Anomalous perovskite PbRuO₃ stabilized under high pressure

Significance

Perovskites had the highest density in oxides and fluorides with the formula ABX₃ before the postperovskite structure was found in MgSiO₃ under high temperature and high pressure. The densification of a perovskite under pressure can be realized by shortening A—X and B—X bond lengths and cooperative rotations of octahedra. In most cases, the densification is within the same space group. The behavior of PbRuO₃ under high pressure offers a case where the perovskite structure can be densified by significantly shortening the A–B distance and distorting the octahedra. Forming such a highly unusual structure by Pb—Ru bonding shows the flexibility of the perovskite structure to avoid collapsing into the postperovskite structure.

Abstract

Perovskite oxides ABO₃ are important materials used as components in electronic devices. The highly compact crystal structure consists of a framework of corner-shared BO₆ octahedra enclosing the A-site cations. Because of these structural features, forming a strong bond between A and B cations is highly unlikely and has not been reported in the literature. Here we report a pressure-induced first-order transition in PbRuO₃ from a common orthorhombic phase (Pbnm) to an orthorhombic phase (Pbn2₁) at 32 GPa by using synchrotron X-ray diffraction. This transition has been further verified with resistivity measurements and Raman spectra under high pressure. In contrast to most well-studied perovskites under high pressure, the Pbn2₁ phase of PbRuO₃ stabilized at high pressure is a polar perovskite. More interestingly, the Pbn2₁ phase has the most distorted octahedra and a shortest Pb—Ru bond length relative to the average Pb—Ru bond length that has ever been reported in a perovskite structure. We have also simulated the behavior of the PbRuO₃ perovskite under high pressure by first principles calculations. The calculated critical pressure for the phase transition and evolution of lattice parameters under pressure match the experimental results quantitatively. Our calculations also reveal that the hybridization between a Ru:t_2g orbital and an sp hybrid on Pb increases dramatically in the Pbnm phase under pressure. This pressure-induced change destabilizes the Pbnm phase to give a phase transition to the Pbn2₁ phase where electrons in the overlapping orbitals form bonding and antibonding states along the shortest Ru—Pb direction at P > P_c.

PbRuO₃ crystallizes in the orthorhombic perovskite structure with the Pbnm space group; it is metallic and exhibits no long-range magnetic ordering down to the lowest temperature. Compared with other Pb-based ferroelectric perovskites like PbTiO₃ (1–4), the orthorhombic Pbnm PbRuO₃ has not been extensively studied in part because it needs to be synthesized at high temperature and under high pressure. PbRuO₃ has gained attention in recent years after the report of a phase transition to a new orthorhombic Imma phase on cooling through a T_t ∼ 90 K (5, 6). An increased octahedral-site distortion in the phase at T < T_t led Kimber et al. (5) to speculate orbital ordering of the 4d electrons at Ru⁴⁺. The bond-length mismatch due to the tolerance factor t ≡ (A—O)/√2(B—O) < 1, where (A—O) and (B—O) are average equilibrium bond lengths, can be relieved by cooperative octahedral-site rotations that give rise to rich tilting systems in the perovskite structure (7–9). Because the thermal expansion coefficient of the A—O bond is normally larger than that of the B—O bond in an ABO₃ perovskite, t increases with increasing temperature, which results in a series of structures with progressively increasing symmetry in the order of Pbnm → Imma (P4/mbm, I4/mcm, R-3c) → Pm-3m (10, 11). The unusual phase transition to a structure with higher symmetry at low temperatures found in PbRuO₃ motivated us to carry out a structural study under high pressure.

Results and Discussion

Generally speaking, the pressure effect on a Pbnm perovskite with t less than but close to 1 is similar to the effect with increasing temperature (11); phase transitions in the order of Pbnm → Imma (P4/mbm, I4/mcm, R-3c) → Pm-3m are expected with increasing pressure. The high-pressure structural study with synchrotron X-ray diffraction (SXRD) in a diamond anvil cell (DAC) (see the Supporting Information for the detail of sample’s preparation and measurements) reveals that at room temperature the Pbnm phase remains stable up to 32 GPa followed by a phase transition with further increase of pressure (Fig. 1A). However, an increased number of diffraction peaks suggested that the high-pressure phase may have an even lower symmetry. We have also confirmed the pressure-induced phase transition with Raman spectroscopy under high pressure (Fig. 1B). The spectra were decomposed by fitting them with Lorentzian components. Almost all major Raman active modes (bands A–H) associated with the Pbnm structure change gradually with pressure to 37 GPa. At least five new Raman active modes (bands I–V) appear abruptly for P > 32 GPa (Fig. 1C). Consistent with the high-pressure SXRD study, an increased number of Raman active modes in the phase at P > 32 GPa indicates that the high-pressure phase has a lower symmetry. However, it is impossible to resolve the crystal structure by Raman spectra alone.

