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.


DOI: 10.1002/advs.202302839
atomic orbitals mainly contribute to the bonding and antibonding orbitals, respectively, the bonding has a strong ionic nature and hence the formal ionic valence of metal can be well defined in general.Nonetheless, when the formal valence of metal is anomalously high, the contribution of the oxygen 2p orbital to the antibonding orbital becomes dominant, presumably resulting in the ligand hole state. [1]13][14][15] SrFeO 3 is an archetypal tetravalent ferrate compound, in which at formally, four electrons occupy the Fe 3d orbitals.It forms the perovskite-type structure with the cubic space group Pm 3m (Figure 1a) and exhibits metallic conductivity. [16]The local symmetry at the Fe site is m 3m.Each Fe atom is surrounded by six O atoms to form a regular octahedron without Jahn-Teller distortion, where the 3d orbitals are split into the lower-lying triplet (t 2g ) and the higherlying doublet (e g ).The high-spin state of 3d 4 corresponds to the t 3 2g 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 3d 4 and 3d 5 L ( L: ligand hole) states. [11,12]In the extreme limit of the 3d 5 L state, the electron density around the Fe site should be spherical because of the t 3 2g e 2 g electron configuration.Theoretically, the ligand hole formed by the 2p-3d hybridization is expected to stabilize novel itinerant magnetic phases. [17,18]In fact, despite its simple crystal structure, various magnetic phases including a quadrupleq topological spin structure appear in the magnetic-field-versustemperature phase diagram in SrFeO 3 . [14,15]Furthermore, the crystal structure and physical properties are greatly changed by slight oxygen vacancies, [19][20][21][22][23][24] because this system has charge instability of unusual tetravalent iron cations.
Although the ligand holes in the crystal have been observed by spectroscopy measurements, [11,12] 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).The number of 3d electrons is estimated from the anisotropic distribution of the valence electron density around the Fe site.It is also confirmed that the valence electron density around the O site along the Fe-O-Fe axis is slightly reduced.

Crystal Structure of SrFeO 3
The XRD experiments of SrFeO 3 detected no structural phase transitions down to 30 K, which is consistent with the previous neutron diffraction experiment. [23]As a result of the structural analysis, no signs of oxygen vacancy and no anomaly in the atomic displacement parameters of oxygen were confirmed.Here, the structural parameters were determined with high accuracy by performing a high-angle analysis utilizing the advantages of high-energy X-rays, [25] where only reflections with sin / > 0.6Å -1 (d < 0.833Å) were used.The obtained structural parameters of SrFeO 3 are summarized in Tables S1 and S2 (Supporting Information).

Valence Electron Density Around the Fe Site
Figure 1b shows the valence electron density distribution of SrFeO 3 at 30 K. No valence electron density larger than 3e/Å 3 is observed around the Sr site, which is consistent with the Sr 2 + (5s 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.
Figure 2a shows the iso-density surface around the Fe site with the site symmetry m 3m.The shape 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 (r) around the Fe site, the density at a distance r = 0.2Å from the Fe nucleus, which corresponds to the peak top of (r) (see Figure 3), is shown by a color map on a sphere (Figure 2b).The maximum and minimum electron densities are present along the <111> and <100> axes, respectively;  max = 10.76e/Å 3 and  min = 9.85e/Å 3 .Figure 2c,d show surface color maps of (, ϕ) for the calculated electron density considering the high-spin 3d 4 and 3d 5 states for an isolated Fe ion, respectively.To accurately evaluate the anisotropy of the obtained valence electron density distribution of SrFeO 3 , a comprehensive comparison using first-principles calculations, considering all electrons, is required.However, in this study, we assume the 3d 4 and 3d 5 states to discuss the anisotropy of the localized 3d electrons around the Fe site.In the case of 3d 4 , we assume that an electron occupies each e g orbital with a probability of 1/2.Note that (, ϕ) for an isolated ion is related just to the spherical harmonics.A clear anisotropy shows up in the 3d 4 state in contrast to the completely isotropic electron density in the 3d 5 state.Here, we extract an approximate relation between the number of Fe 3d electrons N e and  min / max ; N e = 1.773( by considering the experimental resolution (d > 0.28 Å) (see Section 2 and Figure S4, Supporting Information).Since the ratio  min / max obtained by the CDFS analysis is 0.915, the number of Fe 3d 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) [11] and cluster model calculation (N e = 4.8). [26]adial distributions of the electron density along the [100] and [111] axes around the Fe site are shown in Figure 3.The electron density in the [111] direction toward the nearest Sr atom has a single-peak structure derived from the 3d orbital r = 0.2 Å.The electron density of Fe 3d calculated by the Slater-type orbital (STO) of an isolated ion [27][28][29] is also plotted as a red broken line, which is in good agreement with the experimental results in the [111] direction.Here, the experimental resolution d > 0.28 Å is considered when performing the inverse Fourier transform (the details are described in Supporting Information).On the other hand, the electron density in the [100] direction toward the ligand O has one clear peak corresponding to the 3d orbital with two shoulder-like structures around r = 0.5 and 0.8 Å.The peak top of the electron density from the Fe nucleus is 0.05 Å closer in the [100] than in the [111] direction.These features may arise from the hybridization between the Fe 3d and O 2p orbitals.

