Relationship between the structural distortion and the Mn electronic state in La_1−xCa_xMnO₃: a Mn K-edge XANES study

A theoretical study of the X-ray absorption near-edge structure (XANES) spectra at the Mn K-edge in the La_1−xCa_xMnO₃ series is reported. The relationship between the edge shift, the Ca–La substitution and the distortion of the MnO₆ octahedra in these systems has been studied. It is shown that, by correctly considering these effects simultaneously, the experimental XANES data are consistent with the presence of two different Mn local environments in the intermediate La_1−xCa_xMnO₃ compounds. By taking into account the energy shift associated with the modification of the MnO₆ distortion as Ca substitutes for La, it is possible to reproduce the XANES spectra of the intermediate-doped compounds starting from the experimental spectra of the end-members LaMnO₃ and CaMnO₃. These results point out the need to re-examine the conclusions derived in the past from the simple analysis of the Mn K-edge XANES edge-shift in these materials. In particular, it is shown that the modification of the Mn K-edge absorption through the La_1−xCa_xMnO₃ series is well reproduced by considering the simultaneous presence of both distorted and undistorted octahedra and, consequently, that the existence of charge-ordering phenomena cannot be ruled out from the XANES data.

1. Introduction

Manganese oxides with perovskite structure have been the subject of a large number of theoretical and experimental studies in the last two decades owing to their peculiar magnetic, electronic and transport properties. R_1−xA_xMnO₃ compounds, in which R is a rare-earth element and A is a divalent ion like Ca, Sr or Ba, display, depending on composition, a diverse range of interrelated phenomena. These include ferromagnetic, antiferromagnetic, orbital and/or charge ordering, various phase transitions, colossal magnetoresistance etc. (Edwards, 2002; Dagotto et al., 2001; Renner et al., 2002). The competing interactions taking place in these materials result in a complex phase diagram in terms of structural, magnetic and electronic properties as a function of composition, temperature and pressure (Zener, 1951; Anderson & Hasegawa, 1955; de Gennes, 1960; Millis et al., 1995, 1996; Salamon & Jaime, 2001).

The La_1−xCa_xMnO₃ series exemplifies this complex behaviour (Schiffer et al., 1995). These compounds are paramagnetic insulators at room temperature and doping with Ca leads to novel transport and magnetic properties including colossal magnetoresistance (CMR) and ferromagnetism (FM). For samples with Ca concentrations in the range 0.2  x  0.5 the FM transition coincides with a metal–insulator transition (Schiffer et al., 1995). At higher calcium concentrations, the system becomes antiferromagnetic being an insulator both above and below T_N. Moreover, this concentration region also exhibits charge ordering (Ramirez et al., 1996; Chen et al., 1997). The basic mechanism of electronic transport has long been thought to be the double-exchange mechanism (Zener, 1951; Anderson & Hasegawa, 1955; de Gennes, 1960). However, several features of the CMR materials, such as the resistivity data, are inconsistent with a model that only consists of double exchange. Therefore, other mechanisms, such as the spin-lattice interactions through a strong coupling of the carriers to Jahn–Teller (JT) lattice distortions, must be considered (Millis et al., 1995, 1996). Indeed, neutron scattering experiments pointed out that the local atomic structure around Mn ions plays a crucial role in determining these complex phenomena (Radaelli et al., 1997; Louca & Egami, 1999). Consequently, much attention has been given to short-range-order techniques like X-ray absorption spectroscopy (XAS) because they are capable of directly probing the local atomic structure. In this way, numerous EXAFS studies have faced the characterization of the MnO₆ octahedra and the local lattice distortions through the La_1−xCa_xMnO₃ series (Booth et al., 1996, 1998; Lanzara et al., 1998; Meneghini et al., 1997, 2002; Subías et al., 1998; Jiang et al., 2007). Despite all these works using the same experimental technique, different schemes are proposed for both the local distortions and their interpretation in connection with their magnetic properties. As a consequence, there is no agreement of the microscopic description of the local structure in these doped manganites (for a survey see, for example, Subías et al., 2002) and several problems, such as the temperature dependence of the distortion of the MnO₆ octahedra and the coexistence of distorted and undistorted MnO₆ octahedra, still remain open (Booth et al., 1998; Subías et al., 2002). According to Booth et al., the oxygen environment around the manganese becomes less distorted as the calcium concentration is increased. The Mn–O distortions are consistent with a linear interpolation of the end-member compounds LaMnO₃ (Mn³⁺) and CaMnO₃ (Mn⁴⁺) in such a way that a model which includes a JT distortion in proportion to the Ca concentration fits the data well (Booth et al., 1998). EXAFS analysis of these Mn–O distortions is consistent with a model where individual Mn³⁺ sites have strong JT distortions while Mn⁴⁺ sites do not (Booth et al., 1998). In contrast, the interpretation of Subías et al. of similar data does not support the presence of an inhomogeneous mixture of Mn³⁺ and Mn⁴⁺ through the series (Subías et al., 2002).

