Copper(II) oxide (CuO) crystallizes in a monoclinic lattice and has an antiferromagnetic ground state with a band gap of about 1.4 eV despite the incomplete 3d shell filling. This is explained by strong electron correlations, which localize the charge carriers in the d band. In the ZSA model, CuO is classified as a charge transfer insulator with a high U = 8 - 9 eV, which exceeds Δ = 2.2 eV. LCO consists of stacks of LaO - CuO - LaO planes, where each Cu atom is octahedrally coordinated to six oxygen atoms. The oxygen and copper atoms are formally in a divalent ionic state, however with strong hybridization in the CuO planes, whereas the apical oxygen in the La-O planes is weakly hybridized. In the undoped phase, the ground state has antiferromagnetic ordering with the magnetic moments localized in the 3d shell. Upon p-doping, holes in the oxygen p shell provide free charge carriers enabling high Tc superconductivity up to about 40 K at optimum doping levels.
Figure 1 a shows how the on-site oxygen 2p two-hole states are prepared and detected with APECS. In a simplified two-step picture the O 2p double photoionization process can be rationalized as the oxygen KVV Auger decay following oxygen 1s core-ionization. Since the emitted electron pairs are detected in coincidence, they truly contain processes that are leading to the on-site oxygen 2p two-hole final state thus eliminating overlapping features and background from non-local contributions that are present in classical Auger electron spectroscopy. Technically, the required coincidence detection efficiency is gained by the bespoke Coincidence ESCA experiment at the UE52-PGM beamline at the BESSY II electron storage ring with two Angle Resolved Time of Flight (ARTOF) Electron Analysers. The surface termination of TMO's and HTSC's gives rise to chemically inequivalent species of lattice oxygen atoms O and under-coordinated surface oxygen atoms (O), as shown in Fig. 1b. The approach of APECS not only prepares the on-site oxygen 2p two-hole state by coincidences of oxygen 1s (K-shell) ionization and the oxygen KVV Auger decay, but also allows to separate within the coincidence map the contributions from lattice oxygen O and surface oxygen O species completely. This is a particular advantage for the investigation of oxide surfaces because of the surface termination and the fact that in a variety of TMO's and cuprates it is difficult to prepare flat surfaces without step edges and free of defect states.
Figure 1 c shows the two dimensional coincidence map of O 1s photoelectron and O KVV Auger electron pairs emitted from O and O species of the LaCuO sample. Photoelectrons are shown in binding energy and Auger electrons in kinetic energy referenced to the Fermi level. A background from uncorrelated electron pairs (accidental coincidences) has been removed (see Methods for details). Electron pairs emitted from oxygen ions in the crystal lattice (O) are centred at about E = 529 eV, in agreement with previous XPS studies, and E = 514 eV. They are fully separated from the surface oxygen O species and from oxygen containing adsorbed molecules, which appear in a broad feature at about E = 532 eV and E = 510 eV. The depth distribution of these features can be directly inferred from their relative intensities in the very surface sensitive coincidence measurement in comparison to the deeper probing non-coincidence measurement (see Supplementary Fig. 1).
The relatively high intensity from O is due to the small APECS probing depth of a few Å. Figure 1d shows how one by partial integration can create pure on-site two-hole spectra from lattice oxygen and surface oxygen, respectively. This separation is commonly impossible with non-coincidence Auger electron spectroscopy due to spectral overlap. The integration ranges of the photoelectron binding energies that are associated with either the lattice or the surface oxygen contributions are indicated with bars in the coincidence map in Fig. 1c.
