# Stability of the Pb divalent state in insulating and metallic PbCr O 3

Jianfa Zhao, Shu-Chih Haw, Xiao Wang, Lipeng Cao, Hong-Ji Lin, Chien-Te Chen, Christoph J. Sahle, Arata Tanaka, Jin-Ming Chen, Changqing Jin, et al.

► To cite this version:

Jianfa Zhao, Shu-Chih Haw, Xiao Wang, Lipeng Cao, Hong-Ji Lin, et al. Stability of the Pb divalent state in insulating and metallic PbCr O 3. Physical Review B, 2023, 107 (2), pp.024107. 10.1103/PhysRevB.107.024107. [https://arxiv.org/abs/2302.09191] [https://doi.org/10.1103/PhysRevB.107.024107].

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# Stability of the Pb divalent state in insulating and metallic PbCrO$_3$

Jianfa Zhao<sup>1,*,†</sup> Shu-Chih Haw,<sup>2,†</sup> Xiao Wang<sup>3</sup> Lipeng Cao,<sup>4</sup> Hong-Ji Lin,<sup>2</sup> Chien-Te Chen<sup>1,2</sup> Christoph J. Sahle,<sup>5</sup> Arata Tanaka<sup>1,6</sup> Jin-Ming Chen,<sup>2</sup> Changqing Jin,<sup>1,7</sup> Zhiwei Hu,<sup>3,‡</sup> and Liu Hao Tjeng<sup>3,§</sup>

<sup>1</sup>Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

<sup>2</sup>National Synchrotron Radiation Research Center, 101 Hsin-Ann Road, Hsinchu 30076, Taiwan

<sup>3</sup>Max-Planck Institute for Chemical Physics of Solids, Nothnitzer Straße 40, 01187 Dresden, Germany

<sup>4</sup>State Key Laboratory of Materials Science & Technology and Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao, Hebei 066004, China

<sup>5</sup>European Synchrotron Radiation Facility (ESRF), 71 Avenue des Martyrs, Grenoble 38000, France

<sup>6</sup>Department of Quantum Matter, ADSM, Hiroshima University, Higashi-Hiroshima 739-8530, Japan

<sup>7</sup>School of Physics Sciences, University of Chinese Academy of Sciences, Beijing 100190, China

<figure><img src="image_2.png" /></figure>

(Received 9 November 2022; accepted 13 January 2023; published 26 January 2023)

We have investigated the local electronic structure of PbCrO$_3$ by conducting x-ray absorption spectroscopy at the lead L$_3$ and chromium L$_{2,3}$ edges. We found that lead is divalent and chromium is charge-disproportionated into trivalent and hexavalent states at ambient pressures, explaining their insulating behavior. The high-resolution partial fluorescence yield of lead L$_3$ spectra as a function of pressure revealed that the divalent state of lead ions remains unchanged at high pressures, when PbCrO$_3$ changes into metal and its volume collapses by more than 10%. We infer that the insulator-to-metal transition does not involve a Pb-Cr charge transfer, but is associated with the conversion of Cr$^{3+}$/Cr$^{6+}$ charge-disproportionated states into a Cr$^{4+}$ valence state.

DOI: 10.1103/PhysRevB.107.024107

## I. INTRODUCTION

PbCrO$_3$ is an antiferromagnetic insulator with a Néel temperature of about $T_N = 240$ K and is believed to exhibit a cubic perovskite crystal structure [1–3]. It has also been recently discovered to undergo a large volume collapse of more than 9.8% [4], and concurrently, an insulator-to-metal transition [5,6], at a pressure of ~1.6 GPa. The following aspects make PbCrO$_3$ intriguing: (i) Why is PbCrO$_3$ an insulator at ambient pressures? (ii) What is the mechanism behind the insulator-to-metal transition under pressure?

Numerous band structure studies have been conducted to determine the electronic structure of the cubic perovskite PbCrO$_3$ and all found a metallic solution [7–10], which disagrees with the experimentally observed insulating state at ambient pressures. Even the inclusion of the Hubbard U in the calculations to account for electron correlation effects did not resolve the problem [8–10]. In fact, this fits to the experimental observation that all Cr$^{4+}$ oxides with octahedral

coordination exhibit the tendency to be metallic [11–15]. This phenomenon can be related to the heavily negative oxygen 2p to chromium 3d charge transfer energy [16–18] that pins the chemical potential inside the oxygen band [11].