Fig. 1.

(A) Evolution of the SXRD patterns of the PbRuO₃ perovskite as a function of pressure at room temperature. Values are pressure in gigapascals. (B) Raman spectra under different pressures. (C) The pressure dependence of Raman active modes. (D) Pressure dependence of the lattice parameters; arrows inside the plot point to the direction of increasing pressure. The solid lines are the Birch–Murnaghan fitting curves to the experimental V(P) data.

Initial trials with either the C1c1 (No. 9) or the Pbn2₁ (No. 33) structural model gave a reasonable fit to the SXRD pattern of the phase at P > P_c, see Figs. S1 and S2 and Tables S1 and S2 for details of the structural refinement. The two structural models differ only in the oxygen positions about which the SXRD provides very limited information. Our density functional theory (DFT) calculation has shown that the Pbn2₁ structure has a lower ground-state energy than that of the Pbnm structure at high pressure. The input of optimized oxygen positions from the DFT calculations improves further the structural refinement. The structural refinement and the DFT calculation are complementary tools for resolving the crystal structure in our study. Although the mirror symmetry plane in the Pbnm structure is missing in the polar Pbn2₁ structure, some GdFeO₃-type perovskites can be refined reasonably well with both the Pbnm and Pbn2₁ structural models (12). The perovskite BiInO₃ is the only case so far where fitting with a polar structural model Pbn2₁ is clearly better than that with the nonpolar Pbnm structure (13). The polar structure of BiInO₃ becomes unstable against the Pbnm structure at P ∼ 1.5 GPa and a first-order change with 2% volume drop on crossing the Pbn2₁ to the Pbnm structural transition has been observed (14), which matches the popular scenario that high pressure prefers a higher symmetry structure in a perovskite structure with t < 1 but close to 1. In the case of perovskite PbRuO₃, however, the polar structure is stabilized under high pressure and the difference of SXRD patterns between the Pbnm and Pbn2₁ phases in Fig. 1A is even more remarkable than in the case of BiInO₃.

The pressure dependences of the unit-cell parameters of PbRuO₃ in Fig. 1D show a general contraction of a, b, c, and V within the Pbnm phase with increasing pressure; but at P_c ∼ 32 GPa, a jumps and all other lattice parameters b, c, and V drop abruptly with as large as 6% volume change on crossing the phase transition. An abrupt change of the cell volume and the pressure hysteresis at P_c indicate a first-order transition. The pressure dependence of the volume for both phases has been fitted with the Birch–Murnaghan (BM) equation of solid lines in Fig. 1D (see the Supporting Information for the detail of BM equation). By using fixed B′ = 4 in the BM equation, we obtained a bulk modulus B₀ = 189.8(3) GPa for the Pbnm phase and B₀ = 205(1) GPa for the Pbn2₁ phase, respectively.

For a perovskite structure with tilting systems, regular octahedra are not compatible with fixed rotations axes (15). As a typical site distortion, the O₂₁—M—O₂₂ bond angle α opening to the b axis becomes less than 90° as t → 1 (16). Development of this angular site distortion changes the relationship between lattice parameters from a < c/√2 ≤ b to a > b ∼ c/√2. PbRuO₃ shows a > b ∼ c/√2 at ambient pressure, which indicates an α < 90°. A further increase of a-b in PbRuO₃ under pressure of Fig. S3 is typical for a Pbnm perovskite like LaGaO₃ (17, 18), LaCrO₃ (19, 20), and SmNiO₃ (21). An increased angular site distortion makes these Pbnm perovskites unstable against the higher symmetry R3-c phase under high pressure. Pressure appears to play the same role in the Pbnm phase of PbRuO₃ as in other Pbnm perovskites in terms of lattice-parameter changes and, therefore, the site distortion; but this regular pressure dependence of lattice parameters in the Pbnm phase of PbRuO₃ ends up with an irregular phase transition to a polar perovskite with even lower symmetry at P > P_c.

