Oxygen 1s excitation and tetragonal distortion ... - APS Link Manager

RAPID COMMUNICATIONS

PHYSICAL REVIEW B 88, 201107(R) (2013)

Oxygen 1s excitation and tetragonal distortion from core-hole effect in BaTiO3 Matthieu Bugnet,1 Guillaume Radtke,2 and Gianluigi A. Botton1,* 1 2

Department of Materials Science and Engineering, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4L7, Canada IMPMC-CNRS UMR 7590, Université Pierre et Marie Curie-Paris 6, Campus Jussieu, 4 place Jussieu, F-75252 Paris Cedex 05, France (Received 2 August 2013; published 18 November 2013) The accurate description of the O 1s excitation in BaTiO3 has been elusive so far. In this Rapid Communication, the electronic structure and the high-resolution electron energy-loss near-edge structures of the O K edge in tetragonal BaTiO3 are investigated using first-principles calculations. The results demonstrate a clear correlation between the broadening of the lower energy fine structure and the anisotropic effects induced by the core-hole potential, which are directly related to the structural distortion occurring in tetragonal BaTiO3 . Moreover, we show that a significant improvement of the description of higher-lying structures can be obtained when correcting the energy position of the Ba 4f states. This demonstrates that the O 1s spectrum can be a very effective probe of the distortion and changes in the local electronic structure, and be used as a sensitive tool for studying new materials and ferroelectric transitions. DOI: 10.1103/PhysRevB.88.201107

PACS number(s): 71.20.Ps, 61.66.Fn, 77.84.Bw, 79.20.Uv

The perovskite oxides ABO3 are of fundamental interest and of technological importance as high-permittivity oxides,1–3 piezoelectrics,4 and ferroelectrics5 in a wide range of applications. Among these materials, BaTiO3 is particularly intriguing because of its intrinsic ferroelectric nature in rhombohedral, orthorhombic, and tetragonal structures, and its ferroelectric-paraelectric (cubic structure) phase transition at 393 K. BaTiO3 has been the subject of intense research for decades and is now used to design materials with new properties based on metal-ultrathin oxide structures,6,7 multilayer assemblies with magnetoelectric capabilities,8 and enhanced dielectric properties,9 in which the control of the interfacial polarization and bonding, and the epitaxial strain-induced distortions drastically influence the electronic structure, and hence the properties of these systems. Even though lattice distortions can be probed with imaging techniques,10,11 their detection remains a challenging issue for tetragonal BaTiO3 because the off-center positioning of the Ti cation is small, and the effects of this tetragonal distortion on local spectroscopic techniques that can probe the structure with atomic resolution are lacking. Electron energy-loss spectroscopy (EELS) is a powerful tool to investigate the electronic structure of materials with a high spatial resolution.12–14 The study of the electron energy-loss near-edge structures (ELNES) of the O K edge in BaTiO3 is of great fundamental and practical interest because of its large sensitivity to chemical bonding, which allows one, for example, to interpret the change in the electronic structure at defects15 or after doping on both Ba and Ti sites,16–19 and because of its easily accessible energy range in EELS coupled to the nanoscale analysis capabilities of a TEM. Due to the interest in designing new materials with novel properties, local probes of electronic structure that provide high spatial resolution are crucially important. In order to understand the origins of the spectral features in terms of the electronic structure and excitation effects, their modeling is required and a detailed interpretation must be carried out through electronic structure calculations. Despite several attempts, the calculation of the ELNES of the O K edge in BaTiO3 , however, has never been fully successful in reproducing the experimental spectrum.9,20–23 The main 1098-0121/2013/88(20)/201107(5)