Figure 2 shows O 1s/ KVV coincidence maps of CuO (Fig. 2a) and LCO (Fig. 2d) in direct comparison. The CuO and LCO maps have both well separated surface and bulk oxygen spectral features. In CuO lattice oxygen is centered at E = 529.5 eV, E = 512.5 eV. Non-stoichiometric excess oxygen at the surface is found at E = 531.2 eV, E = 510.5 eV. In LCO the surface and lattice oxygen assignment is alike, as discussed already in Fig. 1c. Figure 2b and c shows Auger electron spectra derived from the 2D maps of CuO and LCO, respectively, by integrating over the photoelectron part from the lattice oxygen of each crystal (marked with red bars). The direct comparison of the lattice oxygen two-hole final states of CuO and LCO reveals striking differences.The CuO spectrum consists of a broad peak at 513 eV which contains mostly atomic localized O 2p states and due to covalent coupling to copper sites possibly some O 2p 3d final states. In addition, a pronounced tail to higher kinetic energy, also called 'band-like part', indicates a high probability for the two holes to delocalize within the oxygen band. Such oxygen KVV spectral shape has been reported for several three-dimensional metal oxides.
The LCO spectrum is dominated by a well resolved S and D atomic multiplet split by 2 eV at 512 eV and 514 eV, respectively. This is in good agreement with optical data (2.2 eV). Next to these intense atomic peaks a weak band-like part at higher kinetic energy is seen (Supplementary Fig. 2 for extended energy range of the band like part). Actually, LCO has two different lattice oxygen species: in-plane oxygen and apical oxygen. They have not been separated by conventional PES and AES and even with our increased chemical sensitivity of APECS, the LCO measurements find no discernable twins of atomic (D;S) multiplets, but only one set of atomic multiplet fine structure, containing both oxygen species. This implies that the in-plane oxygen to apical oxygen two-hole final state energy difference is below the experimental resolution. Overall, the narrow atomic two-hole final states in LCO reflect the localized ionic character of the valence states in the two-dimensional electronic structure of LCO in contrast to the three-dimensional more covalent electronic structure of CuO which leads to additional non-local final states. For further analysis, a Shirley type background is subtracted from the spectra, indicated by dashed lines in Fig. 2b and c, and the kinetic energy is converted to two-hole binding energy by subtracting the O 1s binding energy.
The Cini-Sawatzky (CS) model provides a powerful framework to obtain U of pure lattice oxygen from experimental spectra of two-hole states in O 2p orbitals. Within this model, U is described by the energy difference between the bound (correlated) state and the band-like (uncorrelated) part of the O 2p two-hole spectrum. Cini and Sawatzky provided numerical expressions of the full spectral distribution simulating the local-interacting two-particle density of states from non-interacting one-particle DOS. Experimentally, the latter can be the oxygen derived valence spectral states or computationally, the oxygen partial density of states (PDOS).
In Fig. 3, we use the Cini-Sawatzky expression (Eq. (1)) to simulate and fit the two-hole spectra in order to extract U:
N(E) is the interacting two-particle DOS, N(E) is the self-convolution of the non-interacting single particle DOS, U is the Coulomb repulsion and H(E) is the Hilbert transform of N(E). For the single particle DOS we use the O 2p PDOS from band structure calculations by Pickett et al. for LCO and by Ching et al. for CuO (see Supplementary Fig. 4). N(E), which would represent the two-hole spectra without electron correlation (U = 0 eV), is shown in Fig. 3 for each simulation. Two CS shapes are used to model the S and D atomic multiplets with the respective O 2p PDOS. A similar approach was previously used to model APECS spectra from transition metal surfaces and magnetic thin films in order to probe electronic correlations.