This controversy also extends to the analysis of the XANES part of the absorption spectra. XANES studies have shown that (i) the Mn K-edge spectra of the La_1−xCa_xMnO₃ compounds have a similar shape for the whole series, and (ii) the edge shifts almost rigidly to higher energy as the Ca concentration is increased (Booth et al., 1998; Subías et al., 1997; Croft et al., 1997; Bridges et al., 2001). It is commonly argued that the sharpness of the edge is suggestive of a transition into a Mn state that is uniform throughout the sample (Booth et al., 1998; Subías et al., 1997). In this way, starting from a naive ionic model in which the electronic state is Mn³⁺ in LaMnO₃ and Mn⁴⁺ in CaMnO₃, the substitution of a di­valent ion for La formally changes the average Mn valence to 3 + x. This conjecture should also be supported by the fact that the observed Mn K-edge absorption of the intermediate La_1−xCa_xMnO₃ compounds cannot be modelled as a weighted sum of the LaMnO₃ and CaMnO₃ spectra (Subías et al., 1997; García et al., 2001b). However, Ignatov et al. have pointed out that a model assuming only one type of manganese fails to reproduce the shake-up feature in the XANES or it assumes a structureless X-ray photoelectron spectrum, both inconsistent with experimental observations (Ignatov et al., 2001). Moreover, Bridges et al. have suggested that using the position of the peak in the first derivative curve as a measure of the average edge position is only an approximate measure of the average edge shift (Bridges et al., 2001). They have proposed an alternative method of obtaining a better estimate of the average edge shift with concentration, concluding that there is a splitting of the Mn—O distances. Therefore, although there is no modification of the sharpness of the edge, which is expected for two well defined valence states, there is evidence of a coexistence of undistorted and distorted MnO₆ octahedra, which indicates some change in the local charge distribution (Bridges et al., 2001). A similar contest also extends to the interpretation of recent X-ray resonant scattering experiments in the so-called charge-ordered compounds (Subías et al., 2002; Murakami et al., 1998; Zimmermann et al., 1999; Nakamura et al., 1999). While the presence of two differently distorted MnO₆ octahedra in the charge-ordered manganites starts to be accepted (Jiang et al., 2007; García et al., 2001a), several authors conclude that these two kinds of Mn atoms cannot be regarded as pure ionic Mn³⁺ and Mn⁴⁺ ions and that no real Mn³⁺/Mn⁴⁺ charge ordering occurs in these compounds (García et al., 2001a).

Therefore, the occurrence of either charge localization, inhomogeneous Mn³⁺ and Mn⁴⁺ or homogeneous Mn^3+x, is still a matter of controversy. We have a scenario in which similar EXAFS and XANES results lead to opposite conclusions regarding the distortion of the local environment of the Mn ions through the La_1−xCa_xMnO₃ series: (i) there is a mixture of ionic-like Mn³⁺ and Mn⁴⁺ ions in the materials or, on the contrary, (ii) all the Mn atoms in the substituted compounds show the same intermediate valence. Within the extended framework identifying the Mn electronic state with the distortion of the MnO₆ octahedron (Booth et al., 1996, 1998; Lanzara et al., 1998; Meneghini et al., 1997, 2002; Subías et al., 1997, 1998, 2002; Jiang et al., 2007; Croft et al., 1997; Bridges et al., 2001; García et al., 2001b), the first possibility implies the coexistence of distorted and undistorted MnO₆ octahedra such as those found in the parent LaMnO₃ and CaMnO₃ compounds (Booth et al., 1998). By contrast, all the MnO₆ octahedra would be equally distorted in the second case, with all the Mn atoms showing an intermediate valence ranging between Mn³⁺ and Mn⁴⁺ (Subías et al., 2002). If this is the case, both the valence and the distortion should evolve linearly through the La_1−xCa_xMnO₃ series as a function of the doping.

This work is aimed at determining whether X-ray absorption spectroscopy at the Mn K-edge is capable of discerning between both aforesaid possibilities. In this way we have performed an extensive and systematic ab initio computation of the Mn K-edge in LaMnO₃, CaMnO₃ and the intermediate La_1−xCa_xMnO₃ compounds within the multiple-scattering framework (Natoli & Benfatto, 1986). In particular, we have studied how the local distortion of the MnO₆ octahedra and the electronic state of Mn ions affect the Mn K-edge XANES spectra of the La_1−xCa_xMnO₃ materials; in particular, how they are related to both the position of the absorption edge and the spectral shape. A comparison between the experimental data and ab initio computations based on multiple-scattering theory indicates that the election of the cluster size is critical in correctly reproducing all of the experimental XANES features. This need is independent of both the electronic state of the Mn atoms and the occurrence of distorted or undistorted MnO₆ octahedra. By fixing the same computational parameters, we have studied the relationship between the edge shift, the Ca–La substitution and the distortion of the MnO₆ octahedra through the series. Our analysis shows that by taking into account these effects simultaneously it is possible to reproduce the spectra of the intermediate La_1−xCa_xMnO₃ compounds. In this way we show that, by considering the variation of the edge shift associated with the modification of the MnO₆ distortion as La is substituted by Ca, it is possible to reproduce the XANES spectra of the intermediate-doped compounds starting from the experimental spectra of the end-member LaMnO₃ and CaMnO₃ compounds. These results show that the experimental XANES data are consistent with the presence of two different Mn local environments in the intermediate compounds, and point out the need to re-examine the conclusions derived in the past from the simple analysis of the Mn K-edge XANES edge-shift in these materials.

2. Computational methods

Computation of the Mn K-edge XANES spectra was carried out using the multiple-scattering code CONTINUUM (Benfatto et al., 1986) based on the one-electron full-multiple-scattering theory (Lee & Pendry, 1975; Natoli & Benfatto, 1986). For a complete discussion of the procedure, we refer the reader to Chaboy & Quarteri (1995) and Natoli et al. (2003).