reasons are the insufficient experimental energy resolution to resolve all the details of the spectrum, and the computational method used, both missing the accurate description of the fine features at the edge threshold but also major features at high energy clearly showing major gaps in the understanding of the electronic structure description of the excited states. Recently, calculations based on a multiple scattering approach22 and on a full projected augmented wave method23 enabled one to reproduce most fine structures, however with significant discrepancies for the shape and intensity ratios of the lower energy fine structures and of the high-lying spectral features, respectively, hence limiting the interpretation of the ELNES. In this Rapid Communication, the calculation of the ELNES of the O K edge in BaTiO3 is performed in the oneparticle approximation, and a substantial agreement with the experiment enables one to interpret small spectral features in terms of electronic structure and excitation effect, thus permitting the use of this method as a structural probe of complex phenomena in an important class of materials. In order to ensure that the effects of strain and defects on the O K ELNES are clearly disentangled from the intrinsic tetragonal distortion, single crystal BaTiO3 was used as a model material to demonstrate the validity of our approach. This work can then form the basis for further investigations on more realistic defective or strained BaTiO3 . A TEM thin foil was prepared from a commercial BaTiO3 single crystal (MTI Corporation) by mechanical polishing using the Multiprep technique (Allied High Tech Products Inc.), followed by ion milling in a Gentle Mill (Technoorg Linda Ltd.). The experimental spectra were recorded in [100] zone axis with a FEI Titan TEM operated at 80 kV in scanning TEM mode. The microscope is equipped with a monochromator and a high-resolution energy-loss spectrometer (Gatan GIF model 865). The energy resolution was ∼0.15 eV, as given by the full width at half maximum of the elastic peak in similar conditions of illumination, hence comparable to the energy resolution currently obtained in x-ray absorption spectroscopy (XAS) and of the order of the initial and final state finite lifetime broadening of the most commonly studied edges in EELS, such as K edges of light

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elements. The experimental observation of fine details at the edge onset has been successfully demonstrated and illustrates the high sensitivity of this technique to small electronic structure changes. Thirty spectra were acquired for 5 s each, with a dispersion of 0.05 eV/channel, while the electron beam remained at the same location on the specimen. Using a homemade script, a random energy shift of a few eV is applied to the energy drift tube of the GIF for each acquisition. The spectra were subsequently aligned and summed. This method has been successful in enhancing the signal-to-noise ratio while maintaining an energy resolution similar to x-ray aborption experiments.24 The calculations of the O K edge were performed with the WIEN2K code,25 using the experimental structural parameters reported in Table I. This code is an implementation of the full-potential linearized augmented plane-waves method based on density functional theory (DFT). The calculations presented in this Rapid Communication were performed using the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof26 for exchange and correlation, muffin-tin radii of 1.64 a.u. for O, 1.85 a.u. for Ti, and 2.5 a.u. for Ba. The plane-wave cutoff was set to RKmax = 7. The core hole was implemented in the calculation using a 2 × 2 × 2 supercell, and in order to ensure the crystal neutrality, an extra electron was added either in the valence band for computing the electron density and core-level shifts, or as a uniform background charge for the calculation of the ELNES. Convergence was achieved with 75 and 125 k points in the irreducible wedge of the Brillouin zone in supercells containing O1 and O2 excited atoms, respectively. In order to correct the Ba 4f state energies, an on-site Hubbard U term was added using the method of Anisimov et al.27 with Ueff = 0.7 Ry (J = 0 Ry), a value typical for f electrons. Finally, high-lying O p and Ba f local orbitals were added to the basis set to accurately calculate the ELNES. The core-level shift for O1 and O2 inequivalent atoms was calculated by supercell total energy difference between excited (1s core hole on the O atom + additional electron in the conduction band) and ground-state electronic configurations. A 0.15 eV shift between O1 and O2 contributions was obtained using this procedure. The instrumental resolution was taken into account by a Gaussian broadening of 0.15 eV, and the finite lifetimes of the core hole and the ejected electron were described by a Lorentzian distribution with energy-dependent full width at half maximum 0.15 + 0.05∗ (E − Ef ), Ef being the Fermi level, giving the best agreement with the experiment. The contributions of O1 and O2 atoms are averaged with a 1:2 ratio, consistent with the number of oxygen atoms in the two inequivalent sites, for comparison with the experimental data. The experimental O K ELNES of BaTiO3 is shown in Fig. 1(a). The spectrum exhibits several features (A–E) that TABLE I. Unit cell and atomic parameters of tetragonal BaTiO3 (Ref. 28). ˚ Lattice parameters (A) a = 3.9945 b = 3.9945 c = 4.0335

