I. INTRODUCTION
A perovskite-like lanthanum cobalt oxide LaCoO3 is a fascinating material studied since the 1950s with controversial explanations of its peculiar structural (Radaelli and Cheong, Reference Radaelli and Cheong2002; Maris et al. Reference Maris, Ren, Volotchaev, Zobel, Lorenz and Palstra2003), transport (Schmidt et al. Reference Schmidt, Wu, Leighton and Terry2009), and magnetic (Zobel et al. Reference Zobel, Kriener, Bruns, Baier, Grüninger, Lorenz, Reutler and Revcolevschi2002; Kyomen et al. Reference Kyomen, Asaka and Itoh2003) properties. With temperature increase a maximum of the magnetic susceptibility was observed near 120 K, whereas the second anomaly followed by a plateau at 500–520 K is associated with the metal–insulator transition. Goodenough (Senaris-Rodriguez and Goodenough, Reference Senaris-Rodriguez and Goodenough1995) originally interpreted these magnetic transitions as spin-state transitions of Co3+ ions from the nonmagnetic ground state low-spin state (LS; t 6 2g e 0 g, S = 0) to a high-spin state (HS; t 4 2g e 2 g, S = 2) due to the close values of the intra-atomic exchange energy (J H) and the crystal field splitting (10Dq) at the Co3+ sites. Thus, depending on the relative values of the J H and 10Dq, either the LS, or the HS were suggested to be more stable. These spin-state transitions are further manifested by observable changes in the crystal structure since the HS Co3+ has a much larger radius (0.61 Å) than the LS state (0.54 Å) (Shannon, Reference Shannon1976).
Later, Potze et al., introduced the concept of intermediate-spin state (IS; t 5 2g e 1 g, S = 1) (Potze et al., Reference Potze, Sawatzky and Abbate1995) and showed that the spin-state transition near 120 K is associated with the thermal excitation of Co3+ ions from the LS ground state to an IS, whereas the second transition around 500 K corresponds to a crossover from the IS state to a mixed state of IS and the HS state. Moreover, this point of view was supported by Korotin (Korotin et al., Reference Korotin, Anisimov, Khomskii, Ezhov, Solovyev, Khomski and Sawatzky1996) who performed the LDA+U band structure calculations assuming that temperature effects and spin state transition can be simulated by the lattice parameter expansion. According to (Korotin et al., Reference Korotin, Anisimov, Khomskii, Ezhov, Solovyev, Khomski and Sawatzky1996) the stabilization of the IS state can be explained by large hybridization between the Co-e g and O-2p levels.
In most recent alternative LS–HS state transition model, the LaCoO3 is assumed to be in an inhomogeneous mixed state of LS and HS areas between 120 and 550 K and it transforms to a metallic HS state above 500 K (Knížek et al. Reference Knížek, Hejtmánek, Jirák, Tomeš, Henry and André2009; Siurakshina et al., Reference Siurakshina, Paulus, Yushankhai and Sivachenko2010). According to this model, the population levels of LS and HS states would be temperature dependent and a coexistence of the cobalt ions being in LS and HS states is supposed to be in the temperature range from about 120 K up to 550 K. Therefore, the problem of the true spin state transitions of the Co3+ ions ~120 and ~500 K for LaCoO3 is still a matter of debate to date.
In this paper, we present an investigation of the anomalous temperature-dependent (17 K ≤ T ≤ 420 K) behavior of displacement correlation function (DCF) and strains within the granules of LaCoO3 powder across the spin-state transition (~150 K) performed by a comparison of the X-ray powder diffraction (XPD) and high-resolution extended X-ray absorption fine structure (EXAFS) spectroscopy data. To distinguish carefully an influence of different spin states we have used a reference LaGaO3, which is characterized by [Ar] 3d 10 configuration for Ga3+ ions as they remain in a LS configuration regardless the temperature change.
II. EXPERIMENTAL
Polycrystalline LaCoO3 and LaGaO3 powders were grown and characterized as described elsewhere (Prabhakaran et al., Reference Prabhakaran, Boothroyd, Wondre and Prior2005). The XPD measurements were performed on the high-resolution diffractometer at the B2 beamline (DORIS III, DESY) in temperature range from 17 to 290 K for LaCoO3 at the wavelength λ = 0.8 Å and on BM01 beamline (ESRF) in temperature range from 80 to 420 K for LaCoO3 and LaGaO3 at the wavelength λ = 0.65 Å.
The obtained powder diffraction data were used for refining the corresponding crystal structures with the Rietveld method using FullProf software package (Rodriguez-Carvajal, Reference Rodriguez-Carvajal1993). Microstraines were refined by a STRAIN-program in the frame of this package using Voigt approximation by variation of Lorentzian contribution in peaks shape, taking into account an anisotropical broadening of the Bragg reflections.
