# Phase transitions of Fe\_2O\_3 under laser shock compression

Alexis Amouretti, Céline Crépisson, S. Azadi, Delphine Cabaret, T. Campbell, D. Chin, B. Colin, G. Collins, L. Crandall, Guillaume Fiquet, et al.

► To cite this version:

Alexis Amouretti, Céline Crépisson, S. Azadi, Delphine Cabaret, T. Campbell, et al. Phase transitions of Fe\_2O\_3 under laser shock compression. 2024. hal-04793717

HAL Id: hal-04793717

https://hal.science/hal-04793717v1

Preprint submitted on 29 Nov 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Phase transitions of Fe₂O₃ under laser shock compression

A. Amouretti,¹,²,* C. Crépisson,³,† S. Azadi,³ D. Cabaret,¹ T. Campbell,³ D. A. Chin,⁴ B. Colin,⁴ G. R. Collins,⁴

L. Crandall,⁴ G. Fiquet,¹ A. Forte,³ T. Gawne,³ F. Guyot,¹ P. Heighway,³ H. Lee,⁵ D. McGonegley,⁶ B. Nagler,⁵ J.

Pintor,¹ D. Polsin,⁴ G. Rousse,⁷,⁸ Y. Shi,³ E. Smith,⁴ J. S. Wark,³ S. M. Vinko,³,⁹ and M. Harmand¹,¹⁰

¹IMPMC, Sorbonne Université, UMR CNRS 7590, MNHN, 75005 Paris, France

²Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan

³Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK

⁴University of Rochester Laboratory for Laser Energetics, Rochester, NY, USA

⁵SLAC National Accelerator Laboratory, 2575 Sand Hill Rd, Menlo Park, CA 94025, USA

⁶Atomic Weapons Establishment, Reading, UK

⁷CSE Lab, UMR 8260, Collège de France, 75231 Paris Cedex 05, France

⁸Sorbonne Université, 4 place Jussieu, 75005 Paris, France

⁹Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, UK

¹⁰PIMM, Arts et Metiers Institute of Technology, CNRS, Cnam, HESAM University, 151 boulevard de l'Hopital, 75013 Paris (France)

(Dated: February 29, 2024)

We present in-situ x-ray diffraction and velocity measurements of Fe₂O₃ under laser shock compression at pressures between 38-116 GPa. None of the phases reported by static compression studies were observed. Instead, we observed an isostructural phase transition from α-Fe₂O₃ to a new α'-Fe₂O₃ phase at a pressure of 50-62 GPa. The α'-Fe₂O₃ phase differs from α-Fe₂O₃ by an 11% volume drop and a different unit cell compressibility. We further observed a two-wave structure in the velocity profile, which can be related to an intermediate regime where both α and α' phases coexist. Density functional theory calculations with a Hubbard parameter indicate that the observed unit cell volume drop can be associated with a spin transition following a magnetic collapse.

The phase diagrams of iron oxides are notoriously rich with a variety of electronic and structural transitions triggered by pressure or temperature. Due to its relevance to geophysical studies, Fe₂O₃ has been extensively studied under static compression using Laser Heated Diamond Anvil Cells (LH-DAC), up to approximately 113 GPa and 2800 K [1–3]. A series of phase transitions were observed, as well as a possible breakdown of Fe₂O₃ at high temperature into Fe₂₅O₃₂ and Fe₅O₇ [1]. Moreover, a Mott transition and a high-spin to low-spin transition have been evidenced at ~50 GPa, although it remains unclear if structural transitions are triggered by the electronic transition or vice versa [4–7]. The α-Fe₂O₃ phase (R3c) is stable up to 40 GPa. For this phase, a continuous decrease in the c/a ratio is observed with increasing pressure [8–12]. From 40 GPa to 47 GPa, the ι-Fe₂O₃ phase (Rh₂O₃-II type structure, Pbcn orthorhombic) is observed [1, 13]. Above ~54 GPa, the ι phase transforms into ζ-Fe₂O₃ phase (a distorted perovskite described in the monoclinic system [8]) stable up to 55 GPa. Above 50-60 GPa, the ζ-Fe₂O₃ phase transforms into η-Fe₂O₃ (Cmcm post-perovskite orthorhombic), while above 67 GPa the possibly metastable θ-Fe₂O₃ (Aba2 orthorhombic), is also observed in a limited region between approximately 1000 and 2000 K [1].

