## Introduction

The importance of the insulator-metal transition (IMT) in compressed nickel monoxide (NiO) for the physics of strongly correlated electronic systems ranks close to the problems of insulator-metal transition and high-temperature superconductivity in cuprates and to other key problems in physics (according to Ref. 1), such as metallization of hydrogen under pressure. NiO was historically the first material, which proved to be a test-bed for the understanding of strongly correlated electronic systems. In pioneering studies by Mott and co-workers, NiO was treated as a typical example of “Mott” insulator with a wide d-d energy gap Eg, which occurs due to strong on-site Coulomb electron repulsion between Ni 3d electrons2,3,4,5. At the same time, Mott predicted possible IMT in compressed NiO. The first suggestions of metallic high-pressure phase of NiO were made by Boer, Verwey, Mott, and Peierls6,7. Recently we observed the IMT transition in NiO at 240 ± 10 GPa in experiments probing the resistance of the samples at high pressure8. Numerous theoretical studies provided contradictory predictions regarding the pressure range and nature of the IMT in NiO. Early theoretical LDA and GGA calculations by Cohen et al.9 predicted that band-broadening effects are responsible for a magnetic collapse in simple oxides FeO, MnO, and CoO; a nearly second-order phase transition accompanied by magnetic collapse at 230 GPa was predicted in NiO9. In the paper by Feng et al.10 it was shown that the more ‘sophisticated’ B3LYP density functional predicts a transition at significantly higher pressure than the GGA functional. More recent predictions from the ab-initio (LSDA + U) calculations performed by the authors of Ref. 11. indicated a transition above 300 GPa; the most recent calculation using DMFT method predicted the transition pressure at 429 GPa in NiO12 (see discussion section for further comments). Thus, the theoretical controversy regarding the pressure of the transition is not resolved by recent publications.

It should be noted here that the existing experimental claim of transition pressure exceeding 280 GPa in NiO11 is based on NFS measurements at just one pressure point with the signal level about ten counts (total) in maximum, which makes it difficult to validate the claimed complicated signal pattern, relevant to the magnetic phase. Moreover, the effect of pressure gradients (which could be of the order of 30 – 40 GPa in non-hydrostatic conditions above 200 GPa) on the experimentally obtained NFS data is not given a proper discussion in11.

Given such controversial situation in the existing literature on the IMT in NiO, it is extremely important to study the NiO by independent experimental techniques. For this purpose, we have performed structural studies of NiO to elucidate possible structural changes at the transition.

Since the reported theoretical and experimental studies8,10,13,14,15,16 suggest a very high pressure of the transition in NiO, we have approached this important problem using multimegabar diamond anvil cell techniques.

The paper presents the results of structural studies of NiO in the widest possible pressure range of (0–240 GPa) to date. Starting from ~110 GPa, we observe a significant trigonal distortion of the initially NaCl-type crystal structure. At higher pressures, a structural transition with a volume drop of ~2.7% was detected experimentally in the region of the insulator-metal transition. Finally, we report here the observation of the first-order structural transition accompanying the insulator-metal transition in NiO.

## Results

We tested original NiO sample at STOE multi-purpose diffractometer system “STADI MP” and found volume and lattice parameter a = 4.1779(2) Å, V = 72.927(2) Å3 for the B1 cubic phase of the NiO structure ($${Fm}\bar{3}m$$) and a = 2.9558(1) Å, c = 7.2283(1) Å, V0 = 54.692(1) Å3 for the trigonal phase ($$R\bar{3}m$$) of the distorted B1 structure. Corresponding X-ray data and lattice parameters are presented in Supplementary Note 1.

We have made five runs of X-ray diffraction (XRD) experiments with NiO up to 238 GPa in standard and beveled diamond anvil cells at hydrostatic and nonhydrostatic conditions at room temperature up to very high pressures (Table 1). The images of the NiO samples in diamond anvils cells from runs 1–5 are shown in Fig. 1.

