Unusual Mott transition associated with charge-order melting in BiNiO$_3$ under pressure

TL;DR

This study reveals a pressure-induced Mott insulator-to-metal transition in BiNiO$_3$, driven by structural changes and charge transfer, with the Ni valence state remaining constant across the transition.

Contribution

It demonstrates the link between structural phase change and electronic transition in BiNiO$_3$, highlighting the melting of charge disproportionation as a key mechanism.

Findings

BiNiO$_3$ undergoes a Mott transition at ~4.8% volume compression.

The transition involves a change from triclinic to orthorhombic structure.

Ni valence remains as Ni$^{2+}$ across the transition.

Abstract

We study the electronic structure, magnetic state, and phase stability of paramagnetic BiNiO$_3$ near a pressure-induced Mott insulator-to-metal transition (MIT) by employing a combination of density functional and dynamical mean-field theory. We obtain that BiNiO$_3$ exhibits an anomalous negative-charge-transfer insulating state, characterized by charge disproportionation of the Bi $6s$ states, with Ni$^{2+}$ ions. Upon a compression of the lattice volume by $\sim$4.8\%, BiNiO$_3$ is found to make a Mott MIT, accompanied by the change of crystal structure from triclinic $P\bar{1}$ to orthorhombic $Pbnm$. The pressure-induced MIT is associated with the melting of charge disproportionation of the Bi ions, caused by a charge transfer between the Bi $6s$ and O $2p$ states. The Ni sites remain to be Ni$^{2+}$ across the MIT, which is incompatible with the valence-skipping Ni$^{2+}$/Ni$^{3+}$ model. Our results suggest that the pressure-induced change of the crystal structure drives the MIT in BiNiO$_3$.

Tables

Table 1. Table S1: Leading Wannier hopping integrals (in meV) between Bi 6 ​ s 6 𝑠 6s and neighbor ions in the ambient-pressure P ​ 1 ¯ 𝑃 ¯ 1 P\bar{1} (left part) and high-pressure P ​ b ​ n ​ m 𝑃 𝑏 𝑛 𝑚 Pbnm (right part) phases of BiNiO 3 .

Atom Atom Distance (a.u.) Hoppings (meV) Bi $6s$ O $2p$ 4.08 -1304, -1234, -71 Bi $6s$ O $2p$ 4.11 -1410, 1037, 631 Bi $6s$ O $2p$ 4.48 -280, -404, 1086 Bi $6s$ O $2p$ 4.62 772, 295, 1144 Bi $6s$ O $2p$ 4.86 -674, 72, 839 Bi $6s$ O $2p$ 4.90 422, 47, -916 Bi $6s$ O $2p$ 5.41 052, -80, -757 Bi $6s$ O $2p$ 5.98 -385, 78, 204 Bi $6s$ Ni $e_g$ 6.03 41, 2 Bi $6s$ Ni $t_{2g}$ 6.03 -37, 75, 163 Bi $6s$ Ni $e_g$ 6.10 -7, 58 Bi $6s$ Ni $t_{2g}$ 6.10 31, -126, -142 Bi $6s$ Ni $e_g$ 6.11 11, 48 Bi $6s$ Ni $t_{2g}$ 6.11 -2, -274, -163 Bi $6s$ Ni $e_g$ 6.16 40, 12 Bi $6s$ Ni $t_{2g}$ 6.16 58, -14, 64

Atom Atom Distance (a.u.) Hoppings (meV) Bi $6s$ O $2p$ 4.24 0, 1709, 242 Bi $6s$ O $2p$ 4.44 -271, -1536, 95 Bi $6s$ O $2p$ 4.44 -271, -1536, -95 Bi $6s$ O $2p$ 4.58 0, 622, 1132 Bi $6s$ O $2p$ 4.85 -69, -103, 957 Bi $6s$ O $2p$ 4.85 -69, -103, -957 Bi $6s$ O $2p$ 4.95 6, -142, 935 Bi $6s$ O $2p$ 4.95 6, -142, -935 Bi $6s$ O $2p$ 5.85 0, -298, -151 Bi $6s$ O $2p$ 5.85 0, -49, -330 Bi $6s$ Ni $e_g$ 5.86 -6, -11 Bi $6s$ Ni $t_{2g}$ 5.86 40, -12, 227 Bi $6s$ Ni $e_g$ 5.86 6, 11 Bi $6s$ Ni $t_{2g}$ 5.86 40, -12, 227 Bi $6s$ Ni $e_g$ 6.11 0, -40 Bi $6s$ Ni $t_{2g}$ 6.11 38, 156, -55

