*Review* **A Short Review of Current Computational Concepts for High-Pressure Phase Transition Studies in Molecular Crystals**

#### **Denis A. Rychkov 1,2**


Received: 1 December 2019; Accepted: 29 January 2020; Published: 31 January 2020

**Abstract:** High-pressure chemistry of organic compounds is a hot topic of modern chemistry. In this work, basic computational concepts for high-pressure phase transition studies in molecular crystals are described, showing their advantages and disadvantages. The interconnection of experimental and computational methods is highlighted, showing the importance of energy calculations in this field. Based on our deep understanding of methods' limitations, we suggested the most convenient scheme for the computational study of high-pressure crystal structure changes. Finally, challenges and possible ways for progress in high-pressure phase transitions research of organic compounds are briefly discussed.

**Keywords:** high-pressure phase transitions; molecular crystals; computational methods; DFT and Force Field methods; energy calculations; intermolecular interactions

#### **1. Introduction**

High-pressure chemistry and particularly crystallography is developing fast in recent decades [1–3]. High-pressure effects are known to be studied originally and mainly by physicists and geologists [4,5]. Such significant interest in various minerals at high pressure and extreme temperatures is caused by questions that usually arise from geology—how substances act in Earth's crust and mantle and how do they transform further when temperature and pressure decreases. To describe mineral behavior, many theoretical and experimental works have been done, resulting in a deep understanding of the formation of our and other planets [6]. Among more practical results, one should point out equations of state (EoS) many of which were originally developed for minerals and combined in special software [7–10] but now used frequently in different fields [11–13].

Construction and functional materials are also known for both precise and vast investigations [14–16]. One can easily understand that many of the materials we use every day are exposed to relatively high pressures and sometimes high temperatures and, for sure, should be studied for possible undesirable phase transitions. Another application of high pressures is discovering new forms of different elements and substances, which may exhibit new valuable properties [17–22]. Stabilizing new forms obtained at high pressures at ambient conditions is an ambitious aim for applied science and industry—graphite transforming to diamonds is the most popular example of this possible process. The importance of finding and stabilizing new inorganic and metal-organic phases that may arise at high pressure is evident. These materials are almost in every part of different devices and constructions surrounding us.

Nevertheless, new forms of organic substances are also in demand by industry [23–25]. Production of different forms of active pharmaceutical ingredients is a hot topic of crystallography of organic substances and can be used in practice [25–28]. Among others, one can find the application of high-pressure being a non-trivial way for obtaining new polymorphs of desired substances [29–32]. Several groups are doing extensive work looking over many organic substances for new phases at high pressure. Nowadays, there are more than 1000 structures at high pressure according to the CCDC database, and its number is growing steadily [33].

Thus, one can understand that a high-pressure phase transition study in molecular crystals is an important field of modern chemistry and as any advanced direction should be studied both experimentally and computationally.

#### **2. The Main Research Directions**

High-pressure phase transitions can be studied mainly using two different concepts:

	- a. FF methods are implemented in PIXEL [36,37] and CrystalExplorer17 [38–40] software for convenient work with molecular crystals. Very accurate parametrization [39] makes these methods being reliable and very fast in the estimation of lattice energies of organic crystals.
	- b. DFT methods have many implementations for periodic systems, most popular are VASP [41–43], QuantumEspresso [44,45], CPMD [46], CASTEP [47] and CRYSTAL [48] codes, but researcher's choice is not limited to abovementioned software. Reasonable choice of level of theory (LOT), which combines many parameters, gives very accurate energies of investigated systems but requires much more resources and time in comparison to FF methods.

Here can be also mentioned many specific methods that can shed some light on different aspects of structures' nature or phase transitions, including electron/charge density analysis [49,50]. Nevertheless, these methods are relatively rarely used for molecular crystals at high-pressure conditions and have a specific discussion in literature [51,52], thus would not be described further in this work. We also do not describe molecular dynamics (MD) methods which are very useful [53–55], having not much experience in these methods. Modern machine learning and big data approaches are also not specified here, showing significant progress in the crystal structure and properties prediction, but not being applied to high-pressure phase transitions in molecular crystals [56–60].

Important to understand that both computational DFT and FF methods can barely be used without experiments being done at all because atom coordinates are needed for calculations [13,61]. Nevertheless, computational methods should be used when possible to understand and explain the nature of phase transitions of molecular crystals at high pressure because crystallographic and spectroscopic data rarely gives unambiguous reasons for phase transitions and can be interpreted differently by different scientific groups [61–67].

#### *2.1. Force Field Methods*

Force Field methods represent the functional form and parameter sets used to calculate the potential energy of a system of atoms or coarse-grained particles in molecular mechanics and molecular dynamics simulations. They are known widely due to their implementation in molecular dynamics for different systems, including biological ones [68,69]. Much less known but still frequently used "static" FF methods can evaluate lattice energies and some properties of molecular crystals [70–74]. The first successful attempt (accepted by the scientific community) was made by A. Gavezzotti, showing AA-CLP method for very fast evaluation of lattice energy and enthalpy of molecular crystals, based on atomic charges [36]. In this work [36], it has been postulated that "*Structural papers with discussions of crystal packing involving user-selected atom–atom distances or geometries only should no longer be allowed in the literature*" and gave the right direction of further research on molecular crystals and their forms. Later this method was substituted by more precise and sophisticated PIXEL [37], which used electron density for energy evaluation and Gaussian software [75] as a backend for this type of calculations. The energy of pair-wise interactions was described as a sum of different terms (Etot = Eele + Epol + Edis + Erep), which are given in analytical form [37]. Summation of these pair-wise interactions over a cluster of molecules in the crystal structure of radius equal to 20–50 A<sup>3</sup> (depending on the system) gives total lattice energy (Etot). This leads to a very fast estimation of energies and, what is more important, to the "chemical" partition of different energy terms. Definitely, this very clear energy concept together with DFT was applied to high-pressure research to find the reasons for phase transition at extreme conditions [67,76,77]. One of the pioneer works in this direction was done by Wood et al. [67] who combined experimental study with extensive computational work, where both DFT and FF methods were used. Relatively good convergence with DFT methods has been shown, taking into account some limitations applied to DFT optimization procedure. Moreover, energies of structures of L-serine polymorphs were reasonable and close for both DFT and PIXEL calculations. The most valuable feature is that the energy of intermolecular interactions can be monitored for experimental structures at different pressures, and it is possible to divide into chemically sensible terms and visualize using new CE17 implementation [40]. Another important feature is the possibility to monitor the energy of any pair-wise interaction in the crystal structure and thus follow phase transitions at high pressure at a molecular level. If one needs to understand deeply what the reason for a phase transition is and why some interactions or H-bonds are broken and new appeared, energy calculations are mandatory and should be done if atom coordinates are known for different crystal phases at high pressures.

Nevertheless, one should understand that despite FF methods are very fast and relatively easy to use, they should be checked carefully for specific tasks, one of which is high-pressure research. Energy is written as a summation of different terms with coefficients Etot = keleEele + kpolEpol + kdispEdisp + krepErep, where ki is parametrized on DFT energies or experimental enthalpies (depending on implementation) for molecular crystals at *ambient* conditions. H-bond length is also parametrized for ambient condition calculations, and cannot be switched off due to the very low precision of X-ray experimental measurements in defining hydrogen bond lengths. Summing up, an extensive benchmark on high-pressure data is needed to use FF methods unambiguously for high-pressure research in molecular crystals or should be critically checked by DFT calculations.