The potential for the different atomic clusters was approximated by a set of spherically averaged muffin-tin potentials built by following the standard Mattheis' prescription (Mattheis, 1964). The muffin-tin radii were determined following Norman's criterion (Norman, 1974). The Coulomb part of each atomic potential was generated using charge densities for neutral atoms obtained from the tabulated atomic wavefunctions of Clementi & Roetti (1974). We have also checked that using charge densities obtained from non-local self-consistent Dirac–Fock code (Ankudinov et al., 1998; Desclaux, 1975) does not modify the results. The atomic orbitals were chosen to be neutral for the ground state potential, whereas different choices were used to build the final state potential. We have found during the present calculations that the screened and relaxed Z + 1 option (Lee & Beni, 1977) leads to the best performance in simulating the experimental spectra. Finally, we have studied how the different choices for the exchange and correlation part of the final state potential affect the agreement between the experimental and ab initio calculated spectra. The calculated theoretical spectra have been further convoluted with a Lorentzian shape function to account for the core-hole lifetime (Γ = 1.2 eV) (Krause & Oliver, 1979) and the experimental resolution (Γ = 1 eV). The computed spectra have been compared with the experimental XANES data reported by Subías et al. (1997).

3. Results and discussion

The local structure of Mn in CaMnO₃ consists of six O atoms in a near regular octahedral geometry (see Fig. 1) in which four O atoms lie at R₁(Mn—O) = 1.89 Å from Mn, and the other two O atoms are located at a distance R₂(Mn—O) = 1.92 Å (Fawcett et al., 1998). In the case of LaMnO₃, this octahedron is distorted showing three different Mn—O pairs: R₁(Mn—O) = 1.91 Å, R₂(Mn—O) = 1.97 Å and R₃(Mn—O) = 2.18 Å (Iliev et al., 1998). The distortion in LaMnO₃ is due to the JT effect associated with the 3d⁴ electronic configuration in O_h site symmetry of the Mn³⁺ ion. Such a JT distortion is absent in CaMnO₃ where only Mn⁴⁺ ions are present.

Figure 1 Schematic view of the RMnO3 structure. This figure is in colour in the electronic version of this paper.

Previous fingerprint analysis of the Mn K-edge XANES spectra of the intermediate La_1−xCa_xMnO₃ compounds ruled out the existence of a simple mixture of Mn³⁺ and Mn⁴⁺ ions in the substituted La–Ca manganite samples because the absorption edge shifts almost rigidly to higher energy as the concentration is increased. These works assumed that there is no distortion of the MnO₆ octahedra as the cell parameter varies. In this way, the spectra of the substituted compounds are compared with the weighted sum of the XANES spectra of the end compounds LaMnO₃ (Mn³⁺) and CaMnO₃ (Mn⁴⁺) (Booth et al., 1998; Subías et al., 1997; Croft et al., 1997; Bridges et al., 2001). However, one should expect that the modification of the interatomic distances associated with the La–Ca substitution affects the distortion of the MnO₆ octahedra. Consequently, the edge position should change because it is intimately linked to the local structure: when the bond length of a molecule lengthens, the position of the edge shifts to lower energy. Indeed, several authors have shown that, in the case of the La_1−xCa_xMnO₃ systems, the Mn—O distortions are the primary producers of the polarization-dependent splitting of the main line (Benfatto et al., 1999), so that the main line profile is a direct mirror of the degree of JT distortion (Qian et al., 2001). In this respect, Benfatto et al. (1999) and Elfimov et al. (1999) have calculated, using different methods, that the edge should shift about 2 eV between the long and short bonds. Therefore, the modification of the cell parameters through the La_1−xCa_xMnO₃ series may result in changes of the interatomic distances of the MnO₆ octahedra without modification of the electronic state of the Mn ions (Ramos et al., 2007). If this is the case, the XAS spectra of the Mn³⁺ and Mn⁴⁺ ions in the modified crystal cell structures of the intermediate compounds should differ from those of LaMnO₃ and CaMnO₃, respectively, and the above conclusions should be revised.

In an attempt to clarify this problem, we have studied how the local distortion of the MnO₆ octahedra affects the Mn K-edge XANES spectra of the La_1−xCa_xMnO₃ materials. To this end we have performed a detailed ab initio computation of the Mn K-edge XANES through the La_1−xCa_xMnO₃ series. The first objective has been to determine the necessary conditions to obtain an accurate reproduction of the experimental spectra of the end-members of the series, i.e. LaMnO₃ and CaMnO₃, in order to fix the same computational parameters for the computation of the La_1−xCa_xMnO₃ systems. A complete discussion of the different aspects of these computations is detailed in Appendix A. The best agreement between the theoretical and experimental spectra for both LaMnO₃ and CaMnO₃ are reported in Fig. 2. Here, we briefly summarize the main conclusions of this starting study.

Figure 2 Comparison of the experimental Mn K-edge XANES spectra (open circles) of LaMnO3 and CaMnO3 and the theoretical spectra (green, dashed line) calculated on clusters containing 125 atoms by imposing an overlapping factor of 1% and lmax = 4 and by using complex ECP potentials (see Appendix A for details): HL (blue, dotted line) and complex DH (green, dashed line). This figure is in colour in the electronic version of this paper.

(i) The computations performed by increasing the cluster size indicate the need to include scattering contributions from the neighbouring atoms within at least the first 7 Å around the absorbing Mn atom in order to reproduce the experimental Mn K-edge spectra of both LaMnO₃ and CaMnO₃. Computations made for a cluster of 125 atoms yield an accurate reproduction of the high-energy spectral features in the first 60 eV above the edge. The computations performed for medium-size clusters (r_max ≤ 6 Å) fail to reproduce the experimental spectra of both LaMnO₃ and CaMnO₃. This result demonstrates that special caution has to be given to strong conclusions, such as the non-existence of Mn³⁺/Mn⁴⁺ charge ordering, based on computations performed on small clusters (García et al., 2001a).

(ii) It is mandatory to use a high value of l_max in order to account for the spectral features (C, D and E) located between 30 and 60 eV above the edge.

(iii) These computations show the importance of the choice of the overlapping factor among the muffin-tin spheres. It does affect both the intensity and the spectral shape in the first 40 eV of the computed spectra, which results crucially in correctly reproducing the broad resonance B (B₁ and B₂ in the case of CaMnO₃). In this respect, computations performed by using a 1% factor show a better agreement with the experimental spectra than those corresponding to a 10% overlapping factor.