Equations

$$\hat{H}=\sum _{\mathbf{k},\sigma }{\hat{H}}_{\sigma ,\alpha \beta }^{\mathrm{DFT}}(\mathbf{k})+\frac{1}{2}\sum _{i,\sigma {\sigma }^{\prime },\alpha \beta }{U}_{\alpha \beta }^{\sigma {\sigma }^{\prime }}{\hat{n}}_{i,\alpha \sigma }{\hat{n}}_{i,\beta {\sigma }^{\prime }}-{\hat{H}}_{\mathrm{DC}},$$

Full text

The Mott metal-insulator transition driven by correlation effects has been an outstanding problem in condensed matter physics over many decades Imada . In recent years, increasing attention has been drawn to the rare earth nickelate perovskites $R$NiO3 ($R$ = rare earth, $R^{3+}$) with a high oxidation state of nickel, Ni3+ $3d^{7}$ Nickelates ; Subedi_2015 ; Mercy2017 . $R$NiO3 compounds (except for LaNiO3) exhibit a sharp metal-insulator transition (MIT) upon cooling below $T_{\mathrm{MIT}}$ Torrance1992 . The phase transition is accompanied by a structural transformation from an orthorhombic ($Pbnm$, GdFeO3-type) to monoclinic ($P2_{1}/n$) crystal structure, with a cooperative breathing distortion of NiO6 octahedra Torrance1992 .

Based on the Ni-O bond lengths analysis and X-ray absorption spectroscopy, a partial $\mathrm{Ni}^{(3\pm\delta)+}$ charge disproportionation of Ni ions was proposed to occur in the insulating $R$NiO3 phases Torrance1992 ; Medarde2009 . By contrast, further electronic structure calculations explain the insulating state of $R$NiO3 in terms of bond disproportionation, with alternating Ni ions which (nearly) adopt a Ni2+ $3d^{8}$ (Ni2+ ions with local moments) and $3d^{8}\underline{L}^{2}$ (nonmagnetic spin-singlet) electronic configuration ($\underline{L}$ denotes a hole in the O $2p$ band) Park2012 ; Johnston2014 ; Subedi_2015 . The transition temperature $T_{\mathrm{MIT}}$ is strongly related to the degree of structural distortion of $R$NiO3, determined by the size of $R$-ions. With decrease of the $R$-ionic radius, the Ni-O-Ni bond angle, which determines the degree of overlapping of the Ni $3d$ and O $2p$ orbitals (and hence the Ni $3d$ bandwidth), becomes smaller and $T_{\mathrm{MIT}}$ is increased. In accord with this, the least distorted LaNiO3 is found to be a correlated metal Torrance1992 ; Nowadnick2015 . In this context, the replacement of La3+ with a larger ion, such as Bi3+, should in principle result in a metal with (nearly) cubic perovskite structure. By contrast, BiNiO3 has been found to be an insulator with a highly distorted perovskite structure (triclinic, $P\bar{1}$) and unusual valence ordering of the $A$-site Bi ions Ishiwata2002 . In particular, based on X-ray and neutron diffraction, it was proposed that Ni ions adopt a Ni2+ state, with an electronic configuration Bi${}^{3+}_{0.5}$Bi${}^{5+}_{0.5}$Ni*2+*O3 Ishiwata2002 ; Azuma2007 ; Carlsson2008 .