#### *2.2. DFT Methods*

In contrast to FF methods, DFT calculations for systems with periodic boundary conditions prove to give very accurate energies if multiple parameters are used correctly [78–82]. Discussing any phase transition, we assume that Gibbs energy change should be negative for spontaneous phase transition, which can be estimated from enthalpy and entropy terms. Entropy term is frequently neglected (especially if space group preserves after phase transition), supposing to have a small impact on Gibbs energy, while enthalpy can be calculated relatively easy [61,67,80,81,83]. Nevertheless, a lack of entropy calculations can lead to significant mistakes in the prediction of phase stability, which was shown for many inorganic materials [84,85]. The introduction of thermal effects in phase stability (DFT-QHA) increases computational costs drastically, but phonon effects are crucial to define accurate thermodynamic properties and Gibbs energies [86]. Calculation of all terms of Gibbs energy is strongly recommended to correctly predict stability and (subtle) phase transitions at high-pressure and temperature conditions [85,87,88]. Thus, the enthalpy diagram should be used as the first step of an investigation. Enthalpy is a sum of internal energy and PV term, where internal energy can be described

as lattice energy—a sum of intermolecular and intramolecular (conformational) interactions. The thing that can be calculated using FF methods is intermolecular interactions only, while conformational (relaxation) energies should be calculated using DFT methods [80,81]. Constant-pressure (or, more precisely, fixed-stress) geometry optimization has to be carried out in DFT energy calculations to accurately define static pressure. Then, P-V-T EoS of the substance must be known via phonon dispersion calculations to define total pressure as a sum of static, zero-point and thermal contributions. Correct assessment of PV term at high-pressure and temperature conditions could be rather complex and expensive from a computational point of view and could strongly affect P-T location of phase transition boundaries [88]. Despite the abovementioned statements were supported mostly by examples from inorganic materials, we do not see any significant difference when these calculations applied to molecular crystals. Following Gibbs energy contributions can lead to a new understanding of reasons for phase transitions for any crystalline material. In some cases, it is possible to claim volume change (PV), energy (Einter or Eintra), enthalpy (H) or entropy (S) as a driving force for phase transition [61,67,81,89]

DFT methods can be applied to experimental structures, obtained at some pressure, and all the above-mentioned parameters can be calculated. If one needs thermodynamic parameters for crystal structure at a pressure where no experimental data available, there are two main possibilities. The first is to calculate the equation of state for the phase and estimate the volume of the system, which will be fixed during ionic relaxation (structure optimization) to obtain energies. It is important to note that all calculations, in this case, should be performed for fixed unit cell volume. This technique is dependent on the accuracy of the equation of state, which needs at least 5–7 pressure-energy points within a pressure interval of a couple of GPa [90]. In this case, the quality of experimental data is very important because it influences the whole procedure of calculations. More convenient and independent from the number and quality of experimental data is the procedure with programmed pressure, e.g., as a starting structure can be taken one at ambient conditions and optimized to programmed pressure of, e.g., 3 GPa (e.g. PSTRESS option at VASP package). It was shown before that this kind of optimization to programmed pressure works accurately [61,91]. In this case, the volume is not fixed. In the case of DFT calculations enthalpy, the sum of inter- and intramolecular interactions (Ucrystal), entropy and PV term are obtained, which may give unambiguous answers with reasons for a pressure-induced phase transition. It is recommended to verify computational parameters (functional, dispersion correction scheme, k-points, and Ecutoff, etc.) on the structure, which is used as a guess structure for further calculations, usually ambient-pressure experimental data. One of the most important parameters is dispersion correction, which is crucial for accurate simulation of molecular crystals at ambient and non-ambient conditions. Nowadays, highly sophisticated density functionals are available to account for dispersive interactions in DFT (e.g., DFT-D3, B3LYP-D\*, HF-3c, DFT-TS, M06, etc.) [92–99].

In relation to FF methods no "chemical" (electrostatic, polarization, dispersion, repulsion) terms are obtained in case of DFT calculations, but in common case gives more reliable energies. The advantages and disadvantages of DFT and FF methods applied to high-pressure researches are summarized in Table 1.

**Table 1.** Advantages and disadvantages of DFT and FF methods applied for high-pressure research of organic substances.


<sup>1</sup> not mandatory if programmed pressure is used during optimization procedure but preferable for selection of parameters of optimization [61]. <sup>2</sup> Not implemented in PIXEL and CE17 software.

#### *2.3. Combined Techniques*

Recently we suggested the scheme where different phases are simulated not only in the intervals of their stability according to experimental data but also *out of these intervals* [61], and used it later for another system [91]. To the best of our knowledge, these are the first examples of such calculations for organic systems, studying intrinsic vs. extrinsic phase stability of polymorphs for molecular crystals. Nevertheless, it is widely used for inorganic systems, e.g., [85,100]. This helps to understand what would happen to the polymorph structure if no phase transition occurs. Such simulation provides structural and energy data to direct comparison of all phases at the same conditions, even if some phases are not found at these pressures experimentally (Figure 1).

**Figure 1.** Schematic representation of calculated energy parameters (ΔUcrystal, ΔH, etc.) for different phases in the whole pressure range, even at pressures where a specific phase is not found experimentally. Solid dots filled with color, starting experimental structure for DFT optimization; solid empty dots, DFT optimized structure at fixed pressure as observed experimentally; dashed dots, DFT optimized structure at fixed pressure out of experimental pressure range. Blue, phase I; green, phase II; red, phase III. Dashed squares show pressure-energy conditions close to high-pressure phase transitions.

In previous work, we also simulated pair-wise interactions using DFT gas-phase calculations with fixed geometries after solid state optimization. This simulation shows energy changes when distance decreases at pressure, building energy well for each H-bond [61]. This kind of energy well simulation is definitely not perfect due to the absence of molecular conformation change because of the molecular surrounding. This possibly could be also simulated using FF methods as described before and was done in other works [67,80,81,101].

Summing up, we suggest that the following scheme should be applied for high-pressure phase transition research of molecular crystals (Scheme 1).

**Scheme 1.** A suggested scheme for the computational study of high-pressure phase transitions of molecular crystals. All steps are calculated for structures both in and out of structural stability regions.

Finally, we would like to point out that scrupulous checks for the validity of all parameters and methods should be done for every particular system. If this is done correctly, one can assume *this computational scheme is a numerical experiment* aimed at understanding the reasons and mechanisms of phase transitions of molecular crystals at high pressure.

In this review, we put aside many questions related to high-pressure polymorphism of organic compounds: kinetic barriers for phase transitions which play an important role [102–105], temperature corrections for DFT methods [106–108], prediction of new phases (which in future can significantly decrease amount of experimental work) [109–111], etc. Nevertheless, as it is shown above, current computational methods can bring out many more answers than pure experimental results.

#### **3. Prospects**

To the best of our knowledge, there is no specific method or software for computationally studying high-pressure phase transitions in molecular crystals. Still, wise usage of already developed methods and their implementations with appropriate validation of different parameters can unveil reasons and even some mechanisms for phase transitions. We hope that in the future all experimental works be complemented with computational techniques. This may bring out true reasons and a deep understanding of already observed phase transitions and the prediction of new polymorphs. Finally, taking into account progress in crystal structure prediction [109,112], one can expect the prediction of new structures of molecular crystals at extreme conditions. Nevertheless, we are sure that the concept shown in this work gives the most convenient and all-round scheme for high-pressure research of organic compounds using computational methods and can be improved by obtaining different more specific properties: mechanical, electronic, optical, etc. Finally, we do not see any issues that can prevent usage of the proposed scheme for metal-organic and inorganic materials if proper parameters of the simulation are chosen.

**Funding:** Funding for this research was provided by Russian Science Foundation grant No. 18-73-00154.

**Acknowledgments:** The Siberian Branch of the Russian Academy of Sciences (SB RAS) Siberian Supercomputer Center is gratefully acknowledged for providing supercomputer facilities (http://www.sscc. icmmg.nsc.ru). The author also acknowledges the Supercomputing Center of the Novosibirsk State University (http:// nusc.nsu.ru) for provided computational resources. ISSCM SB RAS is acknowledged for free access to the literature used for this review.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**



© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Review* **Pressure-Tuned Interactions in Frustrated Magnets: Pathway to Quantum Spin Liquids?**

#### **Tobias Biesner \* and Ece Uykur**

1. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany;

ece.uykur@pi1.physik.uni-stuttgart.de

**\*** Correspondence: tobias.biesner@pi1.physik.uni-stuttgart.de

Received: 30 October 2019; Accepted: 21 November 2019; Published: 18 December 2019

**Abstract:** Quantum spin liquids are prime examples of strongly entangled phases of matter with unconventional exotic excitations. Here, strong quantum fluctuations prohibit the freezing of the spin system. On the other hand, frustrated magnets, the proper platforms to search for the quantum spin liquid candidates, still show a magnetic ground state in most of the cases. Pressure is an effective tuning parameter of structural properties and electronic correlations. Nevertheless, the ability to influence the magnetic phases should not be forgotten. We review experimental progress in the field of pressure-tuned magnetic interactions in candidate systems. Elaborating on the possibility of tuned quantum phase transitions, we further show that chemical or external pressure is a suitable parameter in these exotic states of matter.