Atomic coordinates Ba(0.0,0.0,0.0) Ti (0.5,0.5,0.514) O1 (0.5,0.5,0.975) O2 (0.0,0.5,0.488)

FIG. 1. (Color online) (a) Experimental O K ELNES (top) and calculations for Ueff = 0.7 Ry (middle) and Ueff = 0 Ry (bottom). The theoretical spectra are aligned with respect to the experimental peak (A) and include the contribution of O1 and O2 . (b) Ground-state empty DOS projected on Ba f (dashed green) and O p (solid black) states for Ueff = 0.7 Ry (top) and Ueff = 0 Ry (bottom).

are all reproduced by the calculation with Ueff = 0.7 Ry. The intense peak (A) at the edge onset is followed by a lower intensity structure (B), and these structures correspond to the hybridization of O p states with Ti d states, split in t2g (A) and eg (B) symmetry under the influence of the dominant octahedral crystal field.29 Feature C is well extended in energy and is related to the hybridization with the Ba 5d states. Its overall shape is rather well reproduced although more details are visible in the calculations. The features lying at higher energy—D1 , D2 , and E—are well reproduced theoretically. The calculation with Ueff = 0 Ry reproduces all the spectral features but D1 and D2 . The influence of Ueff on the ELNES is weak in the 533–542 eV energy range, and a structure can be observed at ∼543 eV, which is not present in the experiment. It is clear from the ground-state local density of states (LDOS) shown in Fig. 1(b) that this latter structure originates from the position of the well localized Ba f states, witness of an existing overlap of Ba f and O p states. The Coulomb term shifts the Ba f bands to higher energies and modifies the empty O p bands accordingly so as to create an increase in intensity corresponding to D1 and D2 . This result demonstrates that D1 and D2 can be identified as the result of the hybridization of O p and Ba f states. Most reported studies do not reproduce D1 and D2 , structures that are not observed in other widely investigated perovskites such as SrTiO3 and CaTiO3 . Thus accounting for the energy shift of the Ba f states solves one of the major problems for the calculation of the O K-edge fine structures, and provides further understanding of the fine structures. In this theoretical framework, the Hubbard term acts therefore as a way to set these spectral features at appropriate energies. A similar effect was reported by Czy˙zyk and Sawatzky30 in the calculation of the O K x-ray absorption near-edge structures in La2 CuO4 . Some discrepancies, however, must be pointed out: The structure D1 is more intense than D2 in the calculation, in disagreement with the experiment, and the structures B, C, and E are at slightly lower energy than experimental features. In particular, the even intensity ratio of D1 and D2 is better reproduced without considering the core hole, as discussed later in this Rapid Communication, hence suggesting that the core hole within the DFT is not well treated, and calculations

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beyond the one-particle approximation need to be considered to further minimize these differences. The treatment of the variations in the self-energy would account for the energy positions of peaks B, C, and E.31 In addition, these differences might reflect the use of the static tetragonal model used in our calculations, considering the uncertainty of its experimental validity.32 The ejection of a core electron by an incident electron beam in the energy-loss process leaves behind a core hole causing a significant redistribution of the electron density and a modification of the local electronic states. The influence of the core-hole potential on the ELNES is investigated in theoretical spectra and displayed in Fig. 2, considering the contributions of O1 and O2 atoms separately. The spectra without inclusion of the core hole are very similar for both oxygen positions. To some extent the inclusion of the core hole has similar effects on the ELNES of O1 and O2 , first with a reduction of the intensity of peak A. In particular, if the core-hole potential does not affect the energy of structures D1 and D2 , it influences their relative intensity. Indeed D1 and D2 have even intensity for a ground-state calculation, and hence are in good agreement with the experimental spectrum, whereas the intensity is essentially provided by D1 when accounting for the core hole. This observation can be interpreted as the effect of the attractive core-hole potential which pulls the unoccupied density of states towards the Fermi level. Again, we attribute these observations to the limits of the DFT for the inclusion of the core-hole potential. A third important modification arises from the formation of a sharp feature corresponding to peak B in the experimental spectrum. This effect appears as a systematic modification of the broad eg bands in perovskite materials due to the presence of the core hole.29 However the core-hole potential also acts on O1 and O2 in very different ways. For O2 , the shape of peak A is slightly modified, with a more pronounced shoulder at the edge onset. For O1 , a splitting