(iv) The best agreement with the experimental spectra is obtained by using complex potentials in which the imaginary part accounts for the photoelectron damping. In addition to the Hedin–Lundqvist (HL) potential we have also used the energy-dependent Dirac–Hara (DH) exchange potential (Natoli et al., 2003) after adding the imaginary part of the HL (hereafter, complex Dirac–Hara). As shown in Fig. 2, computations made by using both potentials show a good agreement with the experimental data. In both the LaMnO₃ and CaMnO₃ cases, the HL potential yields the best reproduction of the intensity ratio of the main spectral features at low energy (A, B), while the complex DH improves the reproduction of the high-energy region (C, D and E features).

It should be noted that during the computations we have used the same charge densities for neutral Mn in both LaMnO₃ and CaMnO₃. The good agreement reached by the computations in the comparison with the experimental data indicate that the influence of the electronic state of Mn, Mn³⁺ or Mn⁴⁺ mainly affects the edge position. Indeed, it has been previously reported that the use of self-consistent-field (SCF) charge densities does not affect the spectral shape and that only the edge position is affected (Benfatto et al., 1997, 2002; Chaboy et al., 2005). The good reproduction of the spectra indicates that, apart from the edge shift, the structural effects are dominant. In other words, the scattering properties of the Mn³⁺ (LaMnO₃) and Mn⁴⁺ (CaMnO₃) atoms are very similar and they manifest their presence in the local geometry through the distortion of the MnO₆ octahedra.

The detailed computation performed on both LaMnO₃ and CaMnO₃ compounds fixes the starting point for evaluating the effect of the chemical substitution through the La_1−xCa_xMnO₃ series. With this aim, we have firstly studied the effect of the chemical substitution on the calculation of the Mn K-edge XANES spectra in the La_1−xCa_xMnO₃ series. Initially, we have considered two situations. In the first model all the La atoms in the LaMnO₃ cluster are substituted by Ca ones, but maintaining a fixed crystal structure. In this way we just change the scattering properties of the neighbouring atoms without modifying the MnO₆ arrangement. In the second model we consider a LaMnO₃ cluster in which the original distorted Mn—O octahedron (2 × 1.91, 2 × 1.97, 2 × 2.18 Å) around the absorbing atom is substituted by the regular one (4 × 1.89, 2 × 1.92 Å) found in CaMnO₃. Conversely, similar modifications have been applied to the CaMnO₃ cluster: (i) the Ca scatterers have been substituted by La ones, maintaining the crystal structure, and (ii) we have substituted the regular octahedron around the absorbing Mn atom in CaMnO₃ by the distorted one of LaMnO₃. According to the results summarized in Fig. 2, all the computations have been performed for clusters of 125 atoms, 1% overlapping factor, l_max = 4 and by using the complex HL exchange and correlation potential (ECP).

The computations, reported in Fig. 3, show two main results regarding the substitution of La by Ca atoms in LaMnO₃ and, conversely, of La at the Ca sites in CaMnO₃. On the one hand, the intensity of the main absorption peak (or white line) is affected by the substitution. In the case of LaMnO₃ it decreases as Ca occupies the La sites. The contrary occurs when La substitutes for Ca in CaMnO₃ and then the white line is enhanced. Moreover, the chemical substitution, without changing the MnO₆ octahedra, also affects the shape of the second main resonance as well as its energy position relative to the main absorption line. These results indicate that independently of the local geometry of the first oxygen neighbouring shell the Mn K-edge XANES is affected by the type of atoms (La or Ca) located in the second coordination sphere. Consequently, the assumption that the XANES of the intermediate La_1−xCa_xMnO₃ compounds could be modelled by simply weighting the spectra of the end-members is not held. Indeed, this simple model would only be valid if the intermediate compounds are a mixture of LaMnO₃ and CaMnO₃ phases, which is not the case. In a similar way to the above findings, the results reported in Fig. 3 show that for unsubstituted clusters the modification of the MnO₆ geometry also induces significant changes in the intensity, the shape and the relative energy position of the main spectral features. According to these results, the Mn K-edge spectra of the partially substituted La_1−xCa_xMnO₃ cannot be considered as made by the addition of those of the end-members. The chemical La–Ca substitution implies a modification of the scattering contribution to the XANES spectra. Therefore, the nature of the scatterer (La versus Ca), and not only the interatomic distance, plays a non-negligible role.

Figure 3 (a) Comparison of the experimental XANES spectrum at the Mn K-edge (open circles) and the theoretical spectra calculated for a 7 Å cluster of LaMnO3 (red, solid line) and (i) by replacing the La atoms by Ca at the same positions (blue, dashed line) and (ii) by substituting the distorted Mn—O octahedron by the regular one (green, dotted line) as found in CaMnO3 (see text for details). (b) Comparison of the experimental XANES spectrum at the Mn K-edge (filled circles) and the theoretical spectra calculated for a 7 Å cluster of CaMnO3 (red, solid line) and by substituting the regular Mn—O octahedron by the distorted LaMnO3-like one (blue, dashed line). The computation performed for the same CaMnO3 cluster by replacing the Ca atoms by La at the same positions (green, dotted line) is also shown. This figure is in colour in the electronic version of this paper.

The next step of our study has been to evaluate the effect of the chemical (La–Ca) substitution on the edge shift. To this end, we have computed the Mn K-edge XANES spectra for the intermediate La_0.67Ca_0.33MnO₃, La_0.5Ca_0.5MnO₃ and La_0.33Ca_0.67xMnO₃ compounds. It should be noted that the energy scale of each computation is referred to its own muffin-tin potential. Therefore, it is necessary to correct the energy scale of the computed spectra in order to compare the calculations for the different compounds on a unique energy scale prior to account for the edge shift associated with the structural modification.