**Keywords:** quantum spin liquids; frustrated magnets; quantum phase transitions; high-pressure measurements

#### **1. Introduction**

Quantum spin liquids (QSLs) possess nontrivial ground states, where a local order parameter does not exist. Moreover, it is not possible to observe spontaneous symmetry breaking even at very low temperatures. It is often thought that the QSLs are associated with topological phase transitions [1,2]. This make these systems a point of interest, and experimental evidences of this state are one of the central topics in the condensed matter physics.

QSLs are discussed in the framework of strongly correlated electron systems, while they are Mott insulators with half-filled electronic bands, and the electron–electron correlations play an important role. Possessing rich physics and properties, QSLs are subject to extensive experimental and theoretical efforts. This also bring the search for candidate materials, especially in 2D or 3D. The geometrically frustrated materials, where the resonating valance bond (RVB) model [3] is applicable, and the Kitaev QSL candidates, where the Kitaev physics [4] is relevant, are two groups of materials of which the candidates are searched for.

Technically speaking, it is difficult to identify the QSL state, as one needs to reach absolute zero temperature that is not achievable. Therefore, within the experimentally reachable limits, temperatures far below (2–3 orders of magnitude) the temperature that identify the magnetic exchange coupling (preferably antiferromagnetic (AFM) spin interactions) are assumed to show properties at the zero-temperature limits. The first step is to deduce the magnetic exchange coupling constant from the high-temperature behavior of the material via magnetic susceptibility measurements. To identify a QSL state, it is crucial to verify that there is no magnetic ordering or spin freezing down to very low temperatures. Magnetic susceptibility measurements are used initially to check the condition, where the absence (or existence) of a magnetic ordering can be identified. Absence of a sharp *λ*-type peak in specific heat vs. temperature curves is another indication of the absence of a magnetic ordering, albeit exceptions exist in the case of topological phase transitions [5]. Specific heat is a useful probe; while it can give insight to the absence of a long-range magnetic order, examination of the entropy release at the measured temperature can also help to estimate the possibility of the system to establish a long-range magnetic order at low temperatures. Beside the above mentioned macroscopic probes, more local probes such as muon spin relaxation and nuclear magnetic resonance are usually in play to detect the possible spin freezing or order. Neutron diffraction is also used to detect magnetic ordering.

While the absence of the long-range magnetic ordering is the first step to check, it is still not very satisfactory to establish a system as a QSL, while in principle, disorder effects can also give rise to such ground states without a long-range magnetic ordering. Another aspect that defines the QSL state is the fractional spin excitations, which might also be the key point to identifying this state more confidently. For instance, spinons predicted within the RVB model are worth seeking. They are fermionic quasiparticles carrying fractional spins with their own dispersion expected to give low-lying excitations and can be eventually used to identify the QSL state.

This review will mainly focus on the inorganic systems of the frustrated lattices, such as pyrochlore, triangular, honeycomb, and kagome compounds. Several review articles are already written on this topic [6–11], while this particular one aims to bring together the published works and to present the ongoing discussion of the QSL state emerging under high pressure. However, owing to the fact that the QSLs are Mott insulators and in light of theoretical proposals [12] that they are the parent states of the high-temperature superconductivity, organic conductors also are promising candidates to search for. Moreover, external pressure has already been successfully used to tune these systems to a superconducting state, albeit the high-temperature superconductivity could not be achieved. Although, it is still experimentally challenging to prove whether the Mott insulator ground state is QSL, the lack of magnetic ground states have been reported by nuclear magnetic resonance (NMR) measurements for several organic charge transfer salts. The QSL state and its evolution with external and/or chemical pressure have been discussed extensively in several review articles [13,14].

In this review, we would like to discuss the search of QSL state from another perspective, from a rather indirect route. Within the search of QSL candidates, many others also come into light that eventually are proven to be not a QSL. On the other hand, they already are very close to the conditions in which are searched for the realization of the QSL state. Perhaps a fine tuning in certain parameters, such as magnetic exchange interactions, lattice parameters, etc., can push these closer to the QSL state. Here, we look into the external pressure as this tuning mechanism. Pressure is generally accepted to be a clean tuning parameter of structural properties and electronic correlations. While it can be compared to the chemical doping effects in some cases, it allows one to eliminate the additional disorder introduced via chemical doping. In this review, we want to discuss the recent progress of the high-pressure studies, especially on the frustrated magnets, systems that are often studied in the search of the QSL candidates. We want to focus on the following questions: How does the pressure affect the frustrated systems? Which phases can we tune? Can we tune magnetic interactions directly? How do chemical and external pressure differ? Finally, can we use external pressure as a pathway to realize QSLs?

#### **2. Pyrochlore Lattice**

The pyrochlore lattice is a prime example for frustrated magnetism in three dimensions. While classical spin ice states are realized in Ho2Ti2O7 and Dy2Ti2O7 [15,16], Yb2Ti2O7 is a candidate system for a quantum spin ice ground state. Here, the magnetic monopoles, obeying an ice rule, become long-range entangled. Necessary conditions for such a quantum mechanical state are small spin quantum numbers and quantum fluctuations within the degenerated ground state manifold. Yb2Ti2O7 hosts a minimal *S* = 1/2 spin of the crystal field Kramers doublet (Yb+<sup>11</sup> <sup>3</sup> ). Strong quantum fluctuations are mediated by anisotropic exchange interactions and an XY g-tensor [17]. Considering the magnetic ground state, a sample-dependency possibly induced by disorder (e.g., excess magnetic ions in the stuffed pyrochlore lattice) might explain different reported results. In particular, ordered ferromagnetic ground states were reported for single-crystal samples, while polycrystalline powders showed no indication of a spin freezing. Kermarrec et al. [17] combined muon spin relaxation (*μ*SR) and neutron diffraction measurements under pressure to explore the low-temperature ground state of Yb2+*x*Ti2−*<sup>x</sup>*O7. Figure 1a shows a pressure-dependent phase diagram. Upon cooling, the paramagnetic state vanishes and most of the Yb magnetic moments were found to be in a fast fluctuating regime even down to low temperatures, reminiscent of a QSL state. Under hydrostatic pressure, pristine samples undergo a transition from this nonmagnetic ground state to a splayed ice-like ferromagnet (the magnetic moments are sketched in Figure 1a). Figure 1b shows the pressure dependency of a developing magnetic fraction upon cooling, leading to the magnetically ordered phase. By applying pressure a freezing of magnetic moments, increasing the magnetic fractions is observed. Additionally, the freezing temperature (defined as a fraction of 50% frozen out magnetic moments) increases with pressure. In contrast, in the stuffed compound (*x* = 0.046), no transition is observed up to the maximal pressure of 2.41 GPa. This study shows how fragile the balance of anisotropic exchange in the quantum spin ice Hamiltonian on the pyrochlore lattice can be against external or chemical pressure. Remarkably, the lattice structure is not expected to change noticeably in the low-pressure range. A structural phase transition is observed only above 29 GPa [18]. This illustrates that pressure is an effective tool to tune magnetic exchange interactions directly.

Chemical pressure on Yb2X2O7 (*X* = Sn, Ti, Ge) was probed on polycrystalline samples [19]. While the *X* = Ti and Sn samples order into a ferromagnet at 0.13 K and 0.25 K, respectively, Yb2Ge2O7 exhibits an antiferromagnetic ground state below 0.62 K. Different to the physical pressure, the lattice parameter increases for the Sn compound and decreases for the smaller Ge4<sup>+</sup> ion. In general, a decreasing Curie–Weiss temperature was found with increasing lattice parameter.

Note that there are other high-pressure studies on the pyrochlore lattice (A2B2O7, A = Eu, Dy; B = Ti, Zr) [20].

**Figure 1.** Results of *μ*SR experiments on Yb2+*x*Ti2−*<sup>x</sup>*O7: (**a**) The pressure-dependent phase diagram hosts three phases in the experimental accessed range. Under ambient pressure, the compound shows a ground state with large quantum fluctuations reminiscent of a quantum spin liquid (QSL) which freezes under pressure in favour of a canted ferromagnet. The dashed purple line marks the hypothetical transition for the stuffed compound *x* = 0.046. (**b**) As the ordered phase is approached, the magnetic fraction gets enhanced due to pressure. The freezing temperature (dashed line) is furthermore increased at the high-pressure side. Graphs are reproduced from Reference [17].