BiNiO3 is known due to its colossal negative thermal expansion across the pressure-induced MIT, as suggested caused by a Bi/Ni charge transfer Azuma2011 . Under ambient conditions, BiNiO3 crystallizes in a triclinic perovskite crystal structure (space group $P\bar{1}$, a subgroup of $P2_{1}/n$) with two inequivalent Bi and four Ni sites Azuma2007 (see Supplementary Fig. S1 supplement and Ref. vesta therein). It is an insulator with an energy gap of 0.68 eV Ishiwata2002 . Below the Néel temperature of ${T_{\mathrm{N}}\sim 300}$ K, BiNiO3 is a $G$-type antiferromagnet with a near-antiferromagnetic alignment of Ni2+ ${S=1}$ spins, implying a predominant role of the antiferromagnetic Ni-O-Ni superexchange Ishiwata2002 ; Carlsson2008 ; footnote1 . Moreover, similarly to the small $R$-ions $R$NiO3 the (charge-disproportionated) paramagnetic insulating phase of BiNiO3 extends well above $T_{\mathrm{N}}$, implying the crucial importance of correlation effects footnote2 ; Park2012 ; Subedi_2015 . BiNiO3 shows a Mott insulator-to-metal phase transition (in the paramagnetic phase) under pressure (above $\sim$4 GPa) or upon substitution of the $A$-site Bi ions with La Ishiwata2005 ; Wadati2005 . In close similarity to $R$NiO3, the MIT is accompanied by the change of crystal structure from the triclinic $P\bar{1}$ (insulating) to orthorhombic GdFeO3-type $Pbnm$ (metallic) phase, with a volume collapse of $\sim$3% and melting of charge disproportionation (Ni and Bi sites are equivalent in the $Pbnm$ structure of BiNiO3). Based on the powder X-ray absorption and neutron diffraction, it was proposed that the melting of charge disproportionation leads to a charge transfer from Ni2+ to Bi3+, so that the electronic state of the $Pbnm$ metallic phase can be described as Bi3+Ni3+O3 Azuma2007 ; Mizumaki2009 . This valence distribution however is in odd with photoemission spectroscopy results for $Pbnm$ BiNiO3 that reveal that the nickel valence is far from being Ni3+ Wadati2005 .

The electronic properties of BiNiO3 have recently been calculated using band-structure methods supplemented with the on-site Coulomb correlations for the Ni $3d$ states within density-functional theory (DFT)+$U$ dft_plus_u and dynamical mean-field theory (DMFT) dmft methods Cai2007 . However, these studies have mostly been focused on the valence skipping model, with a valence transition between the charge-ordered insulating [Bi${}^{3+}_{0.5}$Bi${}^{5+}_{0.5}$][Ni2+] and the uniform metallic [Bi3+][Ni3+] state, assuming a long-range magnetic ordering. In fact, however, the MIT transition in BiNiO3 is known to occur in the paramagnetic state, implying the importance of electronic correlations. Moreover, a recent electronic structure study of BiNiO3 using DFT and slave rotor methods suggests that BiNiO3 is a self-doped Mott insulator Saha_Dasgupta .

In this paper, we explore the evolution of the electronic structure, magnetic state, and phase stability of paramagnetic BiNiO3 near the pressure-induced Mott MIT. We employ a fully self-consistent in charge density DFT+DMFT approach dftdmft implemented with plane-wave pseudopotentials espresso ; Leonov1 which makes it possible to capture all generic aspects of the interplay between the electronic correlations, magnetic states, and crystal structure of BiNiO3 near the Mott MIT dftdmft_aplications . The DFT+DMFT calculations explicitly include the Bi $6s$, O $2p$, and Ni $3d$ valence states, by constructing a basis set of atomic-centered Wannier functions within the energy window spanned by the $s$-$p$-$d$ band complex Wannier . This allows us to take into account a charge transfer between the Bi $6s$, O $2p$, and Ni $3d$ states, accompanied by the strong on-site Coulomb correlations of the Ni $3d$ electrons. We use the continuous-time hybridization-expansion (segment) quantum Monte-Carlo algorithm in order to solve the realistic many-body problem CT-QMC . We take the average Hubbard ${U=6}$ eV and Hund’s exchange ${J=0.95}$ eV as estimated previously for $R$NiO3 Park2012 ; Nowadnick2015 . We use the fully localized double-counting correction, evaluated from the self-consistently determined local occupations, to account for the electronic interactions already described by DFT.

