra of the 2D O2 lattice on Ag(110) (violet), 2D O2 lattice on Au(110) (green), and 1D O2 chain on Au(110) (red). The red and green curves are multiplied by factors of 20 and 4.7, and offset by 14.2 nA/V and 2.1 nA/V, respectively. The dashed black curves show the fits to the data with the Fano equation. (F) The coherence temperature and the resonance magnitude (the conductance change Δσ of the Kondo dip normalized by the zero-bias conductance σ0) as a function of the intermolecule distance for the three O2 lattices.

The localized enhancements in the Kondo image are characterized by a series of elliptical lobes, one of which is highlighted in Fig. 3B (dotted ellipse). These lobes form in pairs and are elongated along the direction nearly perpendicular to the rows of the underlying Au(110) lattice. A more accurate description of the lobes, however, requires Kondo imaging with finer spatial resolution (Fig. 3, C and D). The lobe within the dashed ellipse in Fig. 3B could be resolved into two smaller lobes separated by the trough of the Au(110)-1×2 surface (highlighted by two black dashed ellipses in Fig. 3D). Periodic, fuzzy features appeared in the trough (indicated by the arrows in Fig. 3C) when the tip was brought close to the surface such that the tunneling gap was below that set by 0.2V/0.1nA. We attribute the fuzzy regions to O2 molecules in the trough (Fig. 1C).

Four main features were extracted from Fig. 3, B and D: (i) In both chains a and b, the Kondo enhancements were mainly localized at the ends of O2, but displaced from the molecular axis. (ii) For chain b, the Kondo enhancement was in the middle between two adjacent O2 molecules. (iii) For chain a, the Kondo enhancement was next to the “big circle” of the O2 molecules and aligned with the enhancement in chain b. (iv) The Kondo enhancements arising from chains a and b were correlated with each other to form a linear repeating unit of four lobes (Fig. 3, B and D).

The delocalization of the Kondo signal arises from the collective deconfinement of magnetization in the Kondo lattice below the coherence temperature T* (6, 10, 11). The development of the nonlocal Kondo screening is attributed to the intersite coupling (14). In addition, as shown in Fig. 3, E and F, the measured coherence temperature T* (130 K) of the O2 lattice, with intermolecular distance of 4.19 Å, lies in between that of 1D O2 chain on Au(110) (88 K) with a larger intermolecular distance (8.64 Å) and that of 2D O2 lattice on Ag(110) (187 K) with a smaller intermolecular distance (3.16 Å) (17). The coherence temperature of the O2 lattice is thus enhanced with decreasing intermolecular distance.

Localization of the Kondo enhancement signal at the ends of molecules implies that the 2π* antibonding states of O2 are responsible. The calculated isosurfaces of spin density in the inset in Fig. 4A indicate that the magnetization mainly stems from 2π* orbitals of the triplet O2 (27). Curves of the total density of states (DOS) in Fig. 4A show that the Au d band is well below the Fermi level and that states around EF are free-electron like. The 2π* orbitals of O2 have an exchange splitting of 2.5 eV, as indicated by the local density of states in Fig. 4B, for O2 molecules in chain a. The crystal field of Au(110) causes the in-plane (pip) and out-of-plane (pop) orbitals of O2 to be split and broadened into resonances. The calculated topographic image in Fig. 4C reproduces the main features of the experimental data in Fig. 1B.

Fig. 4

(A) Total density of states. (Inset) Isosurfaces of total spin density of O2/Au(110). (B) Projected density of states at Γ point in O2 molecules of chain a. (Insets) Isosurfaces of energy-sliced charge densities for states within ±0.05 eV around two peaks pointed out by arrows; pip and pop represent the projected DOS of in-plane and out-of-plane orbitals, respectively. Positive and negative values indicate states in the majority and minority spin channels, respectively. Fermi level is at 0. (C) Simulated STM topography based on the Tersoff and Hamann tunneling model, 3 Å above the topmost oxygen atom for states between 0 and 0.5 eV. (D and E) The top and side views, respectively, of the spin density for states within –0.25 eV to Ef [beige vertical bar in (A)]. The red color in (D) and (E) represents negative spin densities. The positions of the horizontal plane in (D) and the vertical plane in (E) are highlighted by the black lines in (E) and (D), respectively. The white dotted ellipses in (D) represent the lobes of Kondo enhancement highlighted as black dashed ellipses in Fig. 3D.

The Kondo effect depends on the responses of itinerant electrons, so it is instructive to analyze the spin density near the Fermi level from states within a range of –0.25 eV to Ef, in both horizontal and vertical planes (Fig. 4, D and E). This spin density is mostly negative (antiparallel to the local magnetization of O2), a common ground-state feature of the Kondo liquid. The induced spin polarization in Au is rather delocalized (Fig. 4E), in good accordance to the uniform background Kondo signal shown in Fig. 3, B and D.

The experimental image of the Kondo enhancement could be related to the DFT spin density of free-electron states around the Fermi level. The Kondo signal is mostly strong at locations where O2-induced spin clouds start to overlap, as highlighted by white ellipses in Fig. 4D. The Kondo enhancements shift away from the O sites as a result of the coupling between single-site Kondo screening, which is analogous to orbital hybridization: The “bonding” between Kondo clouds of adjacent O2 molecules results in the Kondo signal enhancements between them. In a disordered O2 lattice, the Kondo enhancement is very sensitive to the intermolecular distance (17). The Kondo magnitude is always enhanced where the neighboring O2 molecules are closer and their “Kondo bond” gets stronger (Fig. 3F and fig. S6C). The O2 molecules in troughs are important in bridging the “Kondo bonds” across chains a and b for the generation of the spatial pattern of the Kondo enhancement in Fig. 3, B and D. Therefore, the Kondo screening in the O2 lattice is collective, and the Kondo moments bind when they are near each other.

During the Kondo scattering process, itinerant electrons flip their spins by interacting with either the pip or pop state of O2, such that the z component of the O2 spin (Sz) is switched between 0 and ±1 without energy cost because the magnetic anisotropy energy is negligible (17). Given that there is only one screening channel available in our experimental geometry (the conduction states from the Au substrate), only one electron spin of O2 can be flipped at a time, such that the O2 spins are only partially screened. The O2 lattice resembles an “underscreened Kondo-lattice,” as discussed for a spin-1 Kondo model (2830) and provides an ideal test ground for studying the competition between the Kondo effect, orbital ordering, and long-range spin coherence.

Supporting Online Material

www.sciencemag.org/cgi/content/full/333/6040/324/DC1

Materials and Methods

SOM Text

Figs. S1 to S7

Table S1

References

References and Notes

  1. Materials and methods are available as supporting material on Science Online.
  2. For the 2D O2 lattice formed on Ag(110) with a smaller intermolecular distance, the resonance magnitude can even exceed 100% of the zero-bias conductance (Fig. 3E).
  3. The intrinsic coherence temperature T* was deconvoluted from the measured Kondo width Γ by subtracting the contributions from the tip temperature (Ttip), sample temperature (Tsample), and the bias modulation (Vac): 2Γ=(3.2kBTtip)2+(5.4kBTsample)2+(22Vac)2+(2kBT*)2.
  4. Acknowledgments: Supported by the National Science Foundation under grant DMR-0606520 (W.H.) and the Department of Energy under grant DE-FG02-05ER46237 (R.W.). Y. J. acknowledges support by the 985 Program of Peking University and the National Science Foundation of China. DFT calculations were performed on supercomputers at the National Energy Research Scientific Computing Center. We thank D. L. Mills, J. M. Lawrence, and W. Ji for enlightening discussions. The authors declare no competing financial interests.
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