*2.1. Tb*2*Ti*2*O*<sup>7</sup>

**Figure 2.** (**a**) The magnetic phase diagram of single crystalline Tb2Ti2O7 under hydrostatic pressure *Pi* = 2.4 GPa and uniaxial stress *Pu* = 0.3 GPa: Under pressure, an ordered AFM ground state forms below *TN*. With a magnetic field of 0.6 T, the AFM order gets lifted in favour of a canted ferromagnet. (**b**) Spin structure of Tb tetrahedron under pressure: The AFM structure (red arrows) is formed under a pressure of *Pi* = 2.4 GPa and uniaxial stress *Pu* = 0.3 GPa along the [011] axis (green arrow). (**c**) Canted ferromagnet for an additional field *H* = 4 T parallel to *Pu*: Blue spheres indicate Tb sites; principal axes of the cubic cell consisting of 4 Tb tetrahedra are indicated by black arrows. Graphs are reproduced from Reference [21].

The low-temperature ground state of the spin liquid compound Tb2Ti2O7 has been extensively studied but remains intriguing. With an antiferromagnetic Curie–Weiss temperature of *θCW* = −13 K (respectively <sup>−</sup>19 K, including crystal field contribution) and Ising-like 5 *<sup>μ</sup><sup>b</sup> Tb*3<sup>+</sup> spins of the crystal-field doublet, the compound, however, shows no onset of static order down to at least 43 mK [22–26]. Interestingly, antiferromagnetic short-range correlations are set below 50 K [22]. Various suggestions to explain the missing Néel state have been given (see Reference [27] and references herein): a quantum spin ice state [28], structural distortion [29], or magnetoelastic excitations [30]. Mirebeau et al. extensively investigated the enigmatic nonmagnetic ground state by disturbing it by means of pressure and magnetic field [21,31–33]. Here, pressure is used to destabilize the balance of superexchange, crystal-field interactions, and dipolar coupling between neighbouring *Tb*3<sup>+</sup> cations. With a decreasing lattice constant of 1% at 8.6 GPa and preserved *Fd*3*m* symmetry, the effect of pressure on the crystal structure was found to be rather small [31,34]. Neutron diffraction on polycrystalline samples under pressure reveals a complex antiferromagnetic structure below *TN* = 2.1 K, coexisting with the spin liquid ground state. Bragg peaks of this antiferromagnetic structure are observed for a surprisingly low pressure of 1.5 GPa [31]. Interestingly, the Néel temperature seems to be insensitive to hydrostatic pressure but depends on applied strain [21,32]. Moreover, experiments on single crystals [21] show that a combination of isotropic and uniaxial pressures is crucial for disturbing the spin liquid ground state since hydrostatic pressure alone does not introduce a magnetic order in the single crystals.

Combining a magnetic field parallel to uniaxial stress of *Pu* = 0.3 GPa along the [011] direction and an isotropic pressure component of *Pi* = 2.4 GPa leads to suppression of the antiferromagnetic structure in favor of a canted ferromagnet (see the phase diagram in Figure 2a). Simultaneously, *TN* gets increased under magnetic field. Mirebeau et al. argue that, while the dipolar interaction is only weakly affected by pressure, superexchange is strongly influenced. The effect of pressure on the spin structure of the Tb tetrahedron is shown in Figure 2b,c, with and without magnetic field parallel to *Pu*, respectively. Here, the isotropic compound increases exchange energy about *d J JdP* <sup>=</sup> 0.07 GPa−1. A uniaxial strain along the [011] axis lifts the geometrical frustration by compressing 1/3 of Tb–Tb bonds of about 0.3% (for *P* = 0.3 GPa) and by decreasing the remaining 2/3 by about 0.1%. Due to this lifting of frustration, magnetic order is introduced. With increase of magnetic field, the spins are further reoriented in the canted ferromagnetic structure (Figure 2c).

Compared to physical pressure, the effect of chemical pressure on the ground state of Tb2Ti2O7 is different [27,33,35]. A negative chemical pressure for the case of replacing titanium by the larger tin leads to lattice expansion. Despite antiferromagnetic interactions at higher temperatures leading to a Curie–Weiss temperature between −11 to −12 K, the compound shows a ferromagnetic contribution in 37% of the Tb3<sup>+</sup> spins below a transition temperature of 0.87 K. Together with an antiferromagnetic "two in, two out" ice rule, these ferromagnetic domains form the magnetic ground state. Possibly, the compound orders because of the weakened antiferromagnetic exchange compared to the pure Tb2Ti2O7 sample and because of a distortion of the local crystal field [33]. A positive chemical pressure is reached by substituting titanium with germanium, leading to a smaller lattice constant [27]. The contraction was found to be larger (2%) compared to a physical pressure of 8.6 GPa (1% cf. Reference [21]). The reduced Tb–Tb distance results in a stronger antiferromagnetic exchange as indicated by a higher Curie–Weiss temperature of −19.2 K compared to Ti and Sn compounds. Different from the physical counterpart, positive chemical pressure here induces short-ranged ferromagnetic correlations, coexisting with the liquid-like correlations, as observed by neutron scattering [27]. Similar to Tb2Ti2O7, no long-range order is observed down to 20 mK.

#### *2.2. Dichalcogenides*

**Figure 3.** Phase diagram of 1T-TaS2 under pressure: Pressure decreases the swelling of the planes related to the David-star pattern (sketched above and below the diagram). In the light grey areas, deformations are reduced or completely suppressed. Mott phase and CCDW state are suppressed over 0.8 GPa, as the NCCDW state stabilizes between 1–7 GPa. Here, hexagonal domains are formed (see sketch). As the pressure is further increased, the superconducting state develops (with a *Tc* of about 5 K). Superconductivity remains stable up to 25 GPa, with a metallic state above *Tc*. Graphs are reproduced from Reference [36].

Transition metal dichalcogenides (TMDs) attract great attention [37]. Due to the complex interplay of charge, spin, and orbital degrees of freedom, they display a rich phase diagram ranging from charge density waves (CDW), superconductivity, Mott physics, and possibly QSLs [38].

The two-dimensional 1T-TaS2 exhibits multi charge density wave ground states [39], which can be continuously manipulated via external stimuli, such as temperature, chemical [40,41] or optical doping [39], disorder [42], and hydrostatic pressure [36,43]. Under ambient pressure, the compound shows metallic behavior in the high-temperature range. Below 550 K, an incommensurate charge density wave (ICCDW) superlattice develops. As resistivity increases, the ICCDW undergoes a transition to a nearly commensurate order (NCCDW) around 350 K. The low temperature range is governed by Mott physics in the commensurate charge density wave (CCDW) [36]. Thus, a simple model is the Mott–Hubbard Hamiltonian:

$$H = -\sum\_{,\rho} t\_{i,j} \left( c\_{i\sigma}^{\dagger} c\_{j\sigma} + h.c. \right) + lI \sum\_{i} n\_i \left( n\_i - 1 \right). \tag{1}$$

The first term accounts for a hopping between two adjacent lattice sites < *i*, *j* > and can be interpreted as kinetic energy. *t* is the transfer integral, which gives the hopping probability between two sites and is therefore proportional to the atomic overlap and effectively the bandwidth *W*. The creation and annihilation operators of an electron with spin *σ* at site *i* are written as *ci<sup>σ</sup>* and *c*† *<sup>i</sup>σ*, respectively. The second term introduces an on-site Coulomb repulsion *U* if site *i* is fully occupied.