The evolution of the XRD patterns taken from NiO samples in the pressure range 0–40 GPa in a quasi-hydrostatic experiment with PES-5 as a pressure medium (run1) is shown in Fig. 2(a). The evolution of the XRD patterns in the pressure range 31–73 GPa in a hydrostatic experiment with Ne as a pressure medium (run2) is shown in Fig. 2(b). The evolution of the XRD patterns in a quasi-hydrostatic experiment with Ne as a pressure medium in the pressure range 111–161 GPa (run3) is shown in Fig. 2(c). The evolution of XRD patterns in a quasi-hydrostatic experiment with NaCl as a pressure medium in the pressure range 129-238 GPa (run4) is shown in Fig. 2(d).

In the non-hydrostatic measurements (run5) the NiO sample itself was used as a pressure medium in c-BN gasket17. The image of the NiO sample in the non-hydrostatic experiment is shown in Fig. 1(e).

Recent XRD experiments on the distorted rock-salt structure of NiO have found this structure to be stable up to ~147 GPa14. In the most recent study the absence of the transition was claimed up to 212 GPa11.

In this study we determined the experimental V-P relation of NiO at hydrostatic and quasi-hydrostatic conditions up to 238 GPa (Fig. 3). We observed (for run4 with NaCl pressure medium) an onset of an iso-structural transition with a volume drop about 2.65% (estimated at 225 GPa) during pressure increase in the region 208–238 GPa. The Birch-Murnaghan equation of state was fitted to the current experimental data, and its parameters were found to be B0 = 192 ± 7 GPa, and B’ = 4.8 ± 0.1 for the low-pressure phase (LP) below ~208 GPa (see details in Supplementary Note 5). For the high-pressure phase (HP), we used a fit of the experimental data (measured at non-hydrostatic conditions in run5) to a modified Birch-Murnaghan equation of state (see details in Supplementary Note 5); the parameters are presented below. The solid line shown in Fig. 3 represents the calculated Birch-Murnaghan equation of state that fits well all the sets of the experimental data.

We did not find any substantial influence of the non-hydrostaticity on the P-V relation of NiO up to ~100GPa. At pressures higher than ~100GPa for non-hydrostatic measurements the influence of non-hydrostatic strain was taken into account during the fitting procedure18,19,20. From our fit we found that for the higher pressures (above 100 GPa) the effective value of the strain is also higher. We observed the first-order structural transition in NiO with an effective pressure of the transition about 225 ± 15GPa (see Fig. 3 and details in Supplementary Note 5).

We also observed an anomaly in the a/c ratio during hydrostatic compression at about 50 GPa. The anomaly is clearly seen in Fig. 4. This “kink-like” anomaly is in excellent agreement with the kink in the pressure dependence of the optical gap at ~50 GPa (see inset in Fig. 4, and Ref. 8).

The pressure evolution of XRD patterns from non-hydrostatic run5 below and at the structural transition in NiO is shown in Fig. 5. An increase in pressure above 130 GPa leads to a trigonal distortion of the cubic crystal structure. In addition, the observed splitting of the 012 reflection of the trigonal structure at ~206 GPa clearly indicates the coexistence of the high-pressure (HP) and the low-pressure (LP) phases in the region of the structural transition. Figure 6 shows the spatial linear scans of X-ray patterns of NiO at different pressures: (a) for 208 GPa, and (b) for 133 GPa after decompression. It is important to note here, that the pressure during the spatial scan across the phase boundary was constant. Taking into account the small beam spot size (2 × 4 µm2) we believe that the observed splitting of 012 reflection is caused by the coexistence of two different phases and is not related to the pressure gradient. We clearly observe a decrease of the intensity of reflections corresponding to the HP phase and consequent increase of LP reflections intensity when crossing the phase boundary (see Fig. 6). We show the V-P relation of NiO measured in nonhydrostatic experiment (run5) in Fig. 7. The unit cell volume decreases gradually with pressure increase. At ~210–220 GPa we observed a first-order iso-structural transition, which was accompanied by the volume drop of about 2.7%. The difference between the observed pressure values of the structural and the IMT8 phase transitions can be explained by overestimating the pressure of the resistive IMT and underestimating the pressure of the isostructural transition in the X-ray measurements. The overestimation is due to the specificity of the mechanism of formation of the conducting region in the sample through percolation and the underestimation of the transition pressure in the XRD measurements is caused by the pressure drop just after the phase transition. The careful considerations and detailed analysis of the exact pressure value of the structural transition is presented in the Supplementary Note 4.