In Fig. 1 we display our DFT+DMFT results for the phase equilibrium and local magnetic moments of Ni ions of paramagnetic BiNiO3. In these calculations, we adopt the crystal structure data for the ambient pressure triclinic $P\bar{1}$ and high-pressure orthorhombic $Pbnm$ structures (taken at a pressure of $\sim$7.7 GPa) from experiment Azuma2007 , and evaluate the DFT+DMFT total energies as a function of lattice volume. Overall, our results for the electronic structure and lattice properties of BiNiO3 agree well with experimental data Wadati2005 ; Ishiwata2002 ; Azuma2007 ; Carlsson2008 ; Azuma2011 . In particular, the triclinic $P\bar{1}$ phase is found to be thermodynamically stable at ambient pressure, with a total-energy difference between the ambient-pressure and high-pressure phases of $\sim$160 meV/f.u.. The calculated equilibrium lattice volume $V_{0}=248.8~{}\AA^{3}$ and bulk modulus $K_{0}=149$ GPa ($K^{\prime}\equiv dK/dP$ is fixed to $K^{\prime}=4$). Interestingly, all the Ni sites (the insulating $P\bar{1}$ phase has four inequivalent Ni sites) are nearly equivalent and are in the Ni2+ state. The Ni2+ state is also confirmed by the eigenvalues analysis of the reduced Ni $3d$ density matrix, which suggests that the Ni ions are in the $\sqrt{0.63}|d^{8}\rangle+\sqrt{0.32}|d^{9}\rangle$ state (all the rest contributions are below 0.05). Moreover, the calculated local (instantaneous) magnetic moment $\sqrt{\langle\hat{m}^{2}_{z}\rangle}\simeq 1.67\,\mu_{\textrm{B}}$, agrees with the high-spin ${S=1}$ state of the Ni2+ ions.

Our calculations for the insulating $P\bar{1}$ phase of BiNiO3 give a self-doped Mott insulator self-doped with an energy gap of $\sim$0.3 eV (see the left panel of Fig. 2), in agreement with the resistivity and photoemission experiments Wadati2005 ; Ishiwata2002 (see also Supplementary Fig. S3). In particular, the energy gap lies between the occupied and unoccupied Ni $e_{g}$ states, strongly mixed with the O $2p$ and the empty Bi2 $6s$ states (the Bi1 $6s$ states are fully occupied). The O $2p$ states are about -3.6 eV below the Fermi level, but have a substantial contribution both above and below $E_{\textrm{F}}$. The latter is due to the strongly covalent B $6s$–O $2p$ bonding, suggesting creation of a ligand hole caused by a charge transfer between Bi $6s$ and O $2p$. While the occupied Bi1 and Bi2 $6s$ states are seen to be localized deep below $E_{\textrm{F}}$, at about -10 eV, the empty Bi2 $6s$ states appear right at the bottom of the conduction band, with a sharp resonant peak at $\sim$0.4 eV. The top of the valence band has a mixed Ni $3d$ and O $2p$ character, with a resonant peak in the filled $e_{g}$ bands located at about -0.4 eV below the Fermi level, which can be ascribed to the formation of a Zhang-Rice bound state Zhang1988 .