As mentioned, the experimental O 2p two-hole spectra of in-plane and apical oxygen of LCO are spectroscopically overlapping and indistinguishable in our APECS measurement. Therefore, we perform two separate CS fits to the spectrum, one based on the calculated PDOS of in-plane oxygen and a second with PDOS for apical oxygen. For in-plane oxygen of LCO (see Fig. 3a), we obtain an optimum fit for U (D) = 6.3 ± 0.2 eV and U (S) = 8.6 ± 0.2 eV, an intensity ratio I(D)/I(S) = 4.9 ± 0.2 and a broadening of 1.32 ± 0.02 eV. This broadening accounts for effects that are not captured by the Cini-Sawatzky model: After removing experimental contributions, the line width of the multiplet states is similar to the O 1s width (1.1 eV) of lattice oxygen, which suggests a related broadening mechanism present in O 1s and O KVV peaks. Therefore, we favor to attribute the broadening to phonon excitations or small variations of the local potential, which should both effect the PES and AES similarly. Also a small life time broadening and dispersion of the two-hole state might contribute. The U error bar comprises the overall experimental uncertainty (0.1 eV) and the uncertainty in digitization of the DOS (0.1 eV), whereas the uncertainty of the fit is negligible (0.01 eV) (see Methods for details). The uncertainties of I(D)/I(S) and of the broadening are given by standard deviations of the fit parameters. With this fit model, the positions of the atomic multiplet and the shape and intensity of the band like part are quantitatively matching the experimental spectrum. The intensity ratio D/S is in fair agreement with calculations of atomic Auger transition rates for Neon I(D)/I(S) = 6.0, which has formally the same 2p valency as the lattice oxygen ions. For apical oxygen (see Fig. 3b), we obtain U (D) = 9.2 ± 0.2 eV, U (S) = 11.3 ± 0.2 eV, I(D)/I(S) = 4.6 ± 0.2 and a broadening of 1.50 ± 0.02 eV. The fit quality of the band-like part region is substantially reduced in the CS fit based on the PDOS of apical oxygen. From this, we conclude that the major contribution in the experimental O 2p two-hole spectrum arises from in-plane oxygen. This would comply with the most stable La-O (top layer), Cu-O (second layer), La-O (third layer) surface termination. The signal from the under-coordinated oxygen of the top layer will not appear in the spectrum since we discriminate against it in APECS. The intensity of in-plane oxygen from the second layer is expected to be substantially higher in the lattice oxygen O 2p two-hole spectrum than the intensity from apical oxygen in the third layer due to the high surface sensitivity of our APECS measurement.
Figure 3c shows Cini-Sawatzky fits to CuO. Here, we could not get a satisfactory fit over the full energy range with two CS components (D; S). Hence, we have used two different approaches. First the fit was restricted to the energy range of the bound state (15-22 eV). Here, we obtain U (D)=6.9 eV. Since the atomic D and S states can not be resolved, the difference of U (S) and U (D) is fixed to 2.2 eV obtained from the well resolved atomic multiplet of LCO and the intensity ratio D/S is fixed to 4.9. The fitted Gaussian broadening of 4.3 eV is substantially bigger than in LCO and than the O 1s line width of CuO lattice oxygen. This suggests effects beyond phonon broadening or variation of the local potential, as, e.g., coupling to the copper ions. Also the band like intensity is obviously much underestimated in this fit. In a second approach we allow for an energy shift of N(E), which leads to a reasonable fit over the full energy range for a shift of 3.0 eV, equivalent to a shift of the PDOS of 1.5 eV, and U (D)=3.3 eV. We relate all data to the common Fermi level of a metallic sample which still allows for surface shifts in doped gaped materials. For LCO, defect states provide a higher charge carrier density than for CuO. It is worth to mention, that an equally good fit result can also be obtained with a DOS from a band structure calculation including correlation without the need to shift the SCDOS. Supplementary Fig. 3 shows a fit based on a calculated PDOS from Anisimov et al. in a LDA+U framework. Since U is directly related to the energy difference of the SCDOS to the bound (atomic) peak within the CS model, quite different values of U are obtained for the unshifted SCDOS as compared to the shifted SCDOS or the SCDOS obtained from LDA+U calculations. The U values of 6.9 eV and 3.3 eV obtained from the two different modelling approaches should be seen as upper and lower limits of the O 2p Coulomb repulsion energy in CuO, respectively.