In summary, from this analysis, we estimate the pressure value of the transition to be around ~225 ± 15 GPa. The Birch-Murnaghan equation of state was fitted to current experimental data, and its parameters were found as BLP0 = 216 ± 15 GPa, BLP’ = 4.3 ± 0.4 for low-pressure phase (LP) below ~210 GPa. For better comparison of LP an HP phases we performed the calculations with respect to 130 GPa and obtained the following parameters for the modified BM equation of state (see in the Supplementary Note 5) of LP phase: (V/V0)130 ~ 0.735, B130 = 693 ± 5 GPa, B’130 = 4 (fixed). Comparison with parameters for modified BM EOS for HP phase: (V/V0)130~ 0.717, B130 = 699± 7 GPa, B’130 = 4 (fixed). Here V0—cell volume of initial NiO at ambient conditions.

## Discussion

In summary, the structure of nickel monoxide NiO was investigated in a set of experiments at high pressures at room temperature. Different pressure media were used with different level of hydrostaticity. A first-order isostructural transition in NiO was discovered at 225 ±15 GPa.

The non-hydrostatic run5 provides very important information on the isostructural phase transition. Special attention should be paid to a careful and detailed consideration of this measurement. The experimental conditions of run5 agree mostly with the experimental conditions in our previous resistance measurements8, when IMT transition was observed. All these effects (Figs. 5 and 6) present strong evidence of the existence of the first-order structural transition in NiO in the pressure region above ~210 GPa.

We believe it is important to discuss several aspects of the theory and we provide such discussion below. Several preceding theoretical studies have tackled the problem of pressure effects on electronic correlations in simple oxides. Recent dynamical mean field theory calculations (DMFT) of MnO by Kunes et al.21 have demonstrated the importance of the spin-crossover effects induced by the increasing crystal field effects which overcome Hund’s exchange energy under pressure. Notably, it follows that the effective Hubbard energy (Ueff) may be strongly dependent on pressure, which is at odds with the predominant practice of considering Ueff as nearly pressure independent parameter15. Pressure-dependent U values have been derived by Ovchinnikov22,23 within a simple theoretical framework which takes into account crystal field effects. This approach has been supported by extensive experimental results for Fe-based oxide materials23,24. However, for a d8 configuration (a case for NiO) very little change in Hubbard energy is expected during compression23. It has been suggested that the Mott-Hubbard d-d energy U in NiO is comparable in magnitude to the p-d charge transfer energy Δ25,26, and NiO is situated on the borderline between Mott insulator and charge transfer insulator regimes. However, recent resonant inelastic scattering experiments27 indicate that the lowest energy gap Eg in NiO is related to the d-d charge transfer process between neighboring Ni sites strongly hybridized with the p-d charge transfer. The same authors claim that their result is compatible with LDA + U model having effective Hubbard U = 8 eV.

In the most recent theoretical study by the DMFT method, Leonov et al.12 have found transition pressure about 429 GPa for NiO, using U = 10 eV, J = 1 eV. However, they also point to significant reduction of the calculated transition pressure (to 248 GPa), if they use U = 8 eV, J = 1 eV instead. In their paper, they give a long list of references, which actually includes nearly 30 papers, to justify their choice of parameters U and J. However, going through that list of papers, we find very different suggested parameters, especially Hubbard U has quite a broad range from 7 to 10 eV in NiO. For example, the modeling of XAS spectra gives it as low as U = 7.6 eV28. It should be noted that since Leonov et al.12 give no further arguments in support of their choice of U = 10 eV for NiO, the very high predicted transition pressure for NiO is not reliable, given the fact that even their calculations produce transition pressure about 248 GPa for U = 8 eV, which is much closer to the experimentally reported pressure of IMT8 and to the reported values of the Hubbard U as discussed below. The resonant inelastic scattering experiments in NiO at ambient pressure27 provided Hubbard U = 8 eV. The high-pressure studies of the resonant inelastic scattering in NiO29 show that ~8 eV feature is almost independent on pressure and broadens dramatically above 60 GPa. Given all this experimental evidence, it is difficult to accept the value U = 10 eV as suggested by Leonov et al.12. As outlined above, our values of transition pressures from the XRD measurements and from the IMT8 transition confirm the recent theoretical studies by Leonov et al.12 by DMFT calculations with transition pressure about 248 GPa for NiO, using U = 8 eV, J = 1 eV.