The EXAFS experiments have been performed at the BL01B1 beamline of SPring-8 synchrotron. A fixed-exit Si(111) double-crystal monochromator was used, the estimated energy resolution being ΔE/E ~ 0.8·10−4. The EXAFS spectra above the Co K-edge were measured in the energy range 7400–9500 eV in standard transmission mode.
At the Ga K-edge extension of the spectra in k-space reached 22 Å−1 for the cryogenic measurements and 18 Å−1 for high temperature. At least two spectra were measured for every temperature point in order to achieve better quality. Measurement control routine was set up to increase the accumulation time proportionally to the k 2 law in the EXAFS region. Precision of the energy position was controlled with the encoder installed on the Bragg rotation axis of the monochromator.
Standard least-squares curve fitting procedure for the first coordination sphere was used to determine the average R(Co–O) distance and the parallel mean-squared relative displacement (MSRD||) ∆σ 2 Co–O. The experimental scattering amplitude and phase shift functions for the Co–O atom pair were used in the EXAFS analysis. They were obtained from the EXAFS spectra for reference LaGaO3 sample, measured at T = 17 K, where it is assumed that there no an essential anharmonicity in dynamics of Co/GaO6 octahedron and composed of the regular Co/GaO6 octahedra: the cobalt coordination number N ref = 6 and the Co–O distance R ref = 1.925 Å were set according to the results of the Rietveld refinement using our X-ray diffraction (XRD) data of the same LaCoO3 powder.
It should be noted that the fitting result is in very good agreement with the experimental spectra for all three temperature points up to 17.5 Å−1 that guarantees the high-resolution in determination of Co–O bond lengths and MSRDII values.
III. RESULTS AND DISCUSSION
The obtained XPD patterns are shown in Figure 1.
Figure 1. (Colour online) XPD pattern of (a) LaCoO3 at 10 K and (b) LaGaO3 at 80 K. Experimental curve (open red circles), calculated curve (solid black line), and residual curve (solid blue line bottom). The green tick marks indicate the calculated positions of the Bragg peaks.
Typical fits of the XPD patterns for LaCoO3 at 17 K and for LaGaO3 at 80 K are displayed in Figure 1. All observed Bragg peaks for LaCoO3 in temperature range from 17 to 420 K were indexed in the rhombohedral R-3c space group in hexagonal axes setting [Figure 1(a)], while for LaGaO3 in temperature range 80–420 K were indexed in orthorhombic space group Pbnm [Figure 1(b)]. Note that these results (bond lengths for all samples) agree well within approximately ±7·10−4 Å with that obtained before in (Radaelli and Cheong, Reference Radaelli and Cheong2002; Maris et al. Reference Maris, Ren, Volotchaev, Zobel, Lorenz and Palstra2003).
EXAFS technique allows establishing directly the Debye–Waller factor of selected pairs of atoms. The EXAFS Debye–Waller factor gives the information on the correlated parallel MSRD||〈∆σ 2 ||(Co–O)〉, which is equal to the sum of the uncorrelated mean-squared displacements (MSD or isotropic thermal parameters) amplitudes (measured by diffraction) of the pair of absorber 〈(R Co–O·σ Co)2〉 and back-scattered 〈(R Co-O·σ O)2〉 atoms along the bonding direction R Co–O = |〈r O〉 − 〈r Co〉| minus the parallel DCF = 2〈(R Co–O·σ Co)(R Co–O·σ O)〉 (Boysen et al., Reference Boysen, Lerch, Gilles, Krimmer and Többens2002) (σ Co and σ O are instantaneous displacements of the absorber and back-scatter atoms, respectively).
The DCF (i.e. difference between MSD and MSRD||), reflecting the correlation in atomic motion of distant atoms and, as a consequence, the interaction strength between cobalt/gallium and oxygen, grows gradually with temperature for LaCoO3, whereas for LaGaO3 the DCF is approximately constant in the whole-measured temperature range (small decreasing till 300 K and then small increasing at the temperature higher than 300 K) as we can see at Figure 2. Moreover, we observe unusual growth of DCF below ~50 K only in LaCoO3, while in LaGaO3 there are no any features of MSD (Boysen et al., Reference Boysen, Lerch, Gilles, Krimmer and Többens2002) and MSRD|| (Figure 2). Such growth of the DCFCo–O can be explained by a coexistence of several Co3+ spin states during the phase transition: HS in the distorted surface layers of the LaCoO3 granules, LS in the bulk and highly hybridized IS state is in the intermediate layer. Here we imply that electronic configuration of Co3+ changes from HS (ionic radius 0.61 Å) into the IS state (ionic radius 0.56 Å) and finally to the LS state (0.54 Å) (Shannon, Reference Shannon1976; Radaelli and Cheong, Reference Radaelli and Cheong2002; Maris et al. Reference Maris, Ren, Volotchaev, Zobel, Lorenz and Palstra2003). Gradual growth of the DCFCo–O as the sample is heated from 50 to 420 K is associated with gradual growth of the IS/HS ratio up to saturation in basic LS volume and then local range IS/LS ratio.