Here, pressure acts as a natural tuning parameter of the CDW states by affecting the transfer integral, *t*, and on-site Coulomb repulsion, *U*, without introducing chemical disorder. A phase diagram reproduced from Reference [36] is shown in Figure 3. With an increase of *t* and a decrease of *U*, Mott physics melt away at a pressure of about 1 GPa, giving rise to a transition to the NCCDW state, which persists up to 7 GPa, and finally entering to a metallic state. The high-pressure ground state (over 3 GPa) is superconducting (*Tc* of about 5 K) at least up to 25 GPa. While the Mott state CCDW clearly competes with the superconducting region [36,43], the coexistence of NCCDW and superconductivity is intriguing. At present, a macroscopic picture of superconductivity in the NCCDW phase is not fully clear. One proposed suggestion is that the superconducting phase forms within the metallic interdomain spaces of the CDW, which become connected as the CDW domains smear out under pressure [36]. On the other hand, an XRD study under pressure [43] suggests that the distance between the CDW domains decreases while domain boundaries remain sharp, meaning no interconnected metallic regions are formed. According to this picture, the whole NCCDW structure must form a single coherent superconducting phase.

By substituting sulfur by the isovalent selenium, a Mott-insulator-to-metal transition is observed [40,41]. Recent studies [41] show a melting of the Mott state CCDW due to the formation of a pseudogap, suggesting the importance of disorder and further inducing superconductivity [40]. The superconducting ground states is then suppressed in favor of a CCDW in the 1T-TaSe2 compound.

In summary, 1T-TaS2−*x*Se*<sup>x</sup>* is an interesting system to explore quantum phase transitions and various exotic states of matter. Especially, the possibility of a QSL ground state remains intriguing [38]. Optical infrared or Raman measurements at low temperatures and under pressure could give further information about the CDW phases.

#### **3. Triangular Lattice**

The highly frustrated triangular lattice hosts a rich phase diagram of magnetic phases and QSL ground states. Focusing on the case of a Heisenberg magnetic exchange, we want to show the tunability of magnetic phases on this lattice. The general model for an anisotropic Heisenberg antiferromanget on the triangular lattice can be written as

$$\mathcal{H} = \mathcal{J} \sum\_{} \mathbf{S}\_{\mathbf{i}} \cdot \mathbf{S}\_{\mathbf{j}} + \mathcal{J}' \sum\_{} \mathbf{S}\_{\mathbf{i}} \cdot \mathbf{S}\_{\mathbf{j'}} \tag{2}$$

where *J* and *J* are the magnetic exchange interactions along the horizontal and diagonal bonds, respectively, and **Si**, **Sj**, and **Sj'** give the spin-1/2 operators at sites *i*, *j*, and *j* , respectively [44].

#### *3.1. Cs*2*CuCl*<sup>4</sup>

The two-dimensional Heisenberg magnet, Cs2CuCl4 [45], posses *S* = 1/2 spins with slightly different exchange values *J* and *J* (*J* /*J* = 0.3) along the *b*-direction (horizontal bonds) and for the interchain coupling (diagonal bonds), respectively [46]. Furthermore, Dzyaloshinskii–Moriya (DM), an interplane exchange interaction, was found to be important [47,48]. Below *TN* = 0.62 K, an incommensurate spiral ground state is formed (DM spiral), with the spiral along the *b*-axis [49]. A magnetic field was shown to lift this confinement of the spins in the *bc*-plane in favour of a commensurate coplanar AFM ground state within the *ab*-plane [48]. Recently, the tunability of the spin Hamiltonian via external pressure and magnetic field was demonstrated, combining high-pressure electron spin resonance (ESR), radio frequency susceptibility measurements [44]. Here, Heisenberg exchange is continuously enhanced under pressure, leading to an increase of *J* /*J* by 12% at 1.8 GPa, as determined by the ESR (cf. Figure 4a,b) Most importantly, the interchain coupling *J* gets enhanced with increasing pressure. Due to the tuned exchange interactions, new phases are emerging under magnetic field (see Figure 4c,d). The magnetic field favors more classical phases; therefore, suppressing the DM spiral at about 2.2–2.6 T, a coplanar order is stabilized in the *ab*-plane. Due to the enhanced *J* , a non-coplanar frustrated phase becomes stable at around 6.9 T. The emerging magnetic anomalies at 9.2 and 9.8 T under a pressure of 1.8 GPa are interpreted as double-cone and single-cone order, respectively (see Reference [44] and references herein). Furthermore, the fully polarized ferromagnetic high-field phase is shifted from around 9 T at ambient pressure to 11.5 T at 1.8 GPa.

**Figure 4.** (**a**,**b**) Pressure-dependent magnetic exchange interactions *J* and *J* along the horizontal and diagonal bonds, respectively (see inset of the crystallographic structure): As the pressure is decreased, the Heisenberg exchange is continuously altered. (**c**) Simultaneously increasing a magnetic field (*H b*) at *T* = 350 mK unveils five different magnetic phases beside the DM spiral. (**d**) Proposed phase diagram under pressure (1.8 GPa) and magnetic field. Graphs are reproduced from Reference [44].

#### *3.2. YbMgGaO*<sup>4</sup>

YbMgGaO4 [50] consists of *S* = 1/2 Yb3<sup>+</sup> spins on triangular lattices, separated by nonmagnetic Mg2<sup>+</sup> and Ga3<sup>+</sup> ions (Figure 5a–c). The edge-sharing YbO6 octahedra in *R*3*m* are characterized by equal Yb–O distances and two equal angles, the Yb–O–Yb bridging angle *α* and the O–Yb–O angle *β*. Structural randomness is induced by a random distribution of the Mg2<sup>+</sup> and Ga3<sup>+</sup> ions. The material became of recent interest as a QSL candidate, when an absence of magnetic order down to at least 50 mK was shown [51], although possibly a weak spin freezing takes place at around 100 mK. More interesting, a magnetic continuum at low temperatures is possibly related to gapless spinons or a nearest-neighbour RVB state (see the references in Reference [52]). Focusing on combined *μ*SR, XRD, and DFT studies [52], we are going to review the pressure dependency of the intriguing ground state. XRD shows no changes of the crystal symmetry up to pressures as high as 10 GPa. However, the Yb–O distances are shrinked by about 0.6% at 2.6 GPa. Importantly, the angles *α* and *β* are weakly decreasing with a change of about 0.07◦ at 2.6 GPa and 0.2◦ at 10 GPa. Figure 5d shows the temperature dependency of the zero-field *μ*SR spectra at ambient conditions and under pressures as high as 2.6 GPa. Of interest here is the increase of the zero-field muon relaxation rate below 4 K. This was interpreted as the onset of spin–spin correlations, which are fully developed around 0.8 K, leading to a dynamic spin state in YbMgGaO4. Comparing the ambient and high-pressure data, the external pressure seems to have no effect on the development of such a ground state. While comparably strong pressure-induced structural changes have been proven in other compounds to have an effect on magnetic couplings, here, the structural randomness, which is not affected by pressure, seems to be crucial in stabilizing the QSL ground state.

**Figure 5.** (**a**) Crystallographic structure of YbMgGaO4: Edge-sharing YbO6 octahedra are separated by slabs of nonmagnetic Mg2<sup>+</sup> and Ga3<sup>+</sup> ions. (**b**) YbO6 octahedra with characteristic parameters. (**c**) Trigonal distortion of the YbO6 octahedra induced by mixing of Mg2<sup>+</sup> and Ga3<sup>+</sup> sides: Importantly, no changes of the structural symmetry are observed under pressure. (**d**) The temperature dependence of the zero-field muon relaxation rate at different pressures shows the onset of spin–spin correlations below 4 K, fully developed at 0.8 K. Reproduced from Reference [52].

#### **4. Honeycomb Lattice**

Recently frustrated magnets on the honeycomb lattice have attracted attention [8,53–55]. Among them, the Kitaev systems are of particular interest because (a) they are highly relevant for

theoretical considerations, as Kitaev's model is directly solvable, and (b) rich physics in terms of exotic quasiparticles, e.g., Majorana fermions [56,57]. Besides the iridate systems [55], like Li2IrO3 and Na2IrO3, *α*-RuCl3 [58,59] has been extensively studied.

#### *4.1. α-RuCl*<sup>3</sup>

*<sup>α</sup>*-RuCl3 implements the 4d<sup>5</sup> transition metal ruthenium (Ru3<sup>+</sup>) with *<sup>λ</sup>Ru* <sup>≈</sup> 0.15 eV [60,61] on a nearly ideal honeycomb lattice. It renders an edge-sharing geometry with an octahedral cage of chlorine ions. Different polymorphs with an ABC-like stacking of the *ab* honeycomb layers along the *c* axis (*α*-RuCl3), and one-dimensional face-sharing RuCl6 chains (*β*-RuCl3) are known. Regarding the structural symmetry, different space groups (*P*3112, *R*3¯, and *C*2/m) were reported (see the discussion in Reference [55]). This seems to be explained by a majority of samples showing stacking faults with a mixing of the ABC (rhombohedral *R*3¯) and AB (monoclinic *C*2/m) stacking patterns. Due to an only weak van der Waals attraction between the layers, the system is quasi-two-dimensional in the *ab*-plane and susceptible to a mixing of the two stacking patterns [62,63].