FIG. 2. Influence of the core-hole potential on the O K ELNES decomposed on both O1 (solid) and O2 (dashed) inequivalent atomic positions. The calculations are performed with Ueff = 0.7 Ry, and the experimental edge is plotted (dots) for comparison.

of peak A into two narrow subpeaks, separated by ∼0.85 eV, is observed. We interpret this result from real-space mapping of the valence-electron screening cloud around the excited O1 atom, obtained by subtraction of the valence-electron density calculated with and without the core-hole potential, as shown in Fig. 3(a). There is a strong increase of the electron density at the excited oxygen site, which is attributed to the more attractive potential. A depletion of the electron density between the excited O1 atom and the nearest Ti atoms is also observed. The modification of the valence-electron density is not isotropic but oriented along the Ti-O direction because of the covalent character of the bonding between these atoms. This last effect leads to an increase of the density of O 2p states lying along this direction and to the formation of peak B in the theoretical spectrum, which is consistent with previous work on SrTiO3 .33 In tetragonal BaTiO3 , the O1 atom is closer to ˚ than to the other Ti atom (Ti2 , one of the Ti atoms (Ti1 , 1.86 A) ˚ as shown in Fig. 3(b). As a consequence, the screening 2.17 A) cloud along the Ti-O-Ti direction is strongly asymmetric, the electron density depletion being more pronounced on the side

FIG. 3. (Color online) (a) Valence-electron screening cloud around the excited O1 atom (blue = depletion, red = enrichment). Isosurfaces of −0.01 and 0.01 electron.bohr3 have been used. (b) Ilustration of the tetragonal distortion of BaTiO3 along the [001] direction, in terms of distance from O1 to the nearest Ti1 atom, and to the second nearest Ti2 atom. (c) Origin of the ELNES for the excited O1 atom from the LDOS calculated with core-hole included for the two nearest Ti atoms and O1 . (d) Comparison of the O K edge onsets in BaTiO3 and SrTiO3 . The EEL spectra are acquired in the same experimental conditions, and the alignment in energy is performed manually to highlight the difference in the broadening of peak (A).

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of Ti1 . This depletion leads to the formation of peak B but also to the splitting of peak A into two narrow subbands A1 and A2 . As already mentioned, peak A is related to the π hybridization of O 2p with Ti 3d t2g states. More precisely, and as evidenced in Figs. 3(b) and 3(c), A1 is clearly dominated by the contribution of 3d states localized on the site of Ti1 , whereas the origin of A2 is less sharp, with a main contribution from Ti2 , but a non-negligible input from Ti1 . This splitting is not observed in the theoretical spectrum calculated for the O2 atom, located at an equal distance from its two Ti neighbors and for which, the screening cloud (not shown) does not exhibit this asymmetry. Experimentally peak A does not show a splitting, but a significant broadening. The strength of this broadening is highlighted in Fig. 3(d), where it is clear that peak A is broader in the slightly distorted tetragonal BaTiO3 than in the cubic SrTiO3 . The core-level shift was taken into account in the calculations, and peak A for the O2 atoms thus lies in between the split peaks of the O1 atoms (Fig. 2). Hence the sum of the contributions of O1 and O2 to the ELNES, with a 1:2 ratio, fully accounts for the broadening of peak A. This broadening appears only when the core-hole potential is taken into account. More specifically, this effect is visible only via the asymmetric perturbation of the valence electron density attributed to the core-hole potential. Thus, we demonstrate here a clear correlation between the width of the spectral feature O 2p-Ti 3d t2g in the O K edge of BaTiO3 and the symmetry of the site occupied by the excited atom. This result suggests that the O 1s excitation spectrum might be used to probe the distortion of the TiO6 octahedron at a nanometer scale. Thus, interpreting the lower energy fine structure of the O K edge appears complementary to the understanding of the Ti L2,3 near-edge structures, whose calculations with the multiplet method22 and the Bethe-Salpether equation [e.g., SrTiO3 (Refs. 34 and 35)] are still not in full agreement with the experimental spectrum. In modern applications, BaTiO3 may suffer chemical state changes from doping,17,19 contain defects,15 or experience strain as thin films36,37 or superlattices.9 It can be postulated that these effects will affect the lower energy fine structure of the O K edge and therefore be detected provided that sufficient additional distortion of the TiO6 octahedra occurs compared with the perfect crystal model. In addition, it must be noted that the off-center positioning of the Ti atom in the