Our result for the insulating $P\bar{1}$ phase is characterized by a remarkable charge disproportionation of the Bi $6s$ states (due to the appearance of two different Bi sites with sufficiently different oxygen environment in the insulating phase). In fact, while the Bi1 $6s$ states are almost completely occupied, the Bi2 $6s$ Wannier occupancy is only about 1.56. This implies a charge difference of ${\Delta N_{\mathrm{Bi}\text{-}6s}\sim 0.42}$, i.e., it is about 21% of the ideal Bi3+-Bi5+ value. Interestingly, the corresponding Bi $6s$ charge difference is in agreement with a charge disproportionation of $\sim$0.2 (i.e., of $\sim$20% of the ideal valence skipping) found in the low-temperature charge-ordered phases of the mixed-valent oxides, such as Fe3O4 mixed-valent-oxides , and of $\sim$0.2-0.3 charge disproportionation of the Ni ions in $R$NiO3 Torrance1992 . Moreover, previous estimates for the bond-disproportionated insulating phases of the bismuth perovskites BaBiO3 and SrBiO3 show a small charge disproportionation between the Bi ions of $\sim$0.3 Foyevtsova . We also verified our result for $\Delta N_{\mathrm{Bi}\text{-}6s}$ by calculating the corresponding charge difference within the Bi-ion radius of 1.31 Å, a typical value for the Bi3+ ion. Nevertheless, we find that the result is robust, with ${\Delta N_{\mathrm{Bi}\text{-}6s}\sim 0.34}$. While all the Ni’s are in the Ni2+ state (and, as we will show below, the Ni2+ state remains stable above the MIT in the metallic $Pbnm$ phase) this suggests the stabilization of the charge disproportionated $\mathrm{Bi1}^{3+}_{0.5}(\mathrm{Bi2}^{(3+\delta)+}\underline{L}^{2-\delta})_{0.5}$ valence configuration in the insulating $P\bar{1}$ phase of BiNiO3. We argue that the obtained valence configuration can be rationalized as being intermediate between the two limits: the pure valence skipping Bi3+-Bi5+ and the Bi-O bond disproportionation $\mathrm{Bi}^{3+}$-[$\mathrm{Bi}^{3+}\underline{L}^{2}$] models.

Interestingly, the energy gap of the triclinic BiNiO3 phase is seen to increase upon (an uniform) compression (while decreasing and even closing upon expansion) of the unit cell volume (see the lower panel of Fig. 2). This counter-intuitive change of the energy gap value in a Mott insulator is accompanied by a remarkable increase of charge disproportionation of the Bi ions (under pressure), suggesting the importance of a Bi $6s$-O $2p$ charge transfer. In particular, our results show that the Bi $6s$ charge disproportionation becomes larger in the $P\bar{1}$ crystal structure of BiNiO3 upon decrease of the lattice volume (see Fig. 3). Upon compression, the Bi2 $6s$ orbital occupation gradually decreases, whereas the Bi1 $6s$ states are fully occupied, with a nearly constant occupation $N_{\mathrm{Bi1}\text{-}6s}\sim 1.97$. In addition, our DFT+DMFT calculations using different Hubbard $U$ values (${U=5}$ eV and 8 eV) show that the energy gap increases upon increasing of $U$, in agreement with the behavior of a Mott insulator. Interestingly, the Bi $6s$ charge disproportionation becomes larger for the larger $U$ values, by $\sim$5% upon increasing of the $U$ value from ${U=6}$ eV to 8 eV.

This behavior is consistent with the change of the crystal field levels of the Ni $e_{g}$, O $2p$, and Bi $6s$ states under pressure (see Fig. 3). In fact, the O $2p$ levels are found to shift deep below the Ni $e_{g}$ states under pressure, whereas the Bi $6s$ states go up in energy. The change of the O $2p$ and Bi $6s$ crystal field levels leads to the enhancement of the Bi $6s$-O $2p$ hybridization under pressure, supporting the hybridization-switching mechanism proposed by Paul et al. Saha_Dasgupta . Our results suggest that the $P\bar{1}$-structured BiNiO3 is an unconventional Mott insulator in which the correlated insulating state is in much respect controlled by an $s$-$p$ level splitting between the uncorrelated $A$-site Bi $6s$ and ligand O $2p$ states.