Looking closer at the magnetic properties, a transition within the *ab*-plane from a paramagnetic phase, obeying a Curie–Weiss law with *θCW* ≈ +40 K and an effective magnetic moment of about 2.3 *μ<sup>B</sup>* [64], to an antiferromagnetic zigzag order is observed [63]. As well, susceptibility measurements expose an anisotropy (*χab* > *χc*) [65]. While the cleanest crystals with a minimum of stacking faults show a Néel temperature of about *TN* ≈ 7 to 8 K, *TN* is found to increase up to 10 to 14 K with higher amount of ABC and AB mixing, indicating different order temperatures of these patterns [62,63].

Under ambient pressure, *α*-RuCl3 is considered as a spin-orbit assisted *jeff* = 1/2 Mott insulator with a Mott gap of about 1.1 eV [66–70]. Specific heat measurements [71] show a pressure sensitivity of the Néel transition and indicate a suppression of the magnetic order at around 0.7 GPa (in accordance with the theoretical, predicted coupling constants [60]). Resistivity experiments up to 140 GPa clearly prove the persistence of the insulating state [71]. Further NMR and magnetization studies demonstrated the vanishing magnetic order under pressure together with a strongly reduced susceptibility and the absence of the low-energy fluctuations [72]. The pressure-induced state was further investigated by optical infrared spectroscopy and *ab initio* DFT calculations [64] and magnetization measurements combined with high-resolution x-ray diffraction experiments [73].

Here, we want to focus on the spectroscopic study of Reference [64]. First, the phononic part of the optical spectrum with the pronounced 320 cm−<sup>1</sup> mode was investigated to elaborate on a possible structural transition under pressure. The *T* = 10 K optical conductivity is shown in Figure 6a. In addition to the main mode (peak 1, which is assigned to a trio with mostly in-plane contributions at *<sup>ω</sup>*<sup>0</sup> ≈ 321, 322, and 326 cm−1), a weaker out-of-plane mode is located at around 290 cm<sup>−</sup>1. Generally, a hardening together with a broadening of the peaks under pressure is observed. Over 0.7 GPa, the main-mode peak 1 splits while another distinct resonance (peak 2) emerges. As the pressure is increased, both peaks further experience a hardening due to lattice contraction. Since phonon modes are generally strongly dependent on the lattice symmetry, the observed splitting is a direct evidence for a symmetry breaking over a pressure of 0.7 GPa.

**Figure 6.** Pressure-dependent optical spectroscopy of *α*-RuCl3 [64]: (**a**) Splitting of the phononic contributions (peak 1) is a direct evidence for a symmetry breaking over a pressure of 0.7 GPa. (**b**) The ambient pressure honeycomb (left-hand side) transforms to a dimerized structure under pressure (right-hand side). (**c**) The electronic ground state is studied by the pressure dependency of the Mott gap *α*. As the pressure increases, the gap gets suppressed, indicating a collapse of Kitaev magnetism and a breakdown of the *jeff* picture. (**d**–**g**) Results of the GGA+SOC+*U* calculations, showing the breakdown of the *jeff* picture (see text for further explanations).

DFT calculations suggest that parallel dimerization of neighbouring Ru sites set in at high pressure. The homogeneous ambient-pressure honeycomb structure transforms to a triclinic *P*1¯ structure (Figure 6b). As a result, a pressure-driven structural transition at *P* > 1 GPa to a triclinic, dimerized structure is established by the spectroscopic experiment, well in accordance with the calculations.

To further understand the dimerized phase, the electronic part of the optical spectrum is investigated in the region of the optical gap *α* under pressure. The general suppression of the *α* peak strongly indicates a collapse of Kitaev interactions above 0.7 GPa. In this frame, a breakdown of the *jeff* picture in accordance with the suppressed magnetic susceptibility above 0.7 GPa [72] is most probable. Note that, according to transport measurements, the suppression of the *α* peak is not interpreted as a closure of the optical gap. Instead, *α*-RuCl3 stays well in the Mott insulation region at least up to 140 GPa [71].

The orbital-dependent density of states (DOS) was calculated including spin-orbit coupling and electronic correlations (GGA+SOC+*U*) with *U* = 1.5 eV giving insight to the observed optical excitations. The results are shown in Figure 6d–g. For the undimerized structure (*P* = 0 GPa, left-hand side panels), the relativistic *jeff* picture is validated. In Figure 6d. the lower lying *t*2*<sup>g</sup>* DOS with the expected orbital contributions is splitted from the higher *eg* manifold and further gapped by SOC and *U*. Thus, the narrow peak at around 1 eV represents the single *t*2*<sup>g</sup>* hole at each site residing in the upper Hubbard band. Projecting on the atomic *J* orbitals (Figure 6f) shows a mixture of the lower Hubbard band *J* = 5/2 (*jeff* = 1/2) with the *J* = 3/2 (*jeff* = 3/2) states, whereas the upper Hubbard band with mainly *J* = 5/2 contribution is clearly distinguishable. Here, virtual hopping through the ligands via hopping channel *t*<sup>2</sup> induces a strong ferromagnetic Kitaev exchange. In the high-pressure phase (*P* > *Pc*, right-hand side panels), the electronic density of states changes (cf. Figure 6e). The *dxy* orbitals split into a bonding contribution which is lower in energy and an antibonding part at higher energy. This destroys the *jeff* , states as can be seen in the atomic projection Figure 6g. At the former upper Hubbard band, now a pronounced mixture of *J* = 3/2 and *J* = 5/2 states emerges. With this breakdown of the *jeff* picture, we can explain the vanishing magnetic ground state under pressures of around 1 GPa [71,72] as a result of the formation of pseudocovalent bonds in the dimerized structure. In the high-pressure phase, the direct Ru–Ru hopping path *t*<sup>3</sup> is enhanced along these bonds. This leads to a large antiferromagnetic Heisenberg exchange located on the dimers, further destabilizing and suppressing the magnetic low-temperature zigzag order. Consistently, the computed magnetic moments are completely suppressed in the high-pressure structure. Instead of increasing the *t*<sup>2</sup> channel towards a dominant Kitaev regime, hydrostatic pressure promotes the direct *t*<sup>3</sup> hopping. Results, therefore, conclude that the high-pressure nonmagnetic state of *α*-RuCl3 is a valence-bond crystal and excludes a transition to a Kitaev QSL in the dimerized structure.

#### *4.2. Iridates*

The 5d honeycomb iridates A2IrO3 (A=Li, Na) [74,75] have gained attraction as Kitaev candidates [54,55,76,77] and were considered in terms of the Heisenberg–Kitaev model and with additional off-diagonal contribution. Due to strong spin-orbit coupling, they are located in the relativistic Mott insulating limit, hosting *jeff* spins of the magnetic Ir ions [78,79]. Compared to *α*-RuCl3 (4d vs. 5d electronic configuration), a stronger SOC in addition to a weaker Coulomb repulsion is generally expected. While in principle a band-insulating picture featuring quasimolecular orbitals is imaginable to explain the insulating nature of these systems [80], the Mott insulating picture is well backed by experiments and the majority of theoretical approaches. Additional trigonal crystal field splitting of the *jeff* = 3/2 quartet can be sufficient high compared to SOC. This might induce a splitting of the SO-exciton and a mixing of the *jeff* = 3/2 quartet with the *jeff* = 1/2 doublet [78,81,82].

The three polymorphs of the Li-iridates are different in structure. While the *α* type is comparable to Na2IrO3 with a layered honeycomb lattice, the *β* variant shows a more three-dimensional hyper honeycomb. The *γ* type is characterized by a stripy-honeycomb structure. All types show an Ir–O–Ir edge-sharing geometry, allowing a nearly ideal 90◦ bond. The centered Ir4<sup>+</sup> ion is coordinated by a cage of six O2<sup>−</sup> ions. The Ir ions generate a 5d<sup>5</sup> electronic structure with a single *t*2*<sup>g</sup>* hole [83].