The behaviour of Fe₂O₃ under dynamic compression is less well understood and experimental results are scarce, largely due to the complexity of the target design. High-purity Fe₂O₃ samples in LH-DAC experiments are usually powders [2, 3, 5, 6, 14] or grown single-crystals [1]. In contrast, dynamic compression measurement re-

quire bulk, high-purity and homogeneous samples. These are hard to find naturally with the required stoichiometry [15], but are also challenging to synthesize at the relatively large (mm) sizes needed in experiments [16]. Nevertheless, gas gun measurements have been performed up to around 140 GPa [16, 17] showing a significant volume drop of ~10% at approximately 50 GPa, which may be indicative of a phase transition. Another study also reported a significant drop in resistivity at ~44-52 GPa using a double-stage light-gas gun on large natural Fe₂O₃ crystals [15]. However, the crystal structures of Fe₂O₃ under dynamic shock compression remain unknown, and it is unclear how these relate to the flurry of phases observed under static compression. In this letter we present in-situ time-resolved x-ray diffraction measurements in shock-compressed Fe₂O₃ using an x-ray Free Electron Laser (XFEL), at pressures between 38-122 GPa. Our results demonstrate that the behaviour of Fe₂O₃ is indeed very different under dynamic compression: we observe none of the high-pressure phases seen statically, and instead find a single new isostructural phase transition around 50-62 GPa, which we link to the collapse in magnetic ordering.

The experiment was performed at the Matter in Extreme Condition (MEC) end station of the Linac Coherent Light Source (LCLS) [18]. The shock was driven by two synchronized nanosecond lasers (527 nm) incident on the target at an angle of 20° and with a spot size of 300 µm. We used pulse durations of 5, 10 and 15 ns, with a maximum total energy of 60 J on target. In-situ x-ray diffraction (XRD) was performed using the x-ray beam
operating in self-amplified spontaneous emission mode, with a photon energy of 7.08 keV, a spectral bandwidth of 25 eV, and pulse duration of 50 fs FWHM [19, 20]. The x-rays were focused onto the target at an angle of 35° with a spot size diameter of 60 µm, overlapping the focal spot of the optical lasers to probe the planar shock front region. The diffraction signal was measured in transmission geometry on 4 quadruple ePix10k detectors. Azimuthal integration of 2D diffraction images was carried out including solid angle correction, Al filter correction, polarization, and self-attenuation from the target. When this was not possible, integration was performed using the Dioptas software, based on the PyFai library [21, 22], including solid angle correction and polarization. Two Velocity Interferometer System for Any Reflector (VISAR) [23] were used to retrieve the velocity history and the time when the shock left the sample. VISAR sensitivities were 4.5241 and 1.9890 km s⁻¹ fringes⁻¹, respectively, with acquisition time windows of 10 and 20 ns.

Two different target designs were used. The first consisted of 8 µm of Fe₂O₃ deposited on 54 µm of parylen-N. The second contained a 8 µm layer of Fe₂O₃ sandwiched between a 22.1 µm sapphire window on one side, and a 54 µm layer of parylen-N on the other. A 200 nm aluminum flash coating was applied to the front face of all targets to minimize direct heating by the laser prepulse. The Fe₂O₃ was deposited via a physical vapor deposition process, leading to a polycrystalline structure of columnar crystallites with a preferential orientation along the c-axis of the crystal, and perpendicular to the shock wave propagation given the geometry of our setup (for further details see Figs. S1-S8).

We show the radially integrated x-ray diffraction patterns of Fe₂O₃ under shock in Fig. 1, measured when nearly the entire Fe₂O₃ layer is shocked, but before shock breakout and release. The pattern recorded prior to the shock at ambient conditions is shown for comparison. At pressures below 42 GPa, the patterns (i) and (ii) show similar features to that of the ambient sample in terms of both peak positions and intensities. Nine α-Fe₂O₃ peaks are identified and shifted toward larger angles due to sample compression. Overall, strong peak broadening is observed in shocked samples, reminiscent of a decrease in crystallite size and an increase in micro-strain effects (lattice parameters fluctuations) under pressure [25, 26]. At intermediate pressures, patterns (iii) and (iv) show four additional peaks, indexed in red on pattern (iii). We attribute these to the appearance of a second kind of Fe₂O₃ phase, which we dub the α' phase, having the same crystallographic structure as α but a significantly lower volume. These mixed patterns are thus associated with two pressures depending on the phase. For pressures above 81 GPa, only four peaks corresponding to the α'-Fe₂O₃ are observed, with a significant shift toward larger angles due to larger compression. At 122 GPa, pattern (vii) also shows the appearance of a diffuse