The experimental Mn K-edge spectra of the intermediate La_0.67Ca_0.33MnO₃, La_0.5Ca_0.5MnO₃ and La_0.33Ca_0.67xMnO₃, and those of the end-members (Subías et al., 1997), are shown in Fig. 4. The shift of the threshold between LaMnO₃ and CaMnO₃ is determined to be ΔE = 4.2 eV by using the first derivative of the spectra. However, this energy difference decreases to 2.7 eV if one looks at the energy position of the main absorption peak. The theoretical computations show a similar trend, being ΔE = 2.18 eV and 1.64 eV as determined from the first derivative or the main peak position, respectively. Despite the fact that we are using neutral Mn atoms to perform the calculations, the edge and the energy position of the main absorption line are different for both LaMnO₃ and CaMnO₃ compounds. This result demonstrates that the different crystal structure contributes to the experimentally observed edge-shift. As discussed above, the experimental energy separation of the main line is 2.7 eV while the neutral-atom computations yield a value of 1.64 eV. By shifting by 1 eV the theoretical spectrum of CaMnO₃ with respect to that of LaMnO₃, a remarkable agreement with the experimental observations is obtained, as shown in Fig. 4(b). These results show that, despite the fact that it is currently assumed that the shift of the absorption edge is associated with a change of the electronic state of Mn, the edge position also depends on the distortion of the MnO₆ octahedron (Benfatto et al., 1999; Qian et al., 2001; Ramos et al., 2007). As recently illustrated by the Mn K-edge XANES measurements of LaMnO₃ under pressure, the existence of such a distortion does not mean that the electronic state of Mn changes (Ramos et al., 2007). Ramos et al. have shown that for pressures above 8 GPa there is a continuous shift of the absorption threshold towards higher energies along with an enhancement of the structures just above the edge (Ramos et al., 2007). Since the manganese formal valence (Mn³⁺) remains unchanged with pressure, the edge shift (∼0.9 eV) and the modification of the main lines in XANES reflect the structural distortion of the MnO₆ octahedra despite the Mn³⁺ state being preserved. These results are in agreement with the work of Benfatto et al., showing that the edge position is mainly determined by the long Mn—O distance (Benfatto et al., 1999), and thus the edge shift is essentially related to the specific reduction in this bond. Moreover, the evolution of the XANES features reflects therefore a continuous reduction of the average JT distortion from 8 GPa up to 15.3 GPa. The evolution of the edge energy as a function of the applied pressure shows that for small shifts the relationship between the reduction of the bond distance and the associated edge shift is almost linear, in agreement with Natoli's rule (Natoli, 1984).

Figure 4 (a) Comparison of the experimental XANES spectrum at the Mn K-edge through the La1−xCaxMnO3 series: x = 0 (filled circles), x = 0.33 (blue, dotted line), x = 0.5 (green, dot-dashed line), x = 0.67 (red, dashed line) and x = 1 (open circles). (b) Comparison of the experimental spectra of LaMnO3 (filled circles) and CaMnO3 (black, open circles) and the result of the computations plotted on a unique absolute energy scale: LaMnO3 (blue, dotted line), CaMnO3 (green, dashed line). The result of shifting by 1 eV the CaMnO3 computation is also shown (red, dot-dashed line). This figure is in colour in the electronic version of this paper.

In order to ascertain whether this effect is due to the whole crystal structure, the type of scatterer (La or Ca) or to the distortion of the MnO₆ octahedra, we have compared on the same energy scale the computations reported in Fig. 4 and new calculations performed by considering different Mn—O distortions of the MnO₆ octahedron containing the absorbing Mn atom. In this way we have decreased the distortion of the LaMnO₃ octahedron (2 × 1.93, 2 × 1.97, 2 × 2.07 Å), and we have even cancelled this distortion (6 × 1.97 Å). In both cases the rest of the crystal structure remains unaltered. As shown in Fig. 5, the position of the absorption maximum in LaMnO₃ (∼10.97 eV) shifts to higher energy (∼11.52 eV) as the distortion is reduced and it lies at 11.78 eV in the case of considering the regular MnO₆ octahedron. In addition, if we insert the MnO₆ octahedron of CaMnO₃ in the LaMnO₃ cluster, the calculation yields a maximum at 13.15 eV, i.e. the energy shift is ΔE = 2.18 eV, which coincides with the energy separation of the main peak of the experimental LaMnO₃ and CaMnO₃ spectra. Finally, we have also investigated the effect of the progressive substitution of La by Ca in the LaMnO₃ crystal structure: the MnO₆ octahedra and the interatomic distances remain unchanged and only the number of La–Ca scatterers is modified. As shown in Fig. 6, the edge and both the energy position and the shape of the main spectral features gradually changes as the Ca content increases.

Figure 5 Comparison of the experimental Mn K-edge XANES spectrum of LaMnO3 (filled circles) and CaMnO3 (open circles) and the result of the computations, plotted on an absolute energy scale, performed for a 7 Å cluster of LaMnO3 in which the distorted MnO6 octahedron has been substituted by a regular (red, dotted line) and partly distorted (blue, dot-dashed line) one, and by the same regular one as found in CaMnO3 (green, dashed line) (see text for details). This figure is in colour in the electronic version of this paper.

Figure 6 Comparison of the experimental spectra of LaMnO3 (filled circles) and CaMnO3 (black, open circles) and the result of the computations performed for a 7 Å cluster of LaMnO3 in which the La atoms are progressively substituted by Ca: 25% Ca (red, dotted line), 50% (green, dashed line), 75% (blue, dot-dashed line) and 100% (purple, solid line). This figure is in colour in the electronic version of this paper.