Upon further compression the $P\bar{1}$-structured BiNiO3 becomes metallic below ${\sim 0.5\,V_{0}}$, with the (instantaneous) local moment of $\sim 1.36\,\mu_{\textrm{B}}$. The MIT is accompanied with a collapse of local moments due to delocalization of the Ni $3d$ electrons, as seen from the behavior of local spin susceptibility $\chi(\tau)=\langle\hat{m}_{z}(\tau)\hat{m}_{z}(0)\rangle$ (see Fig. 4). In fact, $\chi(\tau)$ is seen to decay fast with the imaginary time $\tau$. In agreement with this, the fluctuating moment is only of $\sim$0.75 $\mu_{\textrm{B}}$ (evaluated as $m_{\textrm{loc}}=[T\int_{0}^{1/T}\chi(\tau)d\tau]^{1/2}$), that differs sufficiently from the instantaneous moment. While the Bi $6s$ charge disproportionation is large in the highly-compressed metallic $P\bar{1}$ phase, ${\Delta N_{\mathrm{Bi}\text{-}6s}\sim 1.04}$, this suggests that the Bi $6s$ charge ordering alone cannot explain the insulating state of BiNiO3. In agreement with this, our results for structural optimization of the $P\bar{1}$ phase within nonmagnetic DFT give a metal with no evidence for the Bi $6s$ charge disproportionation (all the Bi sites are found to have nearly same oxygen environment), implying the crucial importance of strong localization of the Ni $3d$ electrons due to correlation effects Subedi_2015 .

Most importantly, our DFT+DMFT results provide a clear evidence that BiNiO3 undergoes a structural transition from the triclinic insulating $P\bar{1}$ to orthorhombic metallic $Pbnm$ structure below ${\sim 0.95\,V_{0}}$ (above 8 GPa), in agreement with experiment Azuma2007 ; Carlsson2008 ; Azuma2011 . We found that the transition pressure depends very sensitively on the choice of the Hubbard $U$ value, with $P_{c}\simeq 1$ GPa and 15 GPa for ${U=5}$ eV and $8$ eV, respectively. The calculated bulk modulus ($U=6$ eV) is $K_{0}\sim 143$ GPa, i.e., $K_{0}$ is found to decrease by $\sim$4% upon the MIT into the metallic state. The latter is rather uncommon for a Mott MIT, indicating the importance of lattice effects at the MIT in BiNiO3 Subedi_2015 .

The $Pbnm$ phase of BiNiO3 is a correlated metal, characterized by a Fermi-liquid-like behavior with a weak damping of quasiparticles at the Fermi energy and by a substantial mass renormalization of $\frac{m^{*}}{m}\sim 2.5$ of the Ni $e_{g}$ bands. The Ni $e_{g}$ states show a quasiparticle peak at the Fermi level, with the upper Hubbard band at $\sim 1.0$ eV (see Fig. 2 and Supplementary Fig. S3). The calculated Ni-ion local magnetic moment of ${1.3\,\mu_{\textrm{B}}}$ differs sufficiently from the fluctuating one ${\sim 0.5\,\mu_{\textrm{B}}}$, implying delocalization of the Ni $3d$ electrons at the transition. Indeed, our result for the local susceptibility shows itinerant-moment-like behavior, similar to that of the highly-pressurized $P\bar{1}$ phase (see Fig. 4). The $Pbnm$ phase is found to be metallic for all studied here unit cell volumes, as well as even for a large Hubbard ${U=12}$ eV. The pressure-induced MIT is found to be accompanied by a collapse of the lattice volume by ${\sim 5.2\%}$, resulting in the melting of charge disproportionation of the Bi sites. Thus, in the $Pbnm$ phase all the Bi sites are equivalent, whereas the Bi $6s$ states are fully occupied, i.e., Bi3+. Moreover, our analysis of eigenvalues of the reduced Ni $3d$ density matrix suggests that the Ni sites are in a Ni2+ state, with an atomic configuration $\simeq\sqrt{0.56}|d^{8}\rangle+\sqrt{0.30}|d^{9}\rangle$. We also notice a minor, below $\sim$10%, contribution due to the $d^{7}$ atomic state, $\sqrt{0.09}|d^{7}\rangle$. Based on this result, we conclude that no change of the valence state of the Ni2+ ions occurs across the pressure-induced MIT in BiNiO3, i.e., the Ni2+ state remains stable. The latter is in a sharp contrast with the valence skipping Bi/Ni model proposed earlier for BiNiO3 Azuma2007 ; Mizumaki2009 . Our results suggest a novel microscopic mechanism of a Mott MIT under pressure which is controlled by a charge-transfer between the $A$-site Bi $6s$ and ligand O $2p$ states. The pressure-induced MIT in BiNiO3 is accompanied by a transition from the charge-disproportionated $\mathrm{Bi1}^{3+}_{0.5}(\mathrm{Bi2}^{(3+\delta)+}\underline{L}^{2-\delta})_{0.5}$ to the charge-uniform $\mathrm{Bi}^{3+}\underline{L}^{2}$ valence state. The Bi $6s$ charge disproportionation (in the insulating $P\bar{1}$ phase) occurs together with the MIT, which follows rather than produces the structural transition. We therefore conclude that the pressure-induced MIT and the concomitant melting of the Bi $6s$ charge ordering in BiNiO3 is driven by the crystal structure transition. The latter highlights the complex interplay between the electronic structure and lattice effects in the vicinity of a Mott MIT in $R$NiO3 nickelates Subedi_2015 .