In the Pbnm phase of PbRuO₃, Fig. 2A, the Pb ions are located in the void formed by the eight corner–shared RuO_6/2 octahedra, resulting in an average Pb—Ru distance of about (√3/2)a_p ∼ 3.46 Å, where a_p ∼ (a, b, c/√2)/√2 is the primary cell parameter. In the plot of the Pb—Ru distance in Fig. 2B, the average value the Pb—Ru distance decreases gradually from 3.4 to 3.2 Å with increasing pressure from 0 to 47.3 GPa and there is only a very small drop of the averaged value on crossing the transition to the Pbn2₁ phase. The cooperative rotation of the RuO_6/2 octahedra in the Pbnm phase makes the Pb atoms shift slightly away from the center, resulting in four Pb—Ru distances about 0.05 Å shorter than the average value. In comparison, cooperative rotations of highly distorted octahedra in the Pbn2₁ phase of Fig. 2A create eight different Pb—Ru distances. Most strikingly, a single Pb—Ru distance reaches as small as 2.6 Å in the Pbn2₁ phase, which is about 0.6 Å shorter than the average value, which is unprecedented in all known perovskite oxides. The octahedra in the Pbn2₁ phase are highly distorted as is shown in Fig. 2A; the four O^2- ions of an RuO₂ basal plane are not within a plane and the apical oxygen, especially the top one, deviates severely from the axis coming through the center normal to the RuO₂ basal plane of an octahedron to yield a space for the shortest Pb—Ru distance. The average Ru—O—Ru bond angle in the Pbn2₁ phase is reduced by about 20° from that in the Pbnm phase. The pressure-induced phase transition is clearly against the structural rule in the literature for a perovskite and must be correlated to the peculiar electronic structure associated with low-spin Ru⁴⁺:t_2g⁴ and Pb²⁺:6s² as they come closer under pressure.

Fig. 2.

(A) Two perovskite structures of PbRuO₃. (B) Pressure dependence of the average and shortest Pb—Ru distances of the PbRuO₃ perovskite. (C) The temperature dependence of resistance under different pressures.

We have measured the temperature dependence of resistance on crossing the Pbnm to Pbn2₁ phase transition in PbRuO₃ under pressure in Fig. 2C. The R(T) curve at P = 0.53 GPa obtained in a DAC reproduces essentially that measured on a grain of PbRuO₃ crystal in a piston-cylinder device (6). A sharp decrease in resistivity below 100 K with decreasing temperature is related to the phase transition to the Imma phase. This feature fades away gradually as pressure increases, which suggests that the low-temperature Imma phase is suppressed under pressure. Because of an improving electrical contact at grain boundaries and a broadening of the bandwidth, the resistance at room temperature (RRT) decreases under pressure. An increase of RRT on crossing the phase transition indicates that the Pbn2₁ phase must have a narrower electronic bandwidth than that in the Pbnm phase at P_c. Despite the bandwidth narrowing, the Pbn2₁ phase remains a bad metal. A huge residual resistance at T = 0 K and an extremely weak temperature dependence of the resistance make it like a large-polaron conductor.

From a thermodynamic point of view, the relative stability between two different phases can be evaluated by their Gibbs free energy difference (ΔG = ΔE + PΔV − TΔS). The entropy contribution (TΔS) is typically on the order of magnitude of the thermal energy, which is much smaller than the internal energy change (ΔE). Hence, we only considered the enthalpy change (ΔH = ΔE + PΔV) at T = 0 K for simplicity. Fig. 3 shows calculated internal energy variations with respect to volume for the Pbnm and Pbn2₁ structures. By fitting the E–V data to the third-order BM equation, we obtained the ΔH versus P diagram (as shown in Fig. 3, Inset), which clearly demonstrates the crossover in H that favors the Pbn2₁ phase. The critical pressure is predicted to be in local-density approximation (LDA) and 27 GPa in generalized gradient approximations (GGA). Although the LDA has a well-known tendency to underestimate the phase-transition pressure (22), the GGA value is in good agreement with the experimental value of P_c = 32 GPa. In addition, both LDA and GGA calculations capture well other important aspects of the experimentally observed structural changes, including the evolution of lattice parameters, an abrupt volume drop on crossing , and an anomalously short Pb—Ru bond in the Pbn2₁ phase (see Fig. S4 and Tables S3 and S4 for the detailed information). We have also calculated enthalpy barriers for the Pbnm to Pbn2₁ phase transformation by using the climbing image nudged elastic band method (23, 24). The predicted barrier decreases with increasing pressure; it reaches as small as 62 (48) meV at with GGA (LDA), and it decreases with pressure. The relatively low energy barrier suggests that a facile phase transformation can take place even at room temperature.