The results of the theoretical calculations reported here demonstrate the existing relationship between the chemical (Ca–La) substitution and both the energy position and the shape of the different spectral features of the Mn K-edge XANES spectra in the La_1−xCa_xMnO₃ series. Therefore, we have re-examined the model currently used to relate the shift of the absorption edge with the electronic state of the Mn ions through the series. According to this, the XANES spectra of the intermediate-doped compounds was built up by adding, with the appropriate weight, the spectra of LaMnO₃ and CaMnO₃. The results were not satisfactory and the co­existence of Mn³⁺ and Mn⁴⁺ ions in the substituted samples was discarded (Booth et al., 1998; Subías et al., 1997; Croft et al., 1997; Bridges et al., 2001). However, the results of our calculations indicate that the distortion of the MnO₆ octahedra affects both the edge position and the spectral shape. Consequently, the Mn K-edge absorption shifts in energy as a function of the La–Ca substitution through the series. Starting from the LaMnO₃ limit, the distortion of the MnO₆ octahedra decreases as the Ca content increases, shifting the edge towards higher energies. The contrary occurs when CaMnO₃ is considered: as La substitutes for Ca the original regular octahedra become distorted, shifting the edge towards lower energies. Then, we have corrected the naive model by incorporating these energy shifts. In this way, the XANES spectra of the intermediate compounds are calculated as the weighted sum of those of LaMnO₃ and CaMnO₃, in its adequate proportion, but after applying the appropriate energy-shift corresponding to the distortion. This is illustrated in Figs. 7 and 8 in the case of La_0.5Ca_0.5MnO₃ and La_0.33Ca_0.67xMnO₃, respectively. According to our computations, the energy shift between the spectra of LaMnO₃ and CaMnO₃ is 2 eV. Then, in the case of La_0.5Ca_0.5MnO₃ we have shifted the spectrum of LaMnO₃ by 1 eV and that of the CaMnO₃ by −1 eV. The result of this procedure is shown in Fig. 7, where the weighted signal has been multiplied by 1.04 to match the intensity of the main peak. The agreement between the experimental spectrum and the signal constructed starting from the end-members is remarkable. Finally, we have applied an identical procedure to the La_0.33Ca_0.67MnO₃ compound for which charge ordering has been claimed. In this case, the spectrum of LaMnO₃ has been shifted by 1.5 eV and that of CaMnO₃ by −0.5 eV. After applying the appropriate weighting, the obtained signal matches the experimental spectrum as shown in Fig. 8. Therefore, contrary to previous assignments, the experimental Mn K-edge XANES spectra of the La_1−xCa_xMnO₃ compounds support the existence of well defined Mn³⁺ and Mn⁴⁺ ions, i.e. distorted and undistorted octahedra. These results are in agreement with the analysis of Booth et al., showing that, as the calcium concentration increases, the oxygen environment around the manganese becomes less distorted, these Mn—O distortions being consistent with a model which includes a JT distortion in proportion to the Ca concentration (Booth et al., 1998).

Figure 7 Comparison of the experimental XANES spectrum at the Mn K-edge of LaMnO3 (black, filled circles), La0.5Ca0.5MnO3 (green, filled squares) and CaMnO3 (black, open circles), with the averaged sum (50:50) of the end-members spectra (blue, dashed line). In addition, the result of adding the spectra of both LaMnO3 and CaMnO3 after applying a shift of 1 eV and −1 eV, respectively, is also shown (red, open squares). This figure is in colour in the electronic version of this paper.

Figure 8 Comparison of the experimental XANES spectrum at the Mn K-edge of LaMnO3 (black, filled circles), La0.33Ca0.67MnO3 (green, filled squares) and CaMnO3 (black, open circles), with the weighted sum (0.33:0.67) of the LaMnO3 and CaMnO3 after applying a shift of 1.5 eV and −0.5 eV, respectively (red, open squares). This figure is in colour in the electronic version of this paper.

4. Summary and conclusions

We have reported an extensive and systematic ab initio computation of the Mn K-edge in LaMnO₃, CaMnO₃ and the intermediate La_1−xCa_xMnO₃ compounds performed within the multiple-scattering framework.

We have shown the need to use big clusters in order to reproduce all the spectral features, as well as the correct energy position and intensity ratio. In particular, the comparison between the experimental data and the theoretical calculations has demonstrated the need to use large clusters, ∼7 Å around the central photoabsorbing atom, to reproduce the experimental spectra alloys. These needs are independent of the electronic state of the Mn atoms and of the occurrence of distorted or undistorted MnO₆ octahedra through the series.

By fixing the same computational parameters we have studied the relationship between the edge shift, the Ca–La substitution and the distortion of the MnO₆ octahedra. It is shown that by correctly considering these effects simultaneously the experimental XANES data are consistent with the presence of two different Mn local environments through the La_1−xCa_xMnO₃ series. In addition, by taking into account the energy shift associated with the modification of the MnO₆ distortion as Ca substitutes for La, it is shown that it is possible to reproduce the XANES spectra of the intermediate-doped compounds starting from the experimental spectra of the end-member LaMnO₃ and CaMnO₃ compounds. These results point out the need to re-examine the conclusions derived in the past from simple analysis of the Mn K-edge XANES shift in these materials. In particular, we show that the modification of the Mn K-edge absorption through the La_1−xCa_xMnO₃ series is well accounted for by considering the simultaneous presence of both distorted and undistorted octahedra and, consequently, the existence of charge ordering phenomena cannot be ruled out based on the XANES data. The results reported here solve the perennial issue of similar XAS experimental results leading to opposite conclusions.