<figure><img src="image_2.png" /><figcaption>FIG. 1. Radially integrated x-ray diffraction profiles of Fe₂O₃ under shock for targets with a sapphire window between 0-122 GPa. The vertical dotted lines correspond to the ambient α-Fe₂O₃ peak positions [24]. Miller (hkl) indices are displayed for the low- and high-pressure α structures in black and red, respectively. The inset highlights differences between patterns (ii) and (iv).</figcaption></figure>

signal at scattering angles of 45° (Q = 2.7 Å⁻¹) and 55° (Q = 3.4 Å⁻¹), which could be interpreted as an amorphous phase (2D diffraction data are shown in Fig. S9).

It was not possible to perform Rietveld refinements on the data due to the complex microstructure of the samples under shock. Instead, we performed Le Bail refinements, shown in Fig. 2, for data from targets without a sapphire window. At 47(1) GPa a decrease of c/a ratio for the compressed α-Fe₂O₃ phase is observed compared with ambient α-Fe₂O₃. At 94(2) GPa we identify an α-Fe₂O₃ structure with a significantly smaller volume than the α-Fe₂O₃ observed at 47(1) GPa (225.2 Å³ and 265.8 Å³, respectively). In both cases, the α-Fe₂O₃ structure [24] fits the compressed phase well (R_p = 12.4%). For data above 80 GPa, none of the high pressure phases of Fe₂O₃ reported under static compression were observed (θ-Fe₂O₃, η-Fe₂O₃, Fe₂₅O₃₂, or Fe₅O₇ [1]).

Velocity profiles at the Fe₂O₃/Sapphire interface for increasing laser intensities are shown as a function of time in Fig. 3. A double-wave structure is systematically observed in VISAR data when the mixing of the α and α' phases is detected in diffraction, as shown for shots in blue. The first wave is labelled P1 and the second wave P2. From the appearance of the α' phase, the P1 wave velocity remains constant at around 1.3 km s⁻¹ for all mixed shots regardless of the laser intensity. In contrast, the P2 wave velocity increases with laser intensity and its arrival time becomes shorter. The double-wave structure is also observed for targets without a sapphire window.
<figure><img src="image_3.png" /></figure>

FIG. 2. Le Bail refinements of two radially integrated x-ray diffraction patterns just after shock breakout, at pressures of 47(1) GPa and 94(2) GPa. Each pattern was fitted using two α-Fe₂O₃ phases with R3c symmetry: one for the α-Fe₂O₃ ambient at 0 GPa (bottom green tick marks) and one for the compressed α-Fe₂O₃ phase (top green tick marks). Rₚ factors were 10.5% and 12.4% for the 47 GPa and 94 GPa patterns, respectively. Fitted lattice parameters are a₀ = 5.03 Å; c₀ = 13.03 Å for ambient α-Fe₂O₃; a = 4.87(2) Å; c = 12.94(2) Å for 47 GPa; and a = 4.56(2) Å; c = 12.54(2) Å for 94 GPa.

dow, measured directly from the free surface of Fe₂O₃ (Fig. S8). This indicates that the double-wave structure is not due to the sapphire window, but is produced within the Fe₂O₃ layer at specific laser intensities. The splitting of the wavefront into two waves is characteristic of a phase transition with a volume change [27, 28]. We thus identify this observation as a signature of the α → α' phase transition, which is also observed in diffraction, and associate the P1 and P2 waves with the α and α' phases, respectively. The pressures in the α and α' phases can then be determined from the P1 and P2 velocities, similarly to previous work on Bismuth [29].

The unit cell volumes of the α-Fe₂O₃ and α'-Fe₂O₃ phases are plotted against pressure in Fig 4. The α-Fe₂O₃ phase is observed up to 54 ± 2 GPa, and the α'-Fe₂O₃ phase for pressures above 63 ± 2 GPa. We measure a (11.0 ± 1.4)% volume drop between the two phases, calculated from x-ray diffraction data showing both in coexistence. This volume drop indicates that the transition from α to α' is a first-order transition.