A microstructure study [19] provided the first indications that the crystal structure might be more complicated than the widely accepted pure cubic perovskite PbCrO$_3$. Assuming, for example, that CrPbO$_3$ is present in the material, one could arrive at an insulating solution in band structure calculations [9]. Valuable insight was gained from x-ray absorption spectroscopy (XAS) at the chromium L$_{2,3}$ edges, revealing the presence of charge disproportionation of chromium ions into Cr$^{3+}$ and Cr$^{6+}$ configurations at ambient pressures [20]. A careful analysis of neutrons and x-ray diffraction (XRD) data showed anomalously large thermal factors of the lead, chromium, and oxygen ions [6], motivating the proposal of the chromium charge-disproportionated state that will allow density functional theory to produce an insulating state for moderate values of the Hubbard U. The metallic high-pressure phase is the result of lifting the charge disproportionation situation into a phase in which all chromium elements become tetravalent [6]. Another study proposed that lead ions are charge-disproportionated into Pb$^{2+}$ and Pb$^{4+}$, and that all chromium ions are Cr$^{3+}$ at ambient pressures [21]. Accordingly, the high-pressure phase is a transformation that involves a Pb-Cr charge transfer into homogenous Pb$^{2+}$ and Cr$^{4+}$ valence configurations. Recently, unusual lattice elasticity properties have also been observed [22] across the volume collapse and insulator-to-metal transition.

We followed a complementary route of research to understand the peculiar properties of PbCrO$_3$ and to resolve

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

<footnote>*zhaojf@iphy.ac.cn</footnote>

<footnote>†ho.kelman@nsrrc.org.tw</footnote>

<footnote>‡zhiwei.hu@cpfs.mpg.de</footnote>

<footnote>§hao.tjeng@cpfs.mpg.de</footnote>
the debate about the origin of insulator-to-metal transition. We aimed to determine lead valence spectroscopically under ambient and high-pressure conditions. To achieve this objective, we used known information about the PbMO₃ (*M* = 3d transition metal) series [23–25]. PbMO₃ undergoes a sequence of transitions in electronic configuration across the 3d transition metal row from left to right in the periodic table. The valence state gradually evolves from +2/+4 to +4/+2 for Pb/*M* ions—namely, from Pb²⁺M⁴⁺O₃ (*M* = Ti, V) [26,27] to Pb²⁺₀.₅Pb⁴⁺₀.₅Fe³⁺O₃ [28], and further to Pb⁴⁺Ni²⁺O₃ [29]. Manganese and cobalt ions in the middle of the series exhibit a complicated mixed valence state—namely, Pb²⁺₀.₈七Pb⁴⁺₀.₁₂₅Mn³⁺₀.₂₅Mn⁴⁺₀.₇₅O₃ [30] and Pb²⁺₀.₂₅Pb⁴⁺₀.₇₅Co²⁺₀.₅Co³⁺₀.₅O₃ [31,32], respectively. From this series, one may infer that Pb²⁺ valence is likely for PbCrO₃, but also that Pb⁴⁺ state cannot be excluded. In the current study, we used bulk-sensitive lead L₃ XAS by measuring the signal in the transmission mode by using the high-resolution partial fluorescence yield (PFY) mode [28,30,32–35]. We compared the spectra of our PbCrO₃ with those of PbTiO₃ and PbNiO₃. This experiment was accompanied with a detailed XRD and chromium L₂,₃ XAS investigation of our PbCrO₃ sample.

## II. EXPERIMENTAL

Polycrystalline samples of PbCrO₃ were synthesized via a solid-state reaction under high pressure and high temperature of 1273 K. The starting materials PbO (Aldrich, 99.0% pure) and CrO₂ (Alfa, 99.995% pure) were mixed homogeneously in accordance with a molar ratio of 1:1 and sealed in a gold capsule with a diameter of 2 mm. High-pressure experiments were performed in a Walker-type multianvil module (Rockland Research Co.). After pressure was gradually increased to 15 GPa, the system was heated to 1273 K within 10 min, and this temperature was maintained for 30 min. Then, the temperature was quenched to room temperature before releasing the pressure. After the high-pressure and high-temperature process, polycrystalline PbCrO₃ was obtained.

