Correlation of the local and the macroscopic properties of high-temperature superconductors: EXAFS data analysis†

Based on temperature-dependent EXAFS studies of Ba_1−xK_xBiO₃ superconducting oxide, a model of the relationship between the local crystal and the local electronic structures has been proposed. Oxygen ions were found to vibrate in a double-well potential and their vibrations are correlated with the local electron pair transfer due to the dynamical exchange BiO₆ ↔ Bi²O₆, where ² denotes the hole pair in the antibonding Bi 6s O2p_σ* orbital of the octahedral complex. The similarity of the EXAFS spectra features of Ba_1−xK_xBiO₃ and La_2−xSr_xCuO₄ allowed us to propose a similar model for Cu-based superconducting oxides. The model, in a common approach, explains the antiferromagnetic state, metal–insulator phase transition and the appearance of superconductivity at Sr²⁺ doping of La₂CuO₄, and eliminates discrepancy between the neutron-scattering and EXAFS data.

1. Introduction

During the last decade there has been mounting interest in explaining the mechanism of high-T_c superconductivity on the basis of electronic and structural inhomogeneities of the CuO₂ plane (see, for example, Egami & Billinge, 1994; McQueeney et al., 1999; Ichikawa et al., 2000). The most compelling evidence for these inhomogeneities comes from the discovery of a static stripe phase in non-superconducting La_1.48Nd_0.4Sr_0.12CuO₄ (Tranquada et al., 1996). Later, Bianconi et al. (1996) claimed to have found the stripe-like feature for the superconducting composition of La_2−xSr_xCuO₄ based on EXAFS experiments. However, the recent neutron-scattering analysis of the local structure in an La_1.85Sr_0.15CuO₄ single crystal by Braden et al. (2001) refutes the existence of in-plane charge inhomogeneities related to static stripe correlation. Moreover, the inelastic neutron-scattering measurements of McQueeney et al. (1999) showed that the local charge ordering in the superconducting plane must be dynamic, not static. We suppose that this strong contradiction between EXAFS (Bianconi et al., 1996) and neutron-scattering data (Braden et al., 2001; McQueeney et al., 1999) arises from the difficulties in interpretation of the EXAFS spectra due to the existence of several different Cu—O bonds and to short Cu—O distance in the CuO₂ planes of cuprates.

Meanwhile there exists the three-dimensional superconducting perovskite-like oxide Ba_1−xK_xBiO₃ (BKBO), which is more favourable for extraction of the local structure inhomogeneities from the EXAFS spectra due to more simple structure and longer Bi—O distances.

In this paper we present a comparative analysis of our temperature-dependent EXAFS study of Ba_1−xK_xBiO₃ and experimental data concerning La_2−xSr_xCuO₄ which elucidates the nature of the local crystal and charge inhomogeneities and connects the local features with the main macroscopic properties of both compounds.

2. Experiment and data analysis

Temperature-dependent X-ray absorption investigations were carried out for Ba_1−xK_xBiO₃ (Bi L₃-edge) with x = 0.0, 0.25, 0.4, 0.5 and for BaPbO₃ (Pb L₃-edge). The EXAFS spectra were collected at beamline D-21 of the DCI (LURE, Orsay, France) synchrotron operated at an energy of 1.85 GeV and with an average current of ∼250 mA in the positron beam. The energy resolution of the double-crystal Si(311) monochromator at 13 keV was about 2–3 eV. The low-temperature measurements were performed using a liquid-helium circulation-type cryostat with a temperature control of ∼1 K. The background in the experimental spectra was removed as described by Newville et al. (1993) taking care to remove the low-frequency oscillations. The EXAFS functions χ(k)k² obtained from absorption spectra were Fourier transformed in the wavenumber k range from 1.5 to 16.5 Å⁻¹ using the Kaiser–Bessel windowing function.

Since we found that the oxygen vibrations in the first Bi—O shell are strongly anharmonic (Menushenkov et al., 1997) we used the EXAFS-treatment method applied by Mustre de Leon et al. (1992) for the analysis of apical oxygen oscillations in YBa₂Cu₃O₇. In this case we considered the potential of Bi—O vibrations to be a parametric function of interatomic distance, and the potential parameters were extracted from the model to experimental EXAFS-function fits according to (Menushenkov & Klementev, 2000)

where

is the pair radial distribution function of atoms in the jth sphere, N_j is the coordination number, E_n and ψ_n are the nth energy level and its corresponding wavefunction in a model potential, and r_min and r_max are determined by the windowing function of the back Fourier transform. The variable parameters in this case are N_j and the parameters of the model potential. The phase shift φ_j and scattering amplitude F(k) were calculated using the FEFF6 code (Rehr et al., 1991). The above treatment procedure was performed using the new program VIPER (Klementev, 2001; Klementiev, 2003).