The volume drop is accompanied by a pressure gap of around 9 ± 3 GPa. This could be due to experimental detection limitations, such as 1) the VISAR etalon; 2) the temporal range restricted by the multiple waves in our sample design (see Fig. S4 of the supplementary) that might prevent the detection of the P2 waves with breakout time superior to the temporal range; or 3) the inherent laser-shocked x-ray diffraction peak broadness

<figure><img src="image_4.png" /></figure>

FIG. 3. Particle velocities measured at the rear of the Fe₂O₃ sample for the different pressure regimes. The time origin is set to the shock breakout time in the sapphire. In black we show a low-pressure shock where only a single α phase is observed in x-ray diffraction. The blue curves, taken at intensities between 1.9 and 2.4 TW/cm², correspond to thermodynamic conditions where both α and α' are observed in diffraction. The red curve corresponds to conditions where only a single compressed α' phase is observed. The double-wave structure is indicative of a phase transition.

that prevents small α' peaks to be observed. In addition, phase transitions under shock are also subject to temperature effects that might broaden the transition pressure range [27], as well as superheating, kinetic and plasticity effects [30–32] that might affect the onset pressure for α'-Fe₂O₃ synthesis.

Overall, our data yield larger unit cell volumes than previous shock data from gas gun experiments [17] as seen in Fig. 4. However, these previous measurements are intrinsically different to ours, either due to their time scale (ms or µs for gas guns) or by the nature of the measurements (optical and macroscopic compared with x-ray bulk and microscopic). In this work, the volume is extracted from the positions of the diffraction peaks. Further, we note that Fe₂O₃ single-crystals are known to behave differently depending on the relative alignment of the compression direction with the crystal axis [15]. Because of how our samples were deposited they do have a notable preferred orientation, and this may well affect the experimental compression values.

Figure 5 shows the evolution of *a*/*a*₀ and *c*/*c*₀, where *a* and *c* denote the lattice parameters under shock and *a*₀ and *c*₀ the parameters at ambient conditions. Both are deduced from Le Bail refinements. Below 54 GPa, the ratios for α-Fe₂O₃ are consistent with static compression data [11], and can be explained by bonding distortion or uneven modifications of the Fe-O-Fe bond lengths [8–12]. This pressure distortion effect is observed in other corundum-structured oxides [8, 33], and can lead to a
<figure><img src="image_5.png" /></figure>

FIG. 4. V/V₀ for α-Fe₂O₃ and α'-Fe₂O₃ determined from x-ray diffraction as a function of pressure, compared with other published work. Points corresponding to the observation of only the α-Fe₂O₃ phase are plotted in black, of only the α'-Fe₂O₃ phase in red, and of the coexistence of both phases in blue. The two empty symbols correspond to data points determined from the Le Bail fits shown in Fig. 2. A transition from α-Fe₂O₃ to α'-Fe₂O₃ phase is observed at 54-62 GPa. It is associated with a relative volume jump ΔV/V₀ equal to 11.0 % and pressure jump of ΔP ~ 9 GPa.

Mott insulator transition. A discontinuity of 3.6 % is seen between 54-62 GPa for a/a₀, in line with the observed volume drop between the α and α' phases shown in Fig. 4. No discontinuity is observed for c/c₀. Above 62 GPa we observe a change in the slope of c/c₀ with pressure, while the slope of the corresponding a/a₀ line remains unchanged. This indicates that the c-axis becomes less compressible in the new α' phase, and that the volume drop observed is mostly due to a strong decrease of the a lattice parameter.

As the transition is observed without change of symmetry, the α-Fe₂O₃ to α'-Fe₂O₃ transition could be electronically driven. Two electronic transitions are observed at 50 GPa in static compression experiments: a Mott transition and a simultaneous spin transition [7]. These transitions are not limited by the timescale required for atomic displacement, and can therefore be much faster than a structural transition. Moreover, it has been shown that Mott and spin transitions can lead to a significant volume collapse without structural change [7], as seen for example in MnO [34] and FeO [35]. To further investigate such electronic transitions, we performed DFT+U calculations [36–41] of α-Fe₂O₃. As our experimental data show only α-Fe₂O₃ phase, relaxation of cell parameters, atomic positions and magnetic state of iron was performed with R3c symmetry. Our simulations were performed using the v7.1 Quantum-Espresso suite [42, 43]. Scalar-Relativistic ultrasoft pseudopotential (PP) [44] were generated using the PBEsol exchange-

<figure><img src="image_6.png" /></figure>

FIG. 5. Lattice parameters for the α and α' phases as a function of pressure. All c/c₀ data are shifted vertically by -0.05 for clarity. Shock data are represented by solid blue dots (a/a₀) and empty blue dots (c/c₀). Dashed blue lines above 60 GPa are drawn to guide the eye. Lattice parameters for the α phase from static compression are given as solid black lines for ref. [8–10, 12] and black dotted line for ref. [11]. The results from DFT+U using a rhombohedral phase are given in red. The inset figure shows the relative magnetic moment of Fe from DFT+U as a function of pressure. The phase is high spin below 50 GPa, and low spin above 60 GPa.