#### 4.2.1. *α*-Li2IrO3

The lattice structure of *α*-Li2IrO3 (Figure 7a) resembles a honeycomb of edge-sharing IrO6 octahedra (Ir–O–Ir bond angles of around 95◦ with 5.7% difference in bond length) with a centered Li ion as the buffer element and shows a *C*2/*m* monoclinic symmetry [84]. Magnetic susceptibility characterization indicates a Curie–Weiss temperature of −33 K, with an effective moment of *μeff* = 1.83(5) *μB*. A Néel transition at *TN* ≈15 K is further observed in accordance with specific heat measurements [76]. The resulting antiferromagnetic ground state is of an incommensurate counter-rotating type in the Ir plane [84].

X-ray diffraction studies together with DFT calculations [83] showed a structural phase transition under pressure at *Pc* = 3.8 GPa, from the monoclinic *C*2/m to a dimerized triclinic *P*1¯ structure. With an increasing Z1 bond, the dimerization is taking place either in the X1 or in the Y1 Ir–Ir bond of the honeycomb, resulting in two possible order patterns (cf. Figure 7b,c) in the high-pressure phase. Furthermore, it was elaborated that different properties balance, whether an energy gain by forming a magnetic order or a dimerization is higher. These are the size of the buffer ion and the electronic configuration of the metal species. The latter influences the strength of spin-orbit coupling, electronic correlations, and Hund's rule coupling. Larger interactions (SOC, *U*, and *JH*) protect Kitaev physics by ensuring Ising-like spins and by inhibiting dimerization [83]. A larger buffer ion, in principle, inhibits dimerization by an additional hardening of the lattice. Thus, it was argued that *α*-Li2IrO3 is the intermediate case between Na2IrO3 and Li2RuO3. Indeed, Li2RuO3 already dimerizes at ambient conditions [85], whereas Na2IrO3 (discussed below) with a larger center ion size (Na vs. Li) is expected to dimerize at higher pressure.

Furthermore, studies using multiple X-ray techniques—X-ray powder diffraction (XRD) investigating the crystal structure, resonant inelastic X-ray scattering (RIXS) unveiling the electronic

structure, and X-ray absorption spectroscopy (XAS) probing SOC under hydrostatic pressure together with DFT calculations—give additional insights [86]. At low pressures of about 0.1 GPa, the X-ray powder diffraction shows a gradual elongation of the honeycomb, where two long bonds (3.08 *A*˚) and four short bonds (2.92 *A*˚), still within the *C*2/m symmetry, are formed. The XAS data suggest a strongly decreasing SOC up to 1.1 GPa, saturating at around 2.8 GPa. Interestingly, the RIXS spectra in Figure 7d indicate a pressure dependence of the crystal field excitations. At low pressure, the SO-exciton (peak A) with corresponding energy of <sup>3</sup>*<sup>λ</sup>* <sup>2</sup> ≈ 0.72 eV is clearly identified. While this excitation should, in principle, be splitted due to reasonable trigonal crystal field splitting Δ*Tr* ≈ 0.11 eV (see Figure 7e), a substructure is not resolved within the resolution of the setup. Under pressure, the corresponding intensity gets suppressed and peak A slightly shifts to lower energies. A new peak B develops at around 1.4 eV and gets intensified under pressure. This was interpreted as an increase of trigonal crystal field splitting over spin-orbit coupling. Consequently, Clancy et al. argued that the relativistic *jeff* picture breaks down, even at low pressures of around 0.1 GPa, in favour of a localized pseudospin approach or an itinerant quasimolecular orbital (QMO) model (Figure 7f). At around 3 GPa, powder diffraction identified a first-order structural transition in accordance with Reference [83]. Here, a pronounced transfer of spectral weight from peak A to peak B is observed. Fitting of Peak B unveiled a two-peak structure related to the possible transitions to a QMO picture.

Note that there is a pressure-dependent optical study on this compound [87].

**Figure 7.** (**a**) Below *Pc*, the honeycomb of *α*-Li2IrO3 realizes symmetry-equivalent X1, Y1, and distinct Z1 bonds. (**b**,**c**) The high-pressure dimerized phase consists of two degenerate order patterns. Reproduced from Reference [83]. (**d**) Pressure-dependent resonant inelastic X-ray scattering (RIXS) on *α*-Li2IrO3 [86]. At ambient pressure, the SO-exciton (peak A) can be clearly identified according to the level structure of the *jeff* model (**e**). At higher pressure (around 1.4 GPa), a second contribution (peak B) emerges, related to an enhancement of Δ*Tr*. Below 2 GPa, the two peaks A and B can be fitted to the transitions of a pseudospin model or an itinerant quasimolecular orbital (QMO) state equivalently well. In the high-pressure phase, peak B shows a two-peak structure with a contribution at around 1.6 eV, interpreted as a transition from the *jeff* picture to a QMO state (**f**).

#### 4.2.2. *β*-Li2IrO3

The *β*-polymorph forms a hyper-honeycomb structure of edge-sharing IrO6 octahedra with nearly identical Ir–O–Ir bonds (0.2% difference) and angles of around 94.5◦. It extends Kitaev physics in three dimensions [88]. This relativistic Mott insulator has effective moments of *μeff* = 1.6(1) *μB*, and the magnetic susceptibility shows a positive Curie–Weiss temperature of 40 K, which may stem from ferromagnetic Kitaev couplings [89]. A transition to a noncollinear or incommensurate ground state at 38 K is seen under rather strong fluctuations. Furthermore, an unusual cusp in specific heat measurements [88] indicates a second-order transition. The low ferromagnetic Curie–Weiss temperature was interpreted as an effective cancellation of two competitive and nearly degenerate ferromagnetic (possibly Kitaev exchange) and antiferromagnetic ground states. These observations were interpreted as proximity to a Kitaev QSL [88]. Furthermore, Raman spectroscopy indicates signatures of fractionalized excitations [90], similar to *α*-RuCl3.

A relative weak magnetic field of 3 T polarizes the compound with 0.35 *μB*/Ir [88] and induces strongly correlated ferromagnetic zigzag chains. Magnetic resonant X-ray scattering [91] shows a thermal driven crossover from a paramagnetic behavior in this quantum correlated (quantum paramagnetic) state. The field-induced moments were traced by X-ray magnetic circular dichroism (XMCD) [88] to be suppressed under pressure at 1 GPa and vanished over 2 GPa, while the compound remained insulating. Finally, this was interpreted as a rearrangement of the *jeff* moments. By applying pressure without external magnetic field, the order temperature shifts first from around 38 K to 15 K [88]. Under further increase, *β*-Li2IrO3 undergoes an electronic/magnetic phase transition at 1.5 GPa, as observed by X-ray absorption near edge structure (XANES) measurements [92], without breaking the lattice symmetry. Probing the 5d holes, SOC was found to be reduced but remains important. *Ab initio* calculations indicate a dominant Dzyaloshinskii–Moriya regime under pressure, pushed away from the pure *jeff* limit. However, the compound still remains in a relativistic Mott picture with an enlarged mixture between *jeff* = 3/2 and *jeff* = 1/2 states [88,93]. The new ground state remains intriguing [94]. Around 4 GPa further, a phase transition to a monoclinic *C*2/*m* symmetry was observed [92]. The compound dimerizes under a compression of X and Y Ir–Ir bonds, compared to the Z bonds.

#### 4.2.3. *γ*−Li2IrO3

The zigzag chains in *γ*−Li2IrO3 host *jeff* = 1/2 spins with *μeff* = 1.6 *μ<sup>B</sup>* in a noncoplanar, counter-rotating pattern [95,96]. A transition temperature of about 38 K and a strongly anisotropic susceptibility, which rather does not allow a determined Curie–Weiss temperature, were observed. The underlying lattice is of Cccm symmetry. Equally to *β*-Li2IrO3, Raman spectroscopy shows signatures of fractionalized excitations [90]. Resonant X-ray scattering (RXS) measurements under pressure find an abrupt suppression of the spiral magnetic order at 1.4 GPa without indications of a changed lattice symmetry and point out a continuous reduction of the unit cell volume [97]. This non-magnetic pressure state remains of further interest.