3. Results and discussion

The EXAFS study of the nearest oxygen environment of Bi in BKBO showed that oxygen ions vibrate in the double-well potential due to the different electronic structure of the neighbouring octahedral complexes BiO₆ and Bi²O₆, where ² denotes the hole pair in the antibonding Bi 6s O2p_σ* orbital of the octahedral complex (see Menushenkov & Klementev, 2000). We found that these two different types of complexes exist in the full range of the K-doping of BaBiO₃ including the superconducting compositions and are observed in EXAFS spectra as the dynamical local lattice distortions. It allowed us to propose a model of the relationship between the local crystal and the local electronic structures and to establish the correlation between the local and the macroscopic properties of the BKBO system (Menushenkov & Klementev, 2000; Menushenkov et al., 2001). It was shown that oxygen ion vibrations in the double-well potential are correlated with the local electronic pair tunneling between the neighbouring octahedral complexes in accordance with the dynamical exchange: BiO₆ ↔ Bi²O₆. At low temperature the local pair transfer becomes coherent due to the phase coherence between the oxygen ion vibrations in the double-well potential and the breathing-type vibrations along [100]-type axes at the Brillouin zone boundary. It explains the appearance of superconductivity in Ba_1−xK_xBiO₃. The increase in temperature excites longitudinal stretching phonons other than the breathing type, which destroys the phase coherence in the local pair transfer and leads to superconductivity destruction at T > T_c (Menushenkov et al., 2001, 2002).

Observing the abnormal increase of the Cu—O-bond Debye–Waller factor with temperature decreasing below 100 K for La_2−xSr_xCuO₄, the authors (Bianconi et al., 1996) assigned it to the static stripe structure which consists of two types of CuO₆ octahedra with a 0.12 Å difference of in-plane Cu—O bond lengths. It contradicts not only the neutron-diffraction data (Braden et al., 2001) but also the EXAFS study of Niemöller et al. (1998) who found the maximum splitting of the Cu—O bonds to be smaller than 0.06 Å.

We suppose that these contradictions are connected to the dynamic rather than static character of Cu—O bond splitting. The anomalous behaviour of the Cu—O-bond Debye–Waller factor means that it is incorrect to use the harmonic approximation treatment of EXAFS spectra for La_2−xSr_xCuO₄. This situation is identical to what we observed for the Bi—O bond in Ba_1−xK_xBiO₃ which suggests that the oxygen ions in the CuO₂ plane vibrate in a double-well potential.

From this point of view we can propose a model of the relationship between the local crystal and the local electronic structures of La_2−xSr_xCuO₄ in analogy with the Ba_1−xK_xBiO₃ case, presented in Fig. 1.

Figure 1 Scheme of the insulator–metal phase transition in La2−xSrxCuO4. The local crystal structure of the octahedral complexes (at the top) and the local electronic structure (at the bottom) are shown. The occupied states of the Cu 3dO2p valence band are marked in grey. Black and white circles denote electrons and holes, respectively. Arrows show the spin orientation in the neighbouring complexes. The antiferromagnetic phase of the parent insulator La2CuO4 is shown on the left. In the middle the superconducting phase of La2−xSrxCuO4 with 0.05 < x < 0.28 is presented. The metal non-superconducting phase at x > 0.28 (Fermi liquid state with Fermi level EF) is shown on the right.

In the parent La₂CuO₄ compound the upper Cu 3d_x2-y2 O2p_σ* antibonding orbital of every octahedral complex Cu¹O₆ is half filled, which leads to the antiferromagnetic order (see Fig. 1, left). Such a system should behave as a Mott-type insulator since the transfer of an electron from one complex to the neighbouring one changes the electronic structure of both complexes and requires an activation energy E_a ≃ 2 eV.

Doping of La₂CuO₄ by Sr²⁺ leads to the appearance of the octahedral complexes Cu²O₆ with two holes in the antibonding orbital (see Fig. 1, middle), resulting in local hole pairs ², similar to the case of Ba_1−xK_xBiO₃. These pairs can tunnel freely between the neighbouring complexes in accordance with the dynamical exchange Cu¹O₆ ↔ Cu²O₆, producing the oxygen ion vibrations in the double-well potential. At low temperature the local pair transfer is coherent as in Ba_1−xK_xBiO₃, which explains the superconducting state of La_2−xSr_xCuO₄ in the doping region 0.05 < x < 0.28. At T > T_c the coherency is destroyed and local pairs provide the normal conductivity of so-called `strange metal'. In addition, at x > 0.05 the antiferromagnetic order of the alternating Cu¹O₆ complexes with antiparallel local spins is suppressed (see Fig. 1).

In the overdoping case (x > 0.28) the concentration of the hole pairs becomes too large for the pair wavefunctions to be localized and free electronic levels of Cu²O₆ complexes become extended. These ² levels split and overlap with half-filled ¹ levels of Cu¹O₆ complexes, and the partially filled conduction band of the Fermi liquid metal is formed as a result. Thus the hole (Sr²⁺) doping of the p-type parent semiconductor La₂CuO₄ transforms it into n-type metal in the overdoping regime. Since local pairs disappear, this metal becomes non-superconducting.

Footnotes

†Presented at the `XIV Russian Synchrotron Radiation Conference SR2002', held at Novosibirsk, Russia, on 15–19 July 2002.