correlation functionals [45] for Fe and O. The effective Hubbard U parameter was used for the Fe-3d orbitals, with the initial occupations given by the PP. We used a kinetic-energy cutoff of the plane-wave basis set of 100 Ry and an augmentation charge energy cutoff of 800 Ry. The calculations were carried out using a 12×12×12 k-point grid. The DFT+U calculations were performed at ambient pressure using U = 5 eV, leading to an energy band gap of 2.075 eV and magnetic moment per Fe atom of 4.41 µB, in agreement with experimental values of 2.14 eV and 4.6 µB, respectively [46, 47].

The results of the DFT+U calculations are shown in Figs. 4 and 5. All main features of interest observed experimentally around the phase transition at 50-60 GPa are reproduced in the simulations: we find a large V/V₀ volume drop (~10%), a discontinuity in the evolution of a/a₀ but without a change in compressibility, and a change in compressibility but without a discontinuity of c/c₀. While there remains some discrepancy in the absolute values for the calculated parameters, overall the simulations reproduce the observed trends with good fidelity. The volume drop between 50-60 GPa is correlated to a drop in the local magnetic momentum of iron, as shown in the inset in Fig. 5, decreasing by a factor of 5, i.e. changing from a high to a low spin state. Therefore, we posit that the α → α' transition could be explained by a spin transition from a high-spin rhombohedral phase (α-Fe₂O₃) to a low-spin rhombohedral phase (α'-Fe₂O₃)
being a low-spin corundum-structured phase). We note
that, in principle, the value of U in our simulations should
change with pressure. We performed similar calculations
for different values of U (1,3,5,7 eV), and find that while
this affects the pressure at which the transition takes
place, it does not change the calculated volume drop of
~10%, nor the change from high to low spin. While our
DFT+U calculations are not tailored to identify a Mott
transition, it is known from dynamical mean-field theory
calculations that the spin transition and the Mott tran-
sition are linked and occur simultaneously [48]. We thus
propose that the α → α' transition is an electronically
driven spin transition from high-spin to low-spin, possi-
bly associated with a Mott transition. Importantly, this
implies that the electronic transition will occur before
any structural transition takes place. Static compression
experiments reported simultaneous electronic (spin and
Mott transitions) and structural transitions (to η or θ-
Fe₂O₃ phases) [1–7]. Here our time-resolved experiments
show an electronic transition occurring before such struc-
tural transitions, proving that the electronic transition
implies the structural change as indicated by [6], and not
the other way around.

To summarize, we have presented *in-situ* time-resolved
x-ray diffraction measurements in shock-compressed
Fe₂O₃ up to 122 GPa, showing a clear difference in the
phase diagram compared with static compression exper-
iments. None of the high pressure phases seen statically
where observed dynamically. Instead, we observed an
isostructural α → α' phase transition around 50-60 GPa,
characterized by an 11% volume drop due to a high-spin
to low-spin transition, and, possibly, a Mott transition.
Our results thus show that the electronic transition(s) ob-
served in Fe₂O₃ under static compression around 50 GPa
still occur, but without the associated structural transi-
tions. These either cannot happen under dynamic laser
compression, or require timescales longer than those ac-
cessible in our experiment to form. The structures of
the θ and η phases differ significantly from the struc-
ture of the α phase: they are composed of FeO₆ prisms
and octahedra, whereas the α phase is only composed of
FeO₆ octahedra [1]. Our results thus suggest that the
fast electronic transitions (<1 ns) are the ones driving
the comparatively slower reconstructive structural tran-
sitions to the θ and η phases (>1 ns) [49], and not vice
versa.

Use of the Linac Coherent Light Source (LCLS), SLAC
National Accelerator Laboratory, is supported by the
U.S. Department of Energy, Office of Science, Office of
Basic Energy Sciences under Contract No. DE-AC02-
76SF00515. This project has received funding from the
European Research Council (ERC) under the European
Union's Horizon 2020 research and innovation program
(ERC PLANETDIVE grant agreement No 670787). This
work was supported by grants from Japan Society for the
Promotion of Science (JSPS). C.C., S.A., P.H., J.S.W

and S.M.V. acknowledge support from the UK EPSRC
under grants EP/P015794/1 and EP/W010097/1. T.G.
acknowledges support from AWE via the Oxford Cen-
tre for High Energy Density Science (OxCHEDS). T.C.
and S.M.V. acknowledge support from the Royal Soci-
ety. A.F. acknowledges support from the STFC UK
Hub for the Physical Sciences on XFELs. We thank
the microscopy, x-ray diffraction and PVD platforms at
IMPMC for support in producing and characterizing the
Fe₂O₃ samples. We also thank T. De Resseguier, R.
Smith, T. Vinci and A. Benuzzi-Mounaix for helpful dis-
cussions.