In addition, we observed (run5) the coexistence of high- and low-pressure phases in the wide pressure range during decompression from ~230 to ~130 GPa. We also note that we observed a spatial separation of regions of pure high- and low-pressure phases at the same pressure values. The volume drop of about 2.65 % was observed in quasi-hydrostatic conditions, while in non-hydrostatic conditions the volume drop was about 2.7%. The observed structural transition is in a good agreement with the insulator-metal transition observed at 240 GPa in NiO recently8. It is generally believed that the structural transition is a result of Mott-type IMT transition8 which occurs when the effective Hubbard parameter is nearly equal to the total d8 bandwidth, or Ueff ~2 W. Notably, the high-pressure phase was observed during decompression down to ~130 GPa. We found a stratification of the sample into regions of pure high- and low-pressure phases at the same pressure value. It is known that the nanometer scale inhomogeneous regions in transition metal oxides are strongly linked to such phenomena as colossal magnetoresistance, and to the coexistence of several interactions between spin, charge, lattice, and orbital degrees of freedom, such as observed in cuprates30.

We would like to point out here that to our knowledge the electronic transitions in oxides at high pressures are accompanied in most cases by volume discontinuities and sometimes with very pronounced changes in the crystal structure. For example, MnO is another example of a transition metal oxide having isostructural electronic transition around ~105 GPa with 6.6% volume collapse (claimed to be a Mott transition), showing coexisting phases around the transition—see Fig. 5 in Ref. 31, and also “considerable” hysteresis effects on the release of pressure as claimed in the Ref. 32. Moreover, considering other types of electronic transitions, we observed such extreme cases as electronic spin transition accompanied with a structural change to amorphous phase recoverable to ambient pressure in YIG crystals33. Another example is electronic spin transition in NdFeO3 around 40 GPa having both volume collapse and significant hysteresis34. We can additionally give the example of the pressure-induced first-order isostructural Mott insulator-metal transition in cubic PbCrO3, accompanied by a sharp volume collapse which has been interpreted in terms of charge disproportionation in the low-pressure insulating phase35,36,37. These are not the only examples of the concomitant changes in the crystal structure at the electronic transition in transition metal oxides, however, it is extremely difficult to find an example of “pure” iso-structural electronic transition without volume discontinuity in oxides at high pressures. Thus, the hysteresis effects will vary from system to system and are very sensitive to pressure environment. Given the above examples, the behavior of NiO under pressure is not unusual. The “huge” nearly 100 GPa hysteresis in NiO in non-hydrostatic settings is remarkable, and future experiments may help to understand such behavior. Furthermore, the drop in pressure at the central part of the transformed sample is expected since after transition has happened, the volume of the sample in the central part has decreased and there is not enough plasticity in the sample to compensate this decrease by the flow of the material towards the center of the sample.

The spatial scale of regions of HP and LP phases in NiO is not identified at the moment, but the dimensions of the separated phases must be quite large according to the observed relatively narrow X-ray diffraction peaks. To understand the effects of stress on the phase separation, future studies should address the whole pressure interval of the coexistence of the HP and the LP phases in NiO in more hydrostatic pressure media to clarify the hysteresis effects of the reverse transition. Given the simplicity of the material and its fundamental importance to the understanding of strongly correlated electronic systems, our findings should stimulate further experimental and theoretical studies of NiO, a prototype Mott insulator.

## Methods

We used standard NiO powder supplied by “Alpha Aesar” company for sample preparation.

To perform XRD experiments under high pressure in five runs 1-5, NiO samples were loaded in five DACs38 with standard and beveled diamond anvils with different pressure transmitting media (Table 1 and Fig. 1). The detailed characteristics of synchrotron XRD experiments with NiO under high-pressures are presented in Table 2. Linear XRD scans through the NiO sample in run5 were made with 1 μm step. The powder XRD images were integrated to one-dimensional patterns using the FIT2D39 and DIOPTAS software40. The whole profile analysis of the diffraction data and the calculation of the unit cell parameters were performed in JANA200 program41 using the Le Bail method.