APPENDIX A

Computation of the Mn K-edge XANES

Here we present the details of the ab initio Mn K-edge XANES calculations performed in the case of both LaMnO₃ and CaMnO₃, i.e. the end-members of the La_1−xCa_xMnO₃ series. For the computations we have used the crystallographic data of LaMnO₃ and CaMnO₃ reported by Iliev et al. (1998) and Fawcett et al. (1998), respectively.

Initially, we have built up a LaMnO₃ cluster containing 69 atoms, i.e. including contributions from atoms located within the first ∼5.5 Å around Mn. We have tested for this fixed-size cluster the effect of modifying the value of the maximum angular momentum quantum number, l_max, needed to account for the experimental absorption spectrum in the first 60 eV. As shown in Fig. 9, computations performed by using low l_max values fail to reproduce the experimental spectral shape. While the experimental spectrum shows a well defined energy separation between the main absorption peak (A) and the first broad resonance centred at ∼16 eV (B), the l_max = 3 computation exhibits an asymmetric profile in which the broad resonance is attached to the main peak. Moreover, feature C is not reproduced at all and the calculated absorption minima and maxima fall short of the observed ones, which is evident in the case of the absorption minimum between features C and D. In this respect, it should be noted that the comparison of the computed spectrum and the experimental one is limited by the angular momentum expansion of the global scattering function (l_max ≃ kR, where R is the smallest atomic sphere radii and l_max is the maximal momentum for partial waves used inside atomic spheres). Then, we have increased l_max to 4. In this way a better expansion of the angular momentum within the La spheres is obtained and, moreover, the energy range in which the computation can be compared with the experimental spectrum is increased. Fig. 9 shows the improvement of this computation: the main spectral features, A and B, are now well energy-resolved and, in addition, a better energy position of the high-energy feature D (∼45 eV) is obtained.

Figure 9 Comparison of the experimental XANES spectrum at the Mn K-edge in LaMnO3 (filled circles) and the theoretical spectra calculated on a 5.5 Å cluster by using real HL ECP potential and different lmax values: lmax = 2 (black, solid line), lmax = 3 (green, dashed line) and lmax = 4 (blue, dotted line). This figure is in colour in the electronic version of this paper.

However, despite the above progress, both the shape and the width of the second resonance (B) are still poorly accounted for by the computation that, in addition, yields the absorption minimum ∼8 eV below the experimental (∼36 eV) value. Therefore, we have increased the cluster size in order to obtain a better reproduction of the experimental spectrum. Previous works have reported computations performed on a cluster of 87 atoms (Ignatov et al., 2001; Qian et al., 2001; Monesi et al., 2005). Such a cluster covers contributions of atoms within the first 6.125 Å around the absorbing atom. The added coordination shells only include O atoms so that no large differences are expected with respect to the computation for the 5.8 Å cluster reported in Fig. 9. The next neighbouring shells, not included in the 87 atoms cluster, correspond to 24 La (∼6.4 Å) and 8 Mn (∼6.7 Å) atoms. For these shells a greater contribution to the scattering processes compared with that of the O atoms is expected. Therefore, we have performed the computations for clusters including these contributions (119 atoms) and for a bigger one containing 295 atoms. In the last case, all the contributions within the first 9.5 Å around the central Mn are included. For these computations we have used only the real part of the Hedin–Lundqvist complex potential (hereafter, real HL). The reason for this is to avoid the possibility of introducing an excessive damping of the excited photoelectron that can smear the appearance of new contributions to the XANES spectrum coming from the addition of further coordination shells.

As shown in Fig. 10, increasing the cluster size from 87 to 119 atoms slightly improves the computations. By contrast, the use of the biggest cluster (295 atoms) significantly improves the results: (i) the intensity ratio between the A and B features, ∼1.15, approaches the experimental one (∼1.2) whereas it is ∼1.84 for the smaller clusters; (ii) the width and the asymmetric shape of feature B are well reproduced; (iii) the energy position of features E and D matches those observed experimentally; (iv) the computation accounts for the feature C located at the high energy part of the broad B peak, that was missed in the former calculations. Finally, we have also checked the importance of the choice of the overlapping factor among the muffin-tin spheres in the correct reproduction of the absorption spectrum. Our results show that it influences both the intensity and the spectral shape in the first 40 eV of the computed spectra, which results crucially in correctly reproducing the broad resonance B of the LaMnO₃ spectrum. In this respect, computations performed by using a 1% factor show a better agreement with the experimental spectrum than those corresponding to a 10% overlapping factor (see inset of Fig. 10).

Figure 10 Comparison of the experimental XANES spectrum at the Mn K-edge in LaMnO3 (open circles) and the theoretical spectra calculated cluster by imposing an overlapping factor of 1%, lmax = 4 and the real part of the HL potential on clusters of increasing size (87, 119 and 295 atoms) covering up to 6 Å (green, dashed line), 6.75 (red, dotted line) and 9.5 Å (blue, solid line) around the absorbing Mn atom. In the inset, a comparison of the computation performed on the 119 atoms cluster by imposing an overlapping factor of 1% (blue, solid line) and 10% (red, dotted line) is shown. This figure is in colour in the electronic version of this paper.