Fig. 3.

Variations in the relative internal energies (E) per formula unit (f.u.) for the Pbnm and Pbn2₁ phases of PbRuO₃ as a function of volume (V) from the LDA calculation. Inset shows the enthalpy difference between the Pbnm and Pbn2₁ phases (ΔH = H_Pbn21 − H_Pbnm) as a function of pressure (P).

Fig. 4 shows the electron density of states (DOS) projected on the atomic orbitals of the Pb, Ru, and O atoms in the Pbnm and Pbn2₁ phases of PbRuO₃ from our LDA calculations; the corresponding band structures for the Pbnm and Pbn2₁ structures at are also presented. At ambient pressure, the DOS plot of Fig. 4A for the Pbnm phase shows overlap of the Pb 6s, Ru 4d, and O 2p orbitals in the energy range of E_f − 3 eV < E < E_f + 1 eV, which are largely attributed to the antibonding interactions of the Pb 6s and Ru t_2g orbitals with the O 2p orbitals. Notice also a minor contribution of the Pb 6p state overlapping with the Pb 6s state near the Fermi level, E_f. Our LDA calculation predicts the magnetic moment of the Pbnm phase to be negligible (0.2 μ_B per formula unit), consistent with experiments and other LDA calculations (5). The suppressed magnetic moment has been attributed to the Pb 6s–Ru t_2g and Pb 6p–Ru e_g hybridizations (aided by the O 2p state) as well as Ru t_2g–e_g mixing (5). The magnetic moment tends to be overestimated in GGA calculations, which is largely related to the well-known underbinding tendency of the GGA that results in the increase of lattice parameters and thus the reduced mixing of corresponding atomic orbitals.

Fig. 4.

(A) DOS projected on the Pb, Ru, and O atomic orbitals in the Pbnm phase of PbRuO₃ at P = 0 GPa; the arrows ↑ and ↓ indicate spin-up and spin-down, respectively. Band structures (Left) and DOS (Right) for the (B) Pbnm and (C) Pbn2₁ phases at high pressure (P = 18 GPa). Here, the Ru 4d and O 2p DOS are scaled by one-third, and the dotted lines indicated the Fermi level positions. The unbonded Pb 6s electron pair (B) and the bonding interaction between the Pb sp hybrid and Ru t_2g states (C) are also represented by maximally localized Wannier functions (with an isosurface value of 0.41 electron/ų) in the Insets, which were calculated using the Carr-Parrinello Molecular Dynamics (CPMP) package (29). In C, the WFC is indicated.

As shown in Fig. 4B, increasing pressure to leads to a broadening of the DOS peaks near the Fermi level in the Pbnm phase, apparently due to the increased overlap of the constituent atomic orbitals. The DOS analysis also shows some distinctly different features between the Pbnm and Pbn2₁ phases. In the Pbn2₁ case, Fig. 4C, the Pb 6s and 6p and Ru 4d peaks are noticeably enhanced in the energy range of E_f − 2.6 eV < E < E_f − 1.4 eV. It turns out that this enhancement is attributable to a bonding interaction between the Pb sp hybrid and Ru t_2g orbitals, as demonstrated by crystal orbital overlap population (COOP) analysis (Fig. S5). The Pb—Ru bond formation is also well represented by the maximally localized Wannier function shown in Fig. 4C, Inset; note that the Wannier function center (WFC) (25) is located midway between the Pb and Ru atoms. Detailed charge density profiles for the Pbnm and Pbn2₁ structures are presented in Fig. S6. The covalent-like Pb—Ru bond formation appears to weaken the Ru 4d–O 2p interaction; the relatively reduced Ru 4d–O 2p overlap can be demonstrated by the band narrowing below the Fermi level (−1.4 eV < E − E_f < 0 eV) in comparison with the Pbnm case (Fig. 4B). The Pb—Ru bond formation leaves the corresponding antibonding orbitals completely empty and E_f is located at the leading edge of the bonding states, which accounts for the experimental observation that the Pbn2₁ phase remains a bad metal. We have also conducted the same calculation for isostructural SrRuO₃. The phase transition to the Pbn2₁ structure is not an option in SrRuO₃ under high pressure, which is consistent with experiment (26, 27).