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[email protected] R. A. McKee, F. J. Walker, and M. F. Chisholm, Phys. Rev. Lett. 81, 3014 (1998). 2 R. A. McKee, F. J. Walker, and M. F. Chisholm, Science 293, 468 (2001). 3 M. Stengel and N. A. Spaldin, Nature (London) 443, 679 (2006). 4 H. Fu and R. E. Cohen, Nature (London) 403, 281 (2000). 5 R. E. Cohen, Nature (London) 358, 136 (1992). 6 G. Gerra, A. K. Tagantsev, N. Setter, and K. Parlinski, Phys. Rev. Lett. 96, 107603 (2006). 7 M. Stengel, D. Vanderbilt, and N. A. Spaldin, Nat. Mater. 8, 392 (2009). 1

tetragonal lattice of BaTiO3 and the distortion of the TiO6 octahedron are actually small compared to other ferroelectric [e.g., Pb(Zr,Ti)O3 ] and multiferroic (e.g., BiFeO3 ) materials. Therefore, the experimental and theoretical methods described here should be generally applicable to BaTiO3 in more realistic conditions, and also to other perovskites. In conclusion, GGA + U calculations of the ELNES of the O K edge in tetragonal BaTiO3 were performed and show significantly improved agreement with the experiment. We demonstrate that a precise positioning of the empty Ba f bands enables the accurate modeling of all spectral features. We show that consideration of the core hole accounts for the fine structures near the edge onset, as well as uncovers the effect of the tetragonal distortion of BaTiO3 . In particular, a correlation between the effects induced by the core-hole potential and the geometry of the atomic site, i.e., the relative position of the two nearest Ti atoms with respect to the O excited atom, is demonstrated and accounts for the relatively broad peak A. This finding demonstrates that the distortion of the TiO6 octahedra in the BaTiO3 polymorphs can be probed with high-resolution empty state spectroscopy such as EELS and XAS. This study therefore provides a framework for understanding spectroscopically, and at the local level with high-resolution implementation of EELS, the static and dynamic nature of nanometer-sized BaTiO3 structures,32 and the displacive and order-disorder components in the ferroelectric-paraelectric phase transition of this compound.38–40 From a broader point of view, this work highlights that empty state spectroscopy, combined with a full understanding of the electronic structure, are powerful tools that provide significant insight and knowledge into the origin of the ferroelectricity of perovskite oxide materials. M.B. and G.A.B. are grateful to A. Scullion for implementing the broadening of core-loss spectra. We thank S.-W. Cheong for useful comments on the manuscript. We are grateful to NSERC for a Discovery Grant supporting this work. The EELS work was carried out at the Canadian Centre for Electron Microscopy, a National Facility supported by NSERC and McMaster University. We acknowledge the Research and High-Performance Computing Support of McMaster University for the support of the computing cluster.

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