56 Physical Science Research Frontiers 2023 An anomalously high valence state of a transition- metal element sometimes shows up in oxide compounds. In such systems, holes tend to occupy mainly the ligand p orbitals, giving rise to interesting physical properties such as superconductivity in cuprates and rich magnetic phases in ferrates. SrFeO 3 is an archetypal tetravalent ferrate compound, in which, at least formally, four electrons occupy the Fe 3 d orbitals. It forms the perovskite- type structure with the cubic space group P m 3 – m (Fig. 1(a)) and exhibits metallic conductivity [1]. The local symmetry at the Fe site is m 3 – m . Each Fe atom is surrounded by an O 6 regular octahedron without Jahn- Teller distortion, where the 3 d orbitals are split into the lower-lying triplet ( t 2 g ) and the higher-lying doublet ( e g ). The high-spin state of 3 d 4 corresponds to the t 3 2 g e 1 g electron configuration, which causes some anisotropy in the valence electron density. However, previous X-ray photoelectron spectroscopy and X-ray absorption spectroscopy measurements suggest that the ground state consists of mixed 3 d 4 and 3 d 5 L ( L : ligand hole) states [2,3]. In the extreme limit of the 3 d 5 L state, the electron density around the Fe site should be spherical because of the t 3 2 g e 2 g electron configuration. Although the ligand holes in the crystal have been observed by spectroscopy measurements [2,3], no one has ever seen where the ligand holes exist in real space. To observe the spatial distribution of the holes, the measurement with high-wavevector ( Q ) resolution is indispensable. In this study, we observe the valence electron density distribution of SrFeO 3 by electron density analysis using state-of-the-art synchrotron X-ray diffraction (XRD). XRD experiments were performed at SPring-8 BL02B1 . A He-gas-blowing device was employed to cool the crystal to 30 K. The X-ray wavelength was l = 0.31020 Å. A two-dimensional detector CdTe PILATUS, which had a dynamic range of ~10 7 , was used to record the diffraction pattern. The intensities of Bragg reflections with the interplane distance d > 0.28 Å were collected. A core differential Fourier synthesis (CDFS) method [4] was used to extract the valence electron density distribution around each atomic site. [Kr], [Ar], and [He] type electron configurations were regarded as core electrons for Sr, Fe, and O atoms, respectively. Figure 1(b) shows the valence electron density distribution of SrFeO 3 at 30 K. No valence electron density larger than 3 e /Å 3 is observed around the Sr site, which is consistent with the Sr 2+ (5 s 0 ) state. In contrast, valence electrons are observed around the Fe and O sites, as shown by yellow iso-density surfaces. An orange iso-density surface for higher electron distribution is observed only around the Fe site, which is clearly distinct from a sphere: there are six hollow holes toward the six ligand oxygens. To quantify the anisotropy of the valence electron density ρ ( r ) around the Fe site, the density at a distance r = 0.2 Å from the Fe nucleus is shown by a color map on a sphere (Fig. 2(a)). The maximum and minimum electron densities are present along the <111> and <100> axes, respectively. Figures 2(b) and 2(c) show surface color maps of ρ ( θ , φ ) for the calculated electron density considering the high- spin 3 d 4 and 3 d 5 states for an isolated Fe ion, respectively. In the case of 3 d 4 , we assume that an Real-space observation of ligand holes in SrFeO 3 Fig. 1. (a) Crystal structure and (b) valence electron density distribution of SrFeO 3 at 30 K. Yellow and orange iso-density surfaces show electron-density levels of 3.0 and 10.3 e /Å 3 , respectively. (a) (b) Sr Fe O 3.84 Å 3.0 e /Å 3 10.3 e /Å 3 57 Research Frontiers 2023 electron occupies each e g orbital with a probability of 1/2. A clear anisotropy is observed in the 3 d 4 state, in contrast to the completely isotropic electron density in the 3 d 5 state. By comparing the CDFS results and simulations, the number of Fe 3 d electrons is estimated to be N e = 4.64(8), which is consistent with the previous reports of X-ray absorption spectroscopy measurement ( N e = 4.7) [3]. Since the corresponding valence of Fe obtained by the CDFS analysis was 3.36(8), the oxygen valence is estimated to be –1.79(3), which deviates from the ideal closed-shell value of –2. That is, the valence electron density distribution around the O site should not be isotropic. Figure 2(d) shows a color map of the electron density ρ ( θ , φ ) at a distance r = 0.40 Å from the O nucleus, obtained from the CDFS analysis. The observed ρ ( θ , φ ) has some anisotropy, which differs from the isotropic behavior of an ideal O 2– ion (Fig. 2(e)). While the highest electron density exists toward the surrounding four Sr atoms, the lowest electron density is observed in the [100] direction toward Fe. These results suggest the existence of ligand holes accommodated in the O 2 p σ ― Fe 3 d antibonding σ * orbital. The distribution of ligand holes around the O site was captured for the first time by the CDFS analysis [5]. Shunsuke Kitou* and Taka-hisa Arima Department of Advanced Materials Science, The University of Tokyo *Email: kitou@edu.k.u-tokyo.ac.jp Fig. 2. Color map of the electron density (a) at a distance r = 0.2 Å from the Fe nucleus and (b) at a distance r = 0.4 Å from the O nucleus. Color maps of the calculated direction dependence of electron density for the (c) Fe 4+ 3 d 4 , (d) Fe 3+ 3 d 5 and (e) O 2– 2 s 2 sp 6 states assuming isolated Fe and O atoms. The color bar scale is represented by ρ θ φ π [ ( , ) – N e /4 ] π N e /4 × 100(%). N e is the number of valence electrons. +20 % – 20 +10 % – 10 Sr Sr Sr Sr Fe Fe O O O z x y z x y O O O Assuming Fe 3+ (3 d 5 ) Assuming O 2 – (2 s 2 2 p 6 ) Around O Around Fe Assuming Fe 4+ (3 d 4 ) (d) (a) (e) (b) (c) % % % +10 – 10 +20 – 20 +20 –20 References [1] J. B. MacChesney et al. : J. Chem. Phys. 43 (1965) 1907. [2] M. Abbate et al. : Phys. Rev. B 65 (2002) 165120. [3] A. E. Bocquet et al. : Phys. Rev. B 45 (1992) 1561. [4] S. Kitou et al. : Phys. Rev. Res. 2 (2020) 033503. [5] S. Kitou, M. Gen, Y. Nakamura, K. Sugimoto, Y. Tokunaga, S. Ishiwata and T. Arima: Adv. Sci. 10 (2023) 2302839.
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