<footnote>* Amouretti A@eie.eng.osaka-u.ac.jp</footnote>

<footnote>† celine.crepisson@physics.ox.ac.uk</footnote>

<footnote>[1] E. Bykova, L. Dubrovinsky, N. Dubrovinskaia, M. Bykov, C. McCammon, S. V. Ovsyannikov, H. P. Liermann, I. Kupenko, A. I. Chumakov, R. Rüffer, M. Hanfland, and V. Prakapenka, Structural complexity of simple Fe₂O₃ at high pressures and temperatures, Nature Communications 7, 10661 (2016).</footnote>

<footnote>[2] S. Ono and Y. Ohishi, In situ X-ray observation of phase transformation in Fe₂O₃ at high pressures and high temperatures, Journal of Physics and Chemistry of Solids **66**, 1714 (2005).</footnote>

<footnote>[3] S. Ono, T. Kikegawa, and Y. Ohishi, High-pressure phase transition of hematite, Fe₂O₃, Journal of Physics and Chemistry of Solids **65**, 1527 (2004).</footnote>

<footnote>[4] M. P. Pasternak, G. K. Rozenberg, G. Y. Machavariani, O. Naaman, R. D. Taylor, and R. Jeanloz, Breakdown of the Mott-Hubbard State in Fe₂O₃: A First-Order Insulator-Metal Transition with Collapse of Magnetism at 50 GPa, Physical Review Letters **82**, 4663 (1999).</footnote>

<footnote>[5] J. Badro, G. Fiquet, V. V. Struzhkin, M. Somayazulu, H.-k. Mao, G. Shen, and T. Le Bihan, Nature of the High-Pressure Transition in Fe₂O₃ Hematite, Physical Review Letters **89**, 205504 (2002).</footnote>

<footnote>[6] A. Sanson, I. Kantor, V. Cerantola, T. Irifune, A. Carn-
era, and S. Pascarelli, Local structure and spin transition
in Fe₂O₃ hematite at high pressure, Physical Review B
**94**, 014112 (2016).</footnote>

<footnote>[7] E. Greenberg, I. Leonov, S. Layek, Z. Konopkova, M. P. Pasternak, L. Dubrovinsky, R. Jeanloz, I. A. Abrikosov, and G. K. Rozenberg, Pressure-Induced Site-Selective Mott Insulator-Metal Transition in Fe₂O₃, Physical Review X **8**, 031059 (2018).</footnote>

<footnote>[8] E. Bykova, M. Bykov, V. Prakapenka, Z. Konôpková, H.-P. Liermann, N. Dubrovinskaia, and L. Dubrovinsky, Novel high pressure monoclinic Fe₂O₃ polymorph revealed by single-crystal synchrotron X-ray diffraction studies, High Pressure Research **33**, 534 (2013).</footnote>

<footnote>[9] H. Liu, W. A. Caldwell, L. R. Benedetti, W. Panero, and R. Jeanloz, Static compression of alpha-Fe₂O₃: linear incompressibility of lattice parameters and high-pressure transformations, Physics and Chemistry of Minerals **30**, 582 (2003).</footnote>

<footnote>[10] P. Schouwink, L. Dubrovinsky, K. Glazyrin, M. Mer-
lini, M. Hanfland, T. Pippinger, and R. Miletich, High-
pressure structural behavior of α-Fe₂O₃ studied by single-</footnote>
crystal X-ray diffraction and synchrotron radiation up to
25 GPa, American Mineralogist **96**, 1781 (2011).

[11] G. K. Rozenberg, L. S. Dubrovinsky, M. P. Pasternak, O. Naaman, T. Le Bihan, and R. Ahuja, High-pressure structural studies of hematite Fe₂O₃, Physical Review B **65**, 064112 (2002).

[12] L. W. Finger and R. M. Hazen, Crystal structure and isothermal compression of Fe₂O₃, Cr₂O₃, and V₂O₃ to 50 kbars, Journal of Applied Physics **51**, 5362 (1980).