Figure 2. (Colour online) Temperature dependence of uncorrelated MSD (calculated from XRD) for Co–O bond (full squares) in LaCoO3 and Ga–O bond (empty triangle) LaGaO3 as well as the correlated MSRD| | for Co–O bond (full circles) and Ga–O bond in (empty circles).
Note that our experimental MSRD|| values for LaCoO3 are in agreement with the previous EXAFS data (Jiang et al., Reference Jiang, Bridges, Sundaram, Belanger, Anderson, Mitchell and Zheng2009), which are limited to a temperature of 290 K. Moreover, an increased value of MSRD|| in the extended temperature range and a small rise of MSD below 200 K for LaGaO3 compared with the LaCoO3 ones is associated with the static distortions of the GaO6 octahedra because of the existence of three Ga–O distances, so that the average Ga-O distance is bigger than Co–O in LaCoO3 as given by the Pbmn symmetry.
The absence of MSRDII growth in temperature range from 50 to 17 K is probably associated with a high correlation of atomic motion with small amplitude of both LS and HS Co3+ with oxygen as well as with maximal distortion of Co–O–Co angle (maximal deviation from 180°).
Most sensitive effect of mixture of surface-distorted HS layer in basic LS volume with intermediate IS phase in micrograins below 150 K is observed in the temperature dependence of strain within crystallines obtained by Rietveld analysis for LaCoO3 (Figure 3). Note that LaGaO3 does not have similar effect. A broad peak in this curve with a maximum around 50 K is associated with the mixture of the HS states on the surface crystallines, the LS in the inner part of the crystallines and the IS states located in between. Such mixing of three different spin-states leads to the growth of distortion strain in CoO6 octahedra inside the crystallines.
Figure 3. (Colour online) Temperature dependence of strains within granules obtained by Rietveld analysis using high-resolution XPD data for LaCoO3
High sensitivity to local lattice distortions caused by the difference in atomic radii of the Co3+ atoms in different spin states makes DCF a useful indicator of the spin-state transitions. Comparison of the diffraction data with the EXAFS-derived MSRD for in-plane and apical Co–O bonds allows to distinguish between local and long-range effects.
IV. CONCLUSIONS
We have clarified the origin of anomalous temperature behavior of the DCF and strain curves in a wide temperature range for LaCoO3 and LaGaO3 ceramics. Combined analysis of the EXAFS results and XRD data have led us to the conclusion about thermally induced spin-state transition in LaCoO3 from a mixture of HS and LS configurations of the Co3+ ions located respectively in outer layer and inner part of the crystallines into the highly hybridized IS configuration of the cobalt ions, while the majority of Co3+ ions remains in the LS state up to the temperature of ~150 K.
Gradual growth of DCF and strain parameters estimated for the LaCoO3 compound in the temperature range from ~150 to 420 K has been interpreted by assuming an ongoing spin-state transition from basic LS state to the IS specific for local-range domains. The results derived from this study are in accordance with available experimental data on electron spin resonance (Noguchi et al., Reference Noguchi, Kawamata, Okuda, Nojiri and Motokawa2002), MCD measurements (Haverkort et al., Reference Haverkort, Hu, Cezar, Burnus, Hartmann, Reuther, Zobel, Lorenz, Tanaka, Brookes, Hsieh, Lin, Chen and Tjeng2006), and inelastic neutron data (Podlesnyak et al., Reference Podlesnyak, Streule, Mesot, Medarde, Pomjakushina, Conder, Tanaka, Haverkort and Khomskii2006).
ACKNOWLEDGEMENTS
Measurements at SPring-8 were performed with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2015B1176). Authors acknowledge Dr. R. Chernikov (DESY) for the assistance in the measurements and XAS data analysis. Authors are indebted to Dr. Dmitry Chernyshov (SNBL at ESRF, France) for his help with diffraction experiments and data analysis, to Dr. Alexei Bossak for his assistance with sample preparation and numerous discussions. The reported study was funded by RFBR, research project no. 16-32-50088.