In conclusion, we employed the DFT+DMFT approach to determine the electronic structure and phase stability of paramagnetic BiNiO3 across the pressure-induced Mott MIT. Our results for the $P\bar{1}$-structured BiNiO3 under pressure propose a new mechanism for a correlation-driven metal-insulator transition, in which the Mott insulating state is (in much respect) controlled by the $s$-$p$ level splitting between the uncorrelated $A$-site Bi $6s$ and ligand O $2p$ states. We show that the pressure-induced MIT in BiNiO3 is associated with the melting of charge disproportionation of the Bi ions and is accompanied by delocalization of the Ni $3d$ electrons. The phase transition results in a charge transfer between the Bi $6s$ and O $2p$ states, while the Ni sites remain to be Ni2+. Our results suggest that the pressure-induced change of the crystal structure drives the MIT in BiNiO3. We argue that the $R$NiO3 compounds (with $R=$rare earth and Bi) obey an intrinsic instability driven by the interplay of electron correlations and lattice effects, depending on the $R$-ion radius. It is associated with a crossover from charge disproportionation of the perovskite $B$-site Ni-ions (realized for the $R$-ions with the ionic radii smaller than that of La) to that of the $A$-site $R$-ions (for large $R$-ions), with LaNiO3 being in between.

We thank O. Peil for valuable discussions. We acknowledge the support from Russian Foundation for Basic Research (Project No. 18-32-20076).The DFT calculations were supported by the Ministry of Science and Higher Education of the Russian Federation (theme “Electron” No. AAAA-A18- 118020190098-5).

Supplemental Material

Under ambient pressure, BiNiO3 adopts a highly distorted perovskite (triclinic) crystal structure with space group $P\bar{1}$ (see Supplementary Fig. S1). It has two inequivalent Bi and four Ni sites and is characterized by the cooperative breathing Bi-O distortions of the lattice. The Bi sites are arranged in chains along the $c$ axis, with a checkerboard pattern in the $ab$-plane. The $P\bar{1}$-structured BiNiO3 is an insulator with an energy gap of $\sim 0.68$ eV as estimated from the electrical resistivity Ishiwata2002 .

Under pressure above $\sim 4$ GPa, BiNiO3 undergoes a structural transformation to the orthorhombic GdFeO3-type ($Pbnm$) crystal structure, which has a single type of Bi and Ni ions. The phase transition is accompanied by a Mott insulator-to-metal transition and is associated with suppression of the breathing distortions of the lattice (all the Ni and Bi sites become equivalent in the $Pbnm$ phase).

Here, we employed the DFT+DMFT approach to explore the electronic properties and phase stability of paramagnetic BiNiO3 under pressure using the DFT+DMFT method dftdmft implemented with plane-wave pseudopotentials espresso ; Leonov1 . We start by constructing the effective low-energy Hamiltonian [$\hat{H}^{\mathrm{DFT}}_{\sigma,\alpha\beta}(\bf{k})$], which explicitly contains the Bi $6s$, Ni $3d$, and O $2p$ valence states, using the projection onto Wannier functions Wannier1 . For this purpose, for the partially filled Bi $6s$, Ni $3d$, and O $2p$ orbitals we construct a basis set of atomic-centered symmetry-constrained Wannier functions Wannier2 . The Wannier functions are constructed over the full energy range spanned by the $s$-$p$-$d$ band complex using the scheme of Ref. Wannier2 . We obtain the $s$-$p$-$d$ Hubbard Hamiltonian (in the density-density approximation)