Table 1 lists parameters from the fits. The U (D) of in-plane oxygen in LCO is overall in agreement with AES measurements by Rietveld et al. (6.25 eV in LCO) and Bar-Deroma et al. (5 eV in LSCO/LBCO). Also some AES and RAES measurements of other cuprates show similar U between 5 and 7 eV, i.e. YBCO, BSCCO. Many calculations have predicted a somewhat lower U for LCO between 3.6-4.64 eV, although U = 6.1 eV found in a recent ab-initio calculation by Hirayama et al. is in very good agreement with our findings. It should be noted that resonant Photo/Auger electron spectroscopy (RPES/RAES) were also used to investigate two-hole states, which appear as satellites in the valence spectrum, e.g. BSCCO. Here selectivity can arise from resonant population of unoccupied lattice oxygen states and contributions from defective oxygen may be reduced. However, an accurate extraction of the two-hole states, in particular of the band-like part, can be difficult because of the overlap with the one-hole part of the valence spectrum. Furthermore, the final state in RAES contains of one additional electron in the valence, from the core-excitation process, which interacts with the two holes.
Our experimental determination of on-site Coulomb energies in O 2p orbitals of LCO and CuO with Cini-Sawatzky modelling have important implications for correlated two particle states in cuprates: The on-site O 2p Coulomb energy is significantly reduced in the Cu-O planes (6.3 eV) as compared to the La-O planes (9.2 eV) probably due to enhanced screening in the Cu-O planes. This might confine correlated two-hole states to the Cu-O planes in the LCO material due to the favorable energetics. Furthermore, the two-hole states in LCO are strongly localized as revealed by the strong quenching of delocalized (band-like) final states in the spectra in comparison to three-dimensional CuO. These anisotropic two-particle properties in LCO differ substantially from single particle properties, where oxygen 2p PDOS DFT calculations show similar hybridization strength of oxygen in the Cu-O planes of layered LCO and of oxygen in three-dimensional CuO. We thus think that the observed properties of the Cu-O planes, with regard to two hole states, relate to the preference of pairing in cuprate high temperature superconductors in the Cu-O planes alike. A quantitative knowledge of Coulomb energies of two-hole states at oxygen sites is thus relevant for theoretical models, e.g. to link electronic parameters with superexchange.
We conclude with a brief discussion on the precision of U obtained from the CS fits of the experimental O 2p two-hole spectra. The choice of U in a CS fit, for a given SCDOS, has two major implications: First, the energy position of the atomic part is approximately determined by the position of the SCDOS maximum plus U. Secondly, the intensity ratio of the bound to band like part scales with U/W. If only U is allowed to vary, the fit tends to optimize the atomic peak position for systems with predominantly localized two-hole states, whereas the band like intensity and shape has no further degree of freedom. Figure 4 shows a series of CS fits of the LCO data with the calculated in-plane oxygen PDOS for various fixed U including the reference fit from Fig. 3a. In order to achieve acceptable fit results, a free energy shift parameter was introduced (except for the reference fit). The energy shift of the simulated spectrum might be motivated by an uncertainty in energy referencing. Even with a free energy shift, the band like part is not well reproduced by the fit for U (D) = 4 eV (ΔE = 2.1 eV), U (D) = 5 eV (ΔE = 1.3 eV) or U (D) = 8 eV (ΔE = - 1.1 eV). Instead, the entire spectrum is correctly reproduced for U (D) = 6.3 eV (ΔE = 0 eV), which suggests a model related uncertainty in the order of a few hundred meV. This conclusion requires an accurate experimental determination of the band-like part of the two-hole spectrum, which is enabled by the complete removal of the background from uncorrelated electrons by the APECS technique.
In summary, we have investigated on-site Coulomb repulsion of two-hole states in O 2p orbitals and the covalency of LaCuO in comparison to CuO. With time-of-flight based APECS, the two-hole spectra were measured site-selective, which allowed us to separate the lattice oxygen from under-coordinated oxygen states at the surface and also to remove other background contributions. In the three dimensional CuO, we observe substantial delocalization pathways of the two-hole state despite U being as high as 6.8 eV. The delocalization is strongly quenched in LaCuO and the atomic multiplet is well resolved, suggesting a much decreased hybridization strength as compared to CuO. We find U = 6.3 eV for oxygen in the Cu-O planes and for apical oxygen an upper limit of U = 9.2 eV. Our findings of on-site Coulomb repulsion by APECS are relevant for advanced electronic structure models of strongly correlated solids and may contribute, e.g., to the understanding of the pairing mechanism in high temperature superconductivity.