[13] E. Ito, H. Fukui, T. Katsura, D. Yamazaki, T. Yoshino, Y. Aizawa, A. Kubo, S. Yokoshi, K. Kawabe, S. Zhai, A. Shatzkiy, M. Okube, A. Nozawa, and K.-I. Funakoshi, Determination of high-pressure phase equilibria of Fe₂O₃ using the Kawai-type apparatus equipped with sintered diamond anvils, American Mineralogist **94**, 205 (2009).

[14] E. Boulard, M. Harmand, F. Guyot, G. Lelong, G. Morard, D. Cabaret, S. Boccato, A. D. Rosa, R. Briggs, S. Pascarelli, and G. Fiquet, Ferrous Iron Under Oxygen-Rich Conditions in the Deep Mantle, Geophysical Research Letters **46**, 1348 (2019).

[15] K. Kondo, T. Mashimo, and A. Sawaoka, Electrical resistivity and phase transformation of hematite under shock compression, Journal of Geophysical Research **85**, 977 (1980).

[16] R. C. Liebermann and E. Schreiber, Elastic constants of polycrystalline hematite as a function of pressure to 3 kilobars, Journal of Geophysical Research **73**, 6585 (1968).

[17] R. McQueen and S. Marsh, Handbook of Physical Constants (unpublished data), Geological Society of America Memoir **97**, 153 (1966).

[18] B. Nagler, B. Arnold, G. Bouchard, R. F. Boyce, R. M. Boyce, A. Callen, M. Campell, R. Curiel, E. Galtier, J. Garofoli, E. Granados, J. Hastings, G. Hays, P. Heimann, R. W. Lee, D. Milathianaki, L. Plummer, A. Schropp, A. Wallace, M. Welch, W. White, Z. Xing, J. Yin, J. Young, U. Zastrau, and H. J. Lee, The Matter in Extreme Conditions instrument at the Linac Coherent Light Source, Journal of Synchrotron Radiation **22**, 520 (2015).

[19] J. M. J. Madey, Stimulated Emission of Bremsstrahlung in a Periodic Magnetic Field, Journal of Applied Physics **42**, 1906 (1971).

[20] D. A. G. Deacon, L. R. Elias, J. M. J. Madey, G. J. Ramian, H. A. Schwettman, and T. I. Smith, First Operation of a Free-Electron Laser, Physical Review Letters **38**, 892 (1977).

[21] C. Prescher and V. B. Prakapenka, DIOPTAS: a program for reduction of two-dimensional X-ray diffraction data and data exploration, High Pressure Research **35**, 223 (2015).

[22] J. Kieffer, V. Valls, N. Blanc, and C. Hennig, New tools for calibrating diffraction setups, Journal of Synchrotron Radiation **27**, 558 (2020).

[23] L. M. Barker and R. E. Hollenbach, Laser interferometer for measuring high velocities of any reflecting surface, Journal of Applied Physics **43**, 4669 (1972).

[24] R. Blake, R. Hessevick, T. Zoltai, and L. Finger, Refinement of the Hematite Structure, American Mineralogist **51**, 123 (1966).

[25] K. Ichiyanagi, S. Takagi, N. Kawai, R. Fukaya, S. Nozawa, K. G. Nakamura, K.-D. Liss, M. Kimura, and S.-i. Adachi, Microstructural deformation process of shock-compressed polycrystalline aluminum, Scientific

Reports **9**, 7604 (2019).

[26] R. Briggs, M. Gorman, A. Coleman, R. McWilliams, E. McBride, D. McGonegle, J. Wark, L. Peacock, S. Rothman, S. Macleod, C. Bolme, A. Gleason, G. Collins, J. Eggert, D. Fratanduono, R. Smith, E. Galtier, E. Granados, H. Lee, B. Nagler, I. Nam, Z. Xing, and M. McMahon, Ultrafast X-Ray Diffraction Studies of the Phase Transitions and Equation of State of Scandium Shock Compressed to 82 GPa, Physical Review Letters **118**, 025501 (2017).

[27] Y. B. Zel'dovich and Y. P. Raizer, Shock waves in solids, in *Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena* (Elsevier, 1967) pp. 685–784.

[28] R. McQueen, S. Marsh, J. Taylor, J. Fritz, and W. Carter, The equation of state of solids from shock wave studies, in *High-Velocity Impact Phenomena* (Elsevier, 1970) pp. 293–417.