[TABLE]

where $\hat{n}_{i,\alpha\sigma}$ is the occupation number operator for the $i$-th Ni site with spin $\sigma$ and (diagonal) orbital indices $\alpha$. In Supplementary Fig. S2 we show our results for the band structure of BiNiO3 calculated within nonmagnetic DFT in comparison with the Wannier Bi $6s$, Ni $3d$, and O $2p$ band structure for the ambient-pressure $P\bar{1}$ and high-pressure $Pbmn$ phases of BiNiO3. Our results for the leading Wannier hopping integrals between the Bi $6s$ and neighbor ions in the ambient-pressure $P\bar{1}$ and high-pressure $Pbnm$ phases of BiNiO3 are summarized in Table S1. All the calculations are performed in the local basis set determined by diagonalization of the corresponding Ni $3d$ occupation matrices.

In order to solve the realistic many-body problem, we employ the continuous-time hybridization-expansion quantum Monte-Carlo algorithm CT-QMC . The Coulomb interaction has been treated in the density-density approximation. The elements of the $U$ matrix are parametrized by the average Coulomb interaction $U$ and Hund’s exchange $J$ for the Ni $3d$ shell. For all the structural phases considered here we have used the same $U=6$ eV and $J=0.95$ eV values as was estimated previously for $R$NiO3 Park2012 ; Nowadnick2015 . The spin-orbit coupling was neglected in these calculations. Moreover, the $U$ and $J$ values are assumed to remain constant upon variation of the lattice volume. We employ the fully localized double-counting correction, evaluated from the self-consistently determined local occupations, to account for the electronic interactions already described by DFT, $\hat{H}_{DC}=U(N-\frac{1}{2})-J(N_{\sigma}-\frac{1}{2})$, where $N_{\sigma}$ is the total Ni $3d$ occupation with spin $\sigma$ and $N=N_{\uparrow}+N_{\downarrow}$. Here, we employ a fully self-consistent in charge density DFT+DMFT scheme in order to take into account the effect of charge redistribution caused by electronic correlations and electron-lattice coupling.

In Supplementary Fig. S3 we show the spectral functions of paramagnetic BiNiO3 calculated by DFT+DMFT in comparison with photoemission (PES) and X-ray absorption (XAS) spectra taken at room temperature Wadati2005 . Our calculations are performed in the paramagnetic state at a temperature ${T=387}$ K, above the Néel temperature ${T_{\mathrm{N}}\sim 300}$ K. To calculate the spectral functions, we employ the Padé analytical continuation procedure for the self-energy. In our calculations we adopt the experimental crystal structure data (atomic positions for the orthorhombic phase are taken from the experiment at a pressure of $\sim$7.7 GPa Azuma2007 ).

The calculated spectral functions are in overall good agreement with the experimental spectra. In particular, in the insulating triclinic phase, the energy gap lies between the occupied and unoccupied Ni $e_{g}$ states, strongly mixed with the O $2p$ and the empty Bi2 $6s$ states (the Bi1 $6s$ states are fully occupied). Our results indicate that all the Ni sites (the insulating $P\bar{1}$ phase has four inequivalent Ni sites) are nearly equivalent. A sharp peak at about -1.5 eV originates from the occupied Ni $t_{2g}$ states, which form a lower Hubbard band at -9 eV. The PES spectral weight lying at about -3 and -5 eV is mainly due to the O $2p$ states, the hump at -10 eV is predominantly due to the Bi $6s$ states. In the metallic orthorhombic phase, the peak at the Fermi level and the spectral weight at the bottom of the conduction band are predominantly formed by the Ni $e_{g}$ and O $2p$ states. The Ni $e_{g}$ upper Hubbard band appears at $\sim 1.0$ eV. The peak at about -1.5 eV is due to the occupied Ni $t_{2g}$ states. In contrast to the insulating phase, all the Bi states are occupied and are located at about -10 eV.