Valence Electron Density Around the O Site
Finally, we focus on the valence electron density around the O site with the site symmetry 4/mm.m.Since the corresponding va-  We also confirmed that there is no significant anisotropy in the radial direction perpendicular to the [100] direction (Figure S6, Supporting Information).29] The experimentally obtained electron density in the [011] direction (green dots) well agrees with to the electron density of oxygen 2s 2 2p 6 (red broken line), whereas that in the [100] direction (brown dots) is lower.Furthermore, the difference between the electron densities in the two directions (pink line) mainly corresponds to the contribution of the electron density of oxygen 2p 6 (orange broken line).These results suggest the existence of ligand holes accommodated in the O 2p  -Fe 3d antibonding ( * ) orbital, which is consistent with previous p-d charge-transfer cluster-model calculations [12,26] and small holes in O 2p densities 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  STO is arbitrarily scaled.
of states predicted by first-principles calculations. [30,31]Furthermore, while a slight anisotropy in the charge distribution around the Fe site was predicted by the first-principles calculations, [30] the distribution of ligand holes around the O site was captured for the first time by the CDFS analysis.We observed deviations from ideal Fe 4+ and O 2− states caused by the orbital hybridization as valence electron density distributions.The considerable contribution of the 3d 5 L state seems to be related to the metallic nature [16] and absence of the Jahn-Teller distortion. [23][21][22][23][24] Thus, the observed p-d hybridization may support the unstable charge state of this system.Our experimental technique will be useful in investigating changes in oxidation state due to oxygen vacancies in this system and negative charge transfer states in other systems such as YBa 2 Cu 3 O 7− [6] and SrCoO 3 [9] using the electron density analysis in the future.

Conclusion
The orbital state in SrFeO 3 has been investigated by synchrotron XRD experiments using a high-quality single crystal.We have obtained the valence electron density distribution in SrFeO 3 by the CDFS analysis.The number of Fe 3d electrons estimated by the anisotropy is N e = 4.64 (8), which indicates the mixed 3d 4 and 3d 5 L states.The ligand hole is directly observed around the O site.Our experimental observation of the ligand hole may be a touchstone for future theoretical calculations and offers new possibilities for the study of chemical bonding in transition-metal compounds.

Experimental Section
Single Crystal Growth: Single crystals of SrFeO 3 were obtained by highpressure oxygen annealing of large single crystals of the oxygen-deficient perovskite SrFeO 2.5 with brownmillerite-type structure as described in Refs.[14, 32] A single crystal of SrFeO 2.5 was grown by a floating-zone method in an Ar gas flow.The obtained cylindrical crystal with a diameter of ≈4 mm was cut into a suitable size for a gold capsule and then treated with oxidizer NaClO 3 for 1 h at 873 K and 8 GPa.Tiny SrFeO 3 crystals were obtained by crashing a part of the cylindrical crystal.
X-Ray Diffraction Measurements: XRD experiments were performed on BL02B1 at a synchrotron facility SPring-8 in Japan. [33]The dimensions of the SrFeO 3 crystal for the XRD experiment were 50 × 30 × 30 μm 3 .A Hegas-blowing device was employed to cool the crystal to 30 K. The X-ray wavelength was  = 0.31020 Å.A 2D 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 by CrysAlisPro program [34] using a fine slice method, in which the data were obtained by dividing the reciprocal lattice space in increments of Δ = 0.1°.Intensities of equivalent reflections were averaged, and the structural parameters were refined by using Jana2006. [35]lectron Density Analysis: A core differential Fourier synthesis (CDFS) method was used to extract the valence electron density distribution around each atomic site. [25,36][Kr], [Ar], and [He] type electron configurations were regarded as core electrons for Sr, Fe, and O atoms, respectively.As a result, Sr 5s, Fe 3d, and O 2s/2p valence electrons should remain after the subtraction of the core electron density distribution.The detailed process for extracting the valence electron density distribution was described in Ref. [36].

Figure 1 .
Figure 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 10.3e/Å 3 , respectively.

Figure 2 .
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 [(,)−N e ∕4] N e ∕4 × 100 [%].N e is the

Figure 3 .
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  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  STO is arbitrarily scaled.
lence of Fe obtained by the CDFS analysis was 3.36(8) because of N e = 4.64(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.Figure4ashows a color map of (, ϕ), which is the electron density at a distance r = 0.40 Å from the O nucleus, obtained from the CDFS analysis.The observed electron density has some anisotropy.The highest electron density exists toward the surrounding four Sr atoms.On the other hand, the lowest electron density is observed in the [100] direction toward Fe. Brown and green dots in Figure4bshow 1D plots of the valence electron density against the distance from the O nucleus in the [100] and [011] directions, respectively.The difference between the two electron-density profiles is maximum around r = 0.4 Å, as shown in the pink line.

Figure 4 .
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  STO of oxygen 2s 2 , 2p6 , and 2s 2 2p 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  STO is arbitrarily scaled.