Real-Space Observation of Ligand Hole State in Cubic Perovskite SrFeO3

Abstract

An anomalously high valence state sometimes shows up in transition-metal 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. However, no one has ever observed the distribution of ligand holes in real space. Here, a successful observation of the spatial distribution of valence electrons in cubic perovskite SrFeO₃ by high-energy X-ray diffraction experiments and precise electron density analysis using a core differential Fourier synthesis method is reported. A real-space picture of ligand holes formed by the orbital hybridization of Fe 3d and O 2p is revealed. The anomalous valence state in Fe is attributed to the considerable contribution of the ligand hole, which is related to the metallic nature and the absence of Jahn-Teller distortions in this system.

Keywords: electron orbital; ligand hole; orbital hybridization; perovskite oxide; x-ray diffraction.

Figure 1

a) Crystal structure and b) valence electron density distribution of SrFeO₃ at 30 K. Yellow and orange iso‐density surfaces show electron‐density levels of 3.0 and 10.3e/ų, respectively.

Figure 2

a) Iso‐density surface of valence electrons around the Fe site. b) Color map of the electron density at a distance r = 0.2Å from the Fe nucleus. The x ‐, y ‐, and z ‐axes are parallel to the global a ‐, b ‐, and c ‐axes, respectively. Energy diagrams and color maps of the calculated direction dependence of electron density for the c) 3d ⁴ and d) 3d ⁵ states assuming an isolated Fe atom. The color bar scale is represented by $\frac{[\rho (\theta ,\varphi )-N_e/4\pi ]}{N_e/4\pi }\times 100[\%]$. N_e is the number of 3d electrons.

Figure 3

Valence electron densities as a function of the distance r from the Fe nucleus. Brown and green dots show the electron densities in the [100] and [111] directions, respectively, obtained by the CDFS analysis. A red broken line shows the 3d electron density ρ_STO of an isolated Fe ion calculated by the Slater‐type orbital.^{[ 27} , ²⁸ , ^{29 ]} Detailed methods for calculating the valence electron density are described in Supporting Information. Here, the vertical axis for ρ_STO is arbitrarily scaled.

Figure 4

a) Color map of the electron density at a distance r = 0.4Å from the O nucleus at (0, 1/2, 1/2). Fe and Sr atoms are present in the [±100] and [0 ±1 ±1] directions, respectively. b) Valence electron densities as a function of the distance r from the O nucleus. Brown and green dots show the electron densities in the [100] and [011] directions obtained by the CDFS analysis, respectively. Pink line shows the difference in electron density between the [100] and [011] directions. Blue, orange, and red broken lines show the electron densities ρ_STO of oxygen 2s ², 2p ⁶, and 2s ²2p ⁶ calculated by the Slater‐type orbitals,^{[ 27} , ²⁸ , ^{29 ]} respectively. Detailed methods for calculating the valence electron density are described in Supporting Information. The vertical value for ρ_STO is arbitrarily scaled.