[29] M. G. Gorman, A. L. Coleman, R. Briggs, R. S. McWilliams, D. McGonegle, C. A. Bolme, A. E. Gleason, E. Galtier, H. J. Lee, E. Granados, M. Śliwa, C. Sanloup, S. Rothman, D. E. Fratanduono, R. F. Smith, G. W. Collins, J. H. Eggert, J. S. Wark, and M. I. McMahon, Femtosecond diffraction studies of solid and liquid phase changes in shock-compressed bismuth, Scientific Reports **8**, 16927 (2018).

[30] C. M. Pépin, A. Sollier, A. Marizy, F. Occelli, M. Sander, R. Torchio, and P. Loubeyre, Kinetics and structural changes in dynamically compressed bismuth, Physical Review B **100**, 060101 (2019).

[31] E. E. McBride, A. Krygier, A. Ehnes, E. Galtier, M. Harmand, Z. Konópková, H. J. Lee, H.-P. Liermann, B. Nagler, A. Pelka, M. Rödel, A. Schropp, R. F. Smith, C. Spindloe, D. Swift, F. Tavella, S. Toleikis, T. Tschentscher, J. S. Wark, and A. Higginbotham, Phase transition lowering in dynamically compressed silicon, Nature Physics **15**, 89 (2019).

[32] R. F. Smith, J. H. Eggert, D. C. Swift, J. Wang, T. S. Duffy, D. G. Braun, R. E. Rudd, D. B. Reisman, J.-P. Davis, M. D. Knudson, and G. W. Collins, Time-dependence of the alpha to epsilon phase transformation in iron, Journal of Applied Physics **114**, 223507 (2013).

[33] P. A. Cox, Transition metal oxides: an introduction to their electronic structure and properties, The International series of monographs on chemistry No. 27 (Clarendon Press; Oxford University Press, Oxford: New York, 2010).

[34] C. S. Yoo, B. Maddox, J.-H. P. Klepeis, V. Iota, W. Evans, A. McMahan, M. Y. Hu, P. Chow, M. Somayazulu, D. Häusermann, R. T. Scalettar, and W. E. Pickett, First-Order Isostructural Mott Transition in Highly Compressed MnO, Physical Review Letters **94**, 115502 (2005).

[35] K. Ohta, R. E. Cohen, K. Hirose, K. Haule, K. Shimizu, and Y. Ohishi, Experimental and Theoretical Evidence for Pressure-Induced Metallization in FeO with Rock salt-Type Structure, Physical Review Letters **108**, 026403 (2012).

[36] P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. **136**, B864 (1964).

[37] W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. **140**, A1133 (1965).

[38] V. Anisimov, J. Zaanen, and O. Andersen, Band theory and mott insulators: Hubbard u instead of stoner i, Phys.
Rev. B. **44**, 943 (1991).

[39] A. Liechtenstein, V. Anisimov, and J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in mott-hubbard insulators, Phys. Rev. B **52**, R5467 (1995).

[40] S. Dudarev, G. Botton, S. Savrasov, C. Humphreys, and A. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An lsda+u study, Phys. Rev. B **57**, 1505 (1998).

[41] M. Cococcioni and S. de Gironcoli, Linear response approach to the calculation of the effective interaction parameters in the lda+u method, Phys. Rev. B **71**, 035105 (2005).

[42] P. Giannozzi and et al., Quantum espresso: a modular and open-source software project for quantum simulations of materials, Journal of physics: Condensed matter **39**, 395502 (2009).

[43] P. G. et al., Advanced capabilities for materials modelling with quantum espresso, J. Phys.: Condens. Matter **29**, 465901 (2017).

[44] A. D. Corso, Pseudopotentials periodic table: From h to pu, Computational Materials Science **95**, 337 (2014).

[45] J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. **100**, 136406 (2008).

[46] D. Benjelloun, J.-P. Bonnet, J.-P. Doumerc, J.-C. Lau-nay, M. Onillon, and P. Hagenmuller, Mater. Chem. Phys. **10**, 503 (1984).

[47] J. M. D. Coey and G. A. Sawatzky, J. Phys. C **4**, 2386 (1971).

[48] J. Kuneš, D. M. Korotin, M. A. Korotin, V. I. Anisimov, and P. Werner, Pressure-Driven Metal-Insulator Transition in Hematite from Dynamical Mean-Field Theory, Physical Review Letters **102**, 146402 (2009).

[49] G. Burns and A. Glazer, Space Group Applications, in *Space Groups for Solid State Scientists* (Elsevier, 2013) pp. 187–274.