In the polar PbVO₃, (28) the shortest distance between Pb and V in PbVO₃, d =3.35 Å, is still significantly longer than the d = 2.6 Å of the Pb—Ru bond length in the Pbn2₁ PbRuO₃. The following two observations make forming a chemical bond between Pb and Ru along the shortest distortion the primary driving force for the phase transition: (i) the presence of lone pair electrons leaves an anisotropic structure that has four equally short Pb—V distance whereas Pb is clearly bonded with one Ru ion in the Pbn2₁ PbRuO₃; (ii) from the plot of crystal orbital overlap population (COOP) in Fig. S5, the hybridization between the Pb:6sp and Ru4d is so strong that the COOP shows a clear bonding character on crossing the Pbnm to Pnb2₁ phase transition. We note that V⁴⁺ can form a strong double bond in the vanadyl (V = O)²⁺ cation as a result of covalent bonding with yz ± izx orbitals, which allows the polar displacement of the vanadium in PbVO₃. In this case, the Pb:6sp lone pair also interacts with the yz ± izx π-bonding orbitals. The Ru⁴⁺ does not form a Ru = O cation, but its two holes occupy a narrow π* band in which there is no Hund stabilization of an intraatomic S = 1 state. Therefore, the two holes can occupy an a₁ orbital directed through the face of the octahedron to interact with a Pb:6sp lone pair. The strong Pb—Ru bond thus appears to be the driving force for the phase change.

In conclusion, PbRuO₃ undergoes a first-order transition from the orthorhombic Pbnm phase to a lower symmetry Pbn2₁ phase at P_c = 32 GPa. This observation violates the general trend of the perovskite oxides with t ≤ 1 as a function of pressure. The Pbn2₁ phase has one very short Pb—Ru bond length. The RuO₆ octahedra are highly distorted to accommodate the unusually short Pb—Ru bond. The hybridization of the Pb sp and Ru t_2g orbitals, which increases dramatically in the Pbnm phase under pressure, is critical for the transition to the Pbn2₁ phase. Collapsing the Pb—Ru distance in the Pbn2₁ phase is associated with the formation of bonding and antibonding states from the strongly hybridized Pb sp and Ru t_2g orbitals.

Materials and Methods

The PbRuO₃ perovskite used in the present study has been prepared under 9 GPa and 1,400 °C with a Walk-type multianvil module (Rockland Research Co.). Details about the sample synthesis and characterizations can be found elsewhere (30). The in situ high-pressure angle-dispersive SXRD at room temperature was performed at the 16BM-D station of the Advanced Photon Source in the Argonne National Laboratory with a wavelength λ = 0.41326 Ǻ by using a symmetric DAC of 300-μm culet diamonds. Neon gas and silicon oil have been used as the pressure-transmitting media. The ruby fluorescence method was used to monitor the pressure. The diffraction patterns were collected by using a MAR345 image-plate detector and then converted into the format of intensity versus 2θ by using FIT2D software. The structural information was extracted from Rietveld refinement of SXRD patterns with the FullProf program. The Raman spectroscopy measurements were conducted with a Renishaw in Via Spectrometer by using a symmetric Mao-Bell type DAC. The ruby fluorescence method was used to monitor the pressure. The measurements of ρ(T) up to 35 GPa were performed with a four-probe method in a DAC (31).

The calculations reported herein were performed on the basis of DFT within the LDA (32) and GGA-PBE (33) as implemented in the Vienna ab initio Simulation Package (VASP 5.2.2) (34). The projector-augmented wave method with a plane-wave basis set was used to describe the interaction between core and valence electrons (35). The valence-electron configurations considered are: 5d¹⁰6s²6p² for Pb; 4p⁶4d⁷5s¹ for Ru; and 2s²2p⁴ for O. All PbRuO₃ structures were optimized with the conjugated gradient method until the residual forces on constituent atoms become smaller than 0.02 eV/Å. The cutoff energies for the plane-wave expansion were 700 and 500 eV for the geometry (cell shape and atomic position) optimization and electronic structure analysis, respectively. The Brillouin zone sampling was performed with a gamma-centered (6 × 6 × 4) Monkhorst–Pack k-point mesh (36) in the geometry optimization, and the k-point mesh size was increased up to (12 × 12 × 8) to reevaluate the corresponding electronic structures.