Sample quality and crystal structure were characterized via powder XRD using a Huber diffractometer with wavelength $\lambda$ = 1.5406 Å (copper Kα₁ radiation, 40 kV, 30 mA). Diffraction data were collected in the angle (2θ) range from 10° to 100°, with steps of 0.005°. XRD data were analyzed by using the Rietveld refinement program GSAS [36]. The high-resolution PFY lead L₃ XAS spectra with an overall experimental resolution of ~2.5 eV were collected at the ID 20 beamline of the European Synchrotron Radiation Facility in France [37]. The PbTiO₃ and PbNiO₃ samples were also measured to serve as Pb²⁺ (6s²) and Pb⁴⁺ (6s⁰) reference materials, respectively. The chromium L₂,₃ XAS spectra of PbCrO₃ together with Cr₂O₃ as a Cr³⁺ reference and Ag₂Cr₂O₇ as a Cr⁶⁺ reference were measured at BL11A of the National Synchrotron Radiation Research Center in Taiwan.

## III. RESULTS AND DISCUSSION

The experimental XRD pattern of PbCrO₃ collected at room temperature is shown in Fig. 1. In the beginning, the XRD pattern was simulated with a cubic *Pm-3m* perovskite

<figure><img src="image_3.png" /></figure>

FIG. 1. Rietveld structural refinement of the XRD pattern for PbCrO₃ collected at 300 K using the Cr³⁺/Cr⁶⁺ charge disproportionation model. Observed (crosses), calculated (red), and difference (blue) are shown in the figure. The $R_{wp}$, $R_p$, and $\chi^2$ are 3.89%, 3.35%, and 4.276. The ticks indicate the allowed Bragg reflections of PbCrO₃ with the charge disproportionation model.

structure model that provided reliability factors $R_{wp}$ = 3.66%, $R_p$ = 3.16%, and $\chi^2$ = 4.103. However, the isotropic thermal factor $B_{iso}$ of the lead, chromium, and oxygen sites exhibited abnormally high values: $B_{iso}$ (Pb) = 8.95(2) Å², $B_{iso}$ (Cr) = 6.77(5) Å², and $B_{iso}$ (O) = 6.7(1) Å². These findings are similar to those of Cheng *et al.* [6]. We also conducted simulations with the thermal factors fixed to reasonable values. We determined that the reliability factors rapidly increased to $R_{wp}$ = 9.87%, $R_p$ = 7.62%, and $\chi^2$ = 12.28. These findings indicate that the cubic perovskite structure model is inaccurate.

Following the interpretation of Cheng *et al.* [6], we also considered the charge disproportionation scenario as follows: the lead, chromium, and oxygen atoms are allowed to be off from the (0, 0, 0), (0.5, 0.5, 0.5), and (0, 0.5, 0.5) positions and, instead, they occupy the general Wyckoff sites 8 g (0.0619, 0.0619, 0.0619), 8 g (0.5442, 0.5442, 0.5442), and 24 m (0.0489, 0.5348, 0.5348), respectively. With this new structural model, the thermal factor dropped significantly to 1.70(3) Å², 2.95(6) Å², and 3.7(1) Å² for lead, chromium, and oxygen, respectively, providing reliability factors $R_{wp}$ = 3.89%, $R_p$ = 3.35%, and $\chi^2$ = 4.276, and the lattice constant ($a$ = 4.0043 Å) in accordance with previous reports [1,3,4,6,19–21]. Figure 1 displays this refinement model with charge disproportionation and shows that all XRD peaks are reproduced well, indicating that our PbCrO₃ sample prepared under 15 GPa exhibits no evident impurity phases [1,6,19].

Figure 2 presents the PFY lead L₃ XAS spectrum of PbCrO₃, along with those of PbTiO₃ (as Pb²⁺ reference) and PbNiO₃ (as Pb⁴⁺ reference). The sharp pre-edge peak at 13.043 eV in the lead L₃ XAS spectrum for the Pb⁴⁺ reference PbNiO₃ can be assigned to the dipole-allowed transition from the 2p₃/₂ core level to the fully unoccupied 6s shell. By contrast, in the case of PbTiO₃, the pre-edge peak is absent due to the fully occupied 6s shell. Figure 2 shows that PbCrO₃ has a lead L₃ XAS profile similar to that of PbTiO₃. Only a more broader shoulder A at the leading edge (13.047 eV)
<figure><img src="image_4.png" /><figcaption>FIG. 2. High-resolution XAS spectra at the lead $L_3$ edge of PbCrO$_3$ and PbTiO$_3$ (as Pb$^{2+}$ reference) and PbNiO$_3$ (as Pb$^{4+}$ reference).</figcaption></figure>