The results of the calculations performed by using only the real part of the HL ECP point out the need to use quite big clusters in order to reproduce the experimental spectrum of LaMnO₃. However, the relative intensity of the spectral features is not in agreement with those observed experimentally, as expected, because the photoelectron damping was not taken into account in the real HL calculations. Consequently, we have conducted a similar computational procedure as above but using the complex HL ECP potential. As in the case of using the real HL, the importance of the scattering processes involving atoms located beyond the first 6 Å around the absorbing Mn is fundamental in order to reproduce the shape and the intensity of the experimental spectrum. As shown in Fig. 11(a), the agreement between the experimental and theoretical spectrum is not satisfactory when the computations are performed for medium-size, r_max ≤ 6 Å, clusters. The best reproduction of the experimental spectrum is obtained for a cluster made of 295 atoms. The computation made by using this cluster and l_max = 4 yields an accurate reproduction of the high-energy spectral features in the first 50 eV above the edge. Based on these results and in order to reduce the computational time, we have studied the minimum cluster size needed to account for the experimental spectrum. As shown in Fig. 11(b), no significant differences are found among the computations performed on clusters including the coordination spheres within the first 7 Å (125 atoms), 8 Å (167) and 9.5 Å (295) around the absorbing Mn. Therefore, we conclude that the minimum size of the cluster needed to account for the Mn K-edge XANES of LaMnO₃ has to include all the neighbours within the first 7 Å around the absorbing Mn atom.

Figure 11 (a) Comparison of the experimental XANES spectrum at the Mn K-edge in LaMnO3 (open circles) and the theoretical spectra calculated by imposing an overlapping factor of 1%, lmax = 3, and by using the complex HL potential in clusters of 87 atoms (green, dotted line) and 295 atoms (purple, solid line). (b) Comparison of the computations performed by using lmax = 4 on clusters containing 125 atoms (rmax = 7 Å) (red, dotted line), 167 atoms (rmax = 8 Å) (blue, dashed line) and 295 atoms (rmax = 9.5 Å) (green, solid line). This figure is in colour in the electronic version of this paper.

Despite the fact that the agreement between the experimental and the theoretical spectra is remarkable, several problems remain in the high-energy region. Indeed, the computed energy position and the relative intensity of the high-energy features D and E do not match those observed experimentally. We have attempted to improve this result by modifying the exchange and correlation potential used in the computations. In this way we have verified that the energy-dependent DH exchange potential (Natoli et al., 2003) improves the computations in such a way that the energy position of the energy minimum (∼36 eV above the edge) and of both peaks E (∼45 eV) and D (∼60 eV) is now properly accounted for. However, with the DH being a real potential, the intensity of the computed spectral features is too high, as previously obtained for the real HL case. We have added to the DH ECP the imaginary part of the HL one (hereafter, complex DH) in order to account for the photoelectron damping. As shown in Fig. 12, the agreement between the theoretical calculation and the experimental spectrum is excellent in the first 65 eV above the edge, especially regarding the high-energy spectral features.

Figure 12 Comparison of the experimental XANES spectrum at the Mn K-edge in LaMnO3 (open circles) and the theoretical spectra calculated cluster by using the complex DH potential on two clusters containing 125 atoms, rmax = 7 Å (green, dashed line) and 295 atoms, rmax = 9.5 Å, (blue, dotted line). The computations were made by imposing an overlapping factor of 1% and lmax = 4. For the sake of completion the calculation performed on the biggest cluster by using lmax = 3 (red, solid line) is also shown. This figure is in colour in the electronic version of this paper.

The results reported in the previous section show the necessary conditions for obtaining an accurate reproduction of the experimental Mn K-edge XANES spectra in the La_1−xCa_xMnO₃ systems. The conducted methodology pays special attention to several computational aspects that are sometimes overlooked leading to incorrect conclusions because of the inappropriate use of the computer tools. It should be stressed that no fitting parameter has been used during the calculations. The theoretically calculated spectra have been directly compared with the experimental XANES spectrum, i.e. no fitting procedure has been used. Recently, a good agreement between the experimental and computed data has been reported for LaMnO₃ and CaMnO₃ (Monesi et al., 2005; Monesi, 2006) by using a fitting procedure of the parameters which describes both the potential and the structure, and by including an ad hoc energy-dependent broadening. Moreover, a double excitation feature was included during the fitting at 69.4 eV and 75.4 eV for La and Ca compounds, respectively. However, XAS and X-ray magnetic circular dichroism measurements determine that the onset of this secondary channel lies at ∼45 eV above the edge (Subías et al., 2005, 2007). As a result, the parameters used for the computation of both LaMnO₃ and CaMnO₃ significantly differ (Monesi, 2006) and prevent studying of the relationship between the structural distortion and the Mn valence under this fitting approach.

Consequently, we adopt the same prescriptions to compute the Mn K-edge of CaMnO₃. The results, reported in Fig. 13, show that the effect of the cluster size on the calculations is the same as in the case of LaMnO₃. By using the standard 87 atoms cluster, the experimental intensity ratio of the two peaks B₁ and B₂ is not accounted for by the calculation. On the contrary, the computation yields both the correct shape and intensity ratio when a cluster containing 125 atoms is used. While in the case of LaMnO₃ such a cluster includes contributions from neighbouring atoms located within the first 7 Å around the absorbing Mn atom, it ranges only by ∼6.6 Å in the case of CaMnO₃. Therefore, we have extended the computation to a CaMnO₃ cluster including these contributions, i.e. r_max = 7 Å. However, as shown in Fig. 13(a), no significant difference is found between the computations performed on both 125 and 143 atom clusters. As in the case of LaMnO₃, the use of complex potentials leads to the best reproduction of the experimental spectrum, regarding both the energy position and the intensity of the experimentally observed spectral features in the first 70 eV above the absorption edge (Fig. 13b).

Figure 13 (a) Comparison of the experimental XANES spectrum at the Mn K-edge in CaMnO3 (filled circles) and the theoretical spectra calculated for different cluster sizes: (green, solid line) 87 atoms (rmax = 6 Å); (blue, dotted line) 125 atoms (rmax = 6.6 Å); (red, dashed line) 143 atoms (rmax = 7 Å). (b) Comparison of the computations performed on the 125 atoms cluster by using both complex HL (blue, solid line) and DH (red, dotted line) potentials. This figure is in colour in the electronic version of this paper.