was observed in both Pb$^{2+}$ oxides PbCrO$_3$ and PbTiO$_3$. This shoulder A at the leading edge is related to the lowest lead 6d state above Fermi energy, which is mixed with lead 6p and oxygen 2p [38]. The lack of a pre-edge peak in PbCrO$_3$ thus establishes that the lead ion is in the divalent state. This result contradicts the assessment of Yu *et al.* [21] who proposed that lead ions are charge-disproportionated into Pb$^{2+}$ and Pb$^{4+}$ at ambient pressures.

Having determined the divalent state of the lead ion, we must now confirm that chromium is, on average, tetravalent to fulfill the charge balance requirement. The energy position and line shape of the 3d transition-metal $L_{2,3}$ XAS spectra are well known to be highly sensitive to the valence and local environment of the ion [39–42]. In case of a mixed valence material, its spectrum can be obtained by the superposition of some related components [43]. In Fig. 3(a), we present the chromium $L_{2,3}$ XAS spectrum of PbCrO$_3$. This spectrum is extremely different from that of a Cr$^{4+}$ ion that is coordinated octahedrally by oxygen atoms [41,42]. To interpret the spectrum, we also plot in Fig. 3(a) the experimental spectrum of Cr$_2$O$_3$ (red curve) as a Cr$^{3+}$ reference material with CrO$_6$ octahedral coordination, and that of Ag$_2$Cr$_2$O$_7$ (green curve) as a Cr$^{6+}$ reference material with CrO$_4$ tetrahedral coordination [44]. We then construct a superposition of the Cr$_2$O$_3$ and Ag$_2$Cr$_2$O$_7$ spectra with 2/3 and 1/3 weights, respectively. We can observe that this superposition (blue curve) reproduces the experimental spectrum of PbCrO$_3$. Although the PbCrO$_3$ spectrum of Wu *et al.* [20] contains somewhat too much Cr$^{6+}$ signal, we can state that we essentially reproduce their chromium $L_{2,3}$ XAS analysis. Therefore, we can conclude that a Cr$^{3+}$/Cr$^{6+}$ charge disproportionation of chromium occurs in PbCrO$_3$ at ambient pressures as proposed by Wu *et al.* [20] and Cheng *et al.* [6]. Notably, the 2/3 Cr$^{3+}$ and 1/3 Cr$^{6+}$ weights used for the superposition imply that the average valence of chromium is +4, completely fulfilling the charge balance, with lead being divalent.

To obtain a deeper understanding of the local electronic structure of the chromium ion in PbCrO$_3$, we performed cluster calculations that included full atomic multiplet interactions, local ionic crystal field spitting, and oxygen

<figure><img src="image_5.png" /><figcaption>FIG. 3. (a) Chromium $L_{2,3}$ XAS experimental spectra of PbCrO$_3$ (black circles) and sum (blue line) of Cr$^{3+}$ reference Cr$_2$O$_3$ and Cr$^{6+}$ reference Ag$_2$Cr$_2$O$_7$ in a 2:1 ratio. (b) Calculated chromium $L_{2,3}$ XAS of Cr$^{3+}$ in octahedral coordination (red line), Cr$^{6+}$ in tetrahedral coordination (green line), and the sum of them in a 2:1 ratio (blue line).</figcaption></figure>

$2p$-chromium 3d hybridization. The calculations were performed using XTLS 9.0 code [45]. We used an octahedral CrO$_6$ cluster for Cr$^{3+}$ and a tetrahedral CrO$_4$ cluster for Cr$^{6+}$. (The parameter values, in electron volts, are as follows: octahedral Cr$^{3+}$ O$_6$ cluster: Udd = 5.5, Ucd = 7.0, $\Delta$ = 5.0, 10Dq = 1.15, Slater integrals set at 75% of the Hartree-Fock values; tetrahedral Cr$^{6+}$ O$_4$ cluster: Udd = 5.5, Ucd = 7.0, $\Delta$ = -4.0, 10Dq = 0.35, Slater integrals set at 70% of the Hartree-Fock values.) As displayed in Fig. 3(b), we are able to reproduce excellently the spectra of Cr$_2$O$_3$, Ag$_2$Cr$_2$O$_7$, and PbCrO$_3$, confirming our experimental conjectures. Here, we like to stress that we have used a tetrahedral coordination for Cr$^{6+}$ calculations. Our modeling is related to the empirical observation that extremely high-valent chromium oxides (pentavalent and hexavalent) have chromium ions that are not octahedrally, but tetrahedrally, coordinated. A combined experimental and theoretical study on YCrO$_4$ found that tetrahedral coordination can still stabilize an insulating state for high-valent chromium oxides while an octahedral coordination cannot [46]. This finding, along with the notion that a
<figure><img src="image_6.png" /><figcaption>FIG. 4. (a) High-resolution XAS spectra at the lead $L_3$ edge of PbCrO$_3$ as a function of pressure from 0 GPa to 14.1 GPa. The inset shows the simulation of the lead $L_3$ XAS spectrum at 0 GPa. (b) Pressure-dependent FWHM of shoulder A.</figcaption></figure>

Cr$^{3+}$ oxide is readily a Mott insulator, such as Cr$_2$O$_3$, provide the necessary ingredients for PbCrO$_3$ to become an insulator. Through these Cr$^{3+}$/Cr$^{6+}$ charge disproportionation band structure calculations, one can find an insulating solution for modest and realistic values of the Hubbard U [6]. Moreover, the quasi-tetrahedral coordination of the Cr$^{6+}$ ion proposed in a previous study [6] explains why the crystal structure cannot be described as a pure, undistorted cubic perovskite.

We then investigate what happens with lead valence when pressure is applied. Figure 4(a) shows the high-resolution PFY XAS spectra at the lead $L_3$ edge of PbCrO$_3$ over a wide

range of pressures—namely, from 0 GPa to 14.1 GPa—i.e., from the insulating phase under ambient conditions to deep inside the volume-collapsed metallic state. We do not observe a pre-edge peak in all the instances. This result shows that the valence state of the lead ions in PbCrO$_3$ always remains divalent. That is, our pressure-dependent PFY lead $L_3$ XAS results show that no relevant Pb-to-Cr charge transfer occurs in PbCrO$_3$, contradicting the assertions of Yu *et al.* [21]. Moreover, we observe in Fig. 4(a) a systematic variation of the lower energy shoulder A with pressure. To be quantitative, we analyze the spectra by simulating its components. As an example, we show in the inset, the analysis for the 0-GPa spectrum. The curve with the black dots is the experiment, the blue line represents the shoulder A, while the magenta and green lines stand for the main unoccupied lead 6d state [38] and the continuum edge, respectively. We have done the simulation for all pressures. The full width at half maximum (FWHM) of shoulder A as a function of pressure is presented in Fig. 4(b). We can observe that the FWHM of shoulder A increases from 5.8 at 0 GPa to 7.4 at 14.1 GPa. This indeed indicates an increase in the bandwidth of the lowest lead 6d with pressure, reflecting the pressure-induced insulator-metal transition.

## IV. CONCLUSIONS

We found evidence from our high-resolution PFY XAS at the lead $L_3$ edges and soft XAS at the chromium $L_{2,3}$ edges for the divalent state of lead ions and the occurrence of Cr$^{3+}$/Cr$^{6+}$ charge disproportionation in PbCrO$_3$ at ambient pressures. This charge disproportionation, along with the tetrahedral coordination of high-valent chromium, provide the necessary ingredients to form the insulating state and explain the presence of large lattice distortions away from the ideal cubic perovskite. The stability of the Pb$^{2+}$ state as a function of pressure indicates that volume collapse and insulator-metal transition are not connected to Pb-to-Cr charge transfer, but rather to the suppression of the chromium charge disproportionation and the appearance of octahedrally coordinated tetravalent chromium.

## ACKNOWLEDGMENTS

The work was supported by the Natural Science Foundation of China (Grant No. 12204515). We acknowledge the support from the Max Planck-POSTECH-Hsinchu Center for Complex Phase Materials. We also acknowledge the European Synchrotron Radiation Facility and National Synchrotron Radiation Research Center (NSRRC) in Taiwan for provision of synchrotron radiation facilities and technical support at beamline ID20 and BL11A, respectively.

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