4.2.4. Na2IrO3

**Figure 8.** Infrared spectroscopy combined with pressure and isoelectric doping studies on Na2IrO3 of Reference [98]: The effect of Li doping ((Na1−*x*Li*x*)2IrO3 for *<sup>x</sup>* ≤ 0.24 and *<sup>x</sup>* = 1 (represented by *α*-Li2IrO3)) on the electronic spectra (**a**) and phononic part (**c**) is shown. (**a**) While the SO-exciton (peak A) is only marginally affected by Li doping, the direct hopping between *jeff* = 1/2 orbitals (peak B) gets suppressed. A blueshift of the intersite *jeff* = 3/2 → *jeff* = 1/2 transition (peak C) for *x* ≤ 0.24 Li doping indicates a increasing *Ueff* /*t*. (**c**) The phononic part shows a hardening upon increasing the Li doping. Further, the effect of hydrostatic pressure on the electronic spectra (**b**) and on the phononic part (**d**) is shown. (**b**) Under pressure *Ueff* /*t* is slightly lowered, indicated by a redshift of all features while the lattice is contracted (**d**).

The layered honeycomb of Na2IrO3 is similar to *α*-Li2IrO3, with edge-sharing IrO6 octahedra and Na as buffer ion (*C*2/*m* space group). Ir–O–Ir bond angles reach from 98◦ to 99.4◦ [99]. High-temperature moments of *μeff* = 1.79 *μ<sup>B</sup>* are determined together with a Curie–Weiss temperature of −125 K [76]. Below 15–18 K, an antiferromagnetic zigzag order is observed with 0.22(1) *μB*/Ir [99,100]. Spin-wave excitations in this magnetic order were studied by inelastic neutron scattering experiments and compared with theoretical considerations [99], showing the importance of higher-order coupling contributions on the honeycomb lattice [101].

Optical studies established a mostly temperature-independent onset of a Mott gap at around 340 meV [102]. Electronic features below 3 eV are assigned to be transitions, belonging to the Ir 5d *t*2*<sup>g</sup>* multiplets, and above mostly to charge transfer transition from O 2p to Ir 5d *t*2*g*. A clear absorption edge is visible, resulting in an effective on-site Coulomb repulsion of about 1.5 eV. This seems to match the LDA+SOC+*U* calculated DOS with *U* = 3 eV and *JH* = 0.6 eV [102]. The *jeff* picture is clearly valid as pointed out by resonant inelastic X-ray scattering. These studies show a splitted but pronounced SO-exciton, concluding that trigonal distortions are weaker compared to a strong SOC (110 meV and 0.4–0.5 eV, respectively) [78].

Hydrostatic pressure and isoelectric doping studies on Na2IrO3 using infrared spectroscopy and synchrotron X-ray diffraction were performed by Hermann et al. [98]. The optical conductivity under ambient pressure for an as-grown sample is displayed in Figure 8a (black line). The *d*–*d* contributions peak A (0.7 eV), peak B (1.2 eV), and peak C (1.6 eV) (Figure 8a) are assigned as follows: intrasite *jeff* = 3/2 → *jeff* = 1/2, intersite *jeff* = 1/2 → *jeff* = 1/2, and intersite *jeff* = 3/2 → *jeff* = 1/2 transitions, respectively, and thus probing the Mott insulating picture directly (peak A) and Kitaev correlations indirectly (peak B and C). The first intersite excitation peak B reveals a Mott gap with *Ueff* =1.2 eV, in accordance with Reference [102]. On the low-energy side, phononic excitations contribute (Figure 8c). While the *C*2/*m* symmetry hosts 18 infrared-active modes, five were resolved by the experiment in the undoped sample at ambient pressure.

The effect of Li doping, discriminating Na, with (Na1−*x*Li*x*)2IrO3 for *x* ≤ 0.24 and *x* = 1 (represented by *α*-Li2IrO3) is analyzed in detail. Focusing on the electronic part (Figure 8a), the intrasite contribution (peak A) remains mostly stable upon doping, with only a slight redshift, while the intersite excitation (peak C) shifts to higher energies. This indicates an increasing ratio of *Ueff* /*t*, while SOC and a distortion of the crystal field remain only marginally affected. Further, it corresponds to a shift towards the Mott insulating side. According to theoretical predictions [103], the decreasing spectral weight of the *jeff* = 1/2 → *jeff* = 1/2 intersite transition B with increasing amount of doping was related to enhanced Kitaev couplings due to a suppression of the direct Ir–Ir hopping channel. This emphasizes a proximity of the *x* = 0.24 compound to the Kitaev limit. Further X-ray measurements show that the chemical pressure upon Li doping only affects a contraction of the *ab*-plane. The *c* direction remains nearly constant because only in-plane Na sites are affected for a sufficient low doping concentration. This naturally tunes the Ir–O–Ir bond angle, crucially influencing Kitaev magnetism. However, *α*-Li2IrO3 is located not so deep in the Mott insulating state, as indicated by a redshifted absorption edge (Figure 8a), therefore resulting in a lower ratio of *Ueff* /*t*, backed by previous studies [60]. The similar position and shape of transition A prove a comparable SOC and distortion of the crystal field in Na2IrO3 and *α*-Li2IrO3 [55].

On the phononic part (Figure 8c), increasing the Li doping is expressed as a hardening of the in-plane modes due to compression of the *ab*-plane. In addition to this chemical pressure effect, the phonon modes are intrinsically affected by the contribution of Li. The observed modes, previously without any Na contribution, were simulated to have an increasing contribution of Li discriminating Ir. The lowest mode at around 350 cm−<sup>1</sup> was found to be purely Li based, in accordance to the optical spectra.

Hermann et al. further compared the effect of chemical pressure to the physical hydrostatic one. The optical conductivity for pressurized samples is shown in Figure 8b,d. On the electronic part (Figure 8b), hydrostatic pressure over 8 GPa leads to a decreasing intensity of the absorption edge, while the intrasite transition (peak A) remains nearly unaffected. A slight redshift of all features upon increasing pressure is observed. *Ueff* /*t* is therefore only slightly adjusted between 8 GPa and 24 GPa. The nearly unchanged intrasite contribution indicates a smooth monotonic contraction without disturbing the crystal field symmetry. In addition, the phononic contributions (Figure 8d) were found to experience a monotonic hardening while the damping increases with pressure. Overall, no indications for a breaking of lattice symmetry are found. Further X-ray measurements show that, additionally to the *ab*-plane, the *c* direction is contracted upon pressurizing. This naturally explains the different affected intensities of peak B and peak C. While transition C *jeff* = 3/2 → *jeff* = 1/2 is influenced by changes of the Ir–O–Ir bond angle, the direct hopping of peak B is nearly unchanged through the smooth contraction of the *ab*-plane. Thus, it was argued that external hydrostatic pressure, in contrast to the chemical counterpart, drives the compound away from the Kitaev limit.

#### **5. Kagome Lattice**

**Figure 9.** (**a**) Pressure effect on the crystal structure of Herbertsmithite. While the *R*3*m* symmetry is preserved under pressure, trigonal distortion is added by tilting the CuO4-plane. (**b**) Phase diagram under pressure: At 2.1 GPa, a transition from a QSL to an AFM ordered phase takes place, which can be seen in the susceptibility data (inset). (**c**) Neutron diffraction pattern under pressure. The local spin structure under pressure resembles a <sup>√</sup><sup>3</sup> <sup>×</sup> <sup>√</sup>3 type. After Reference [104].

Herbertsmithite ZnCu3(OH)6Cl2 is one of the most highlighted QSL model systems, crystallizing in the highly frustrated Kagome lattice (see Reference [105] and references herein). Cu Kagome planes (*S* = 1/2) are separated by Zn2<sup>+</sup> ions realizing a highly frustrated system. Note that there is a prone to disorder induced by mixing of Cu and Zn ions [106]. Besides strong antiferromagnetic interaction (*J* = 190 K) due to the 120◦ Cu bonds, no signature of magnetic order was found down to the lowest temperatures of around 50 mK [107,108]. Furthermore, Dzyaloshinskii–Moriya interaction was found to be important [109]. Spin freezing was observed under magnetic field [110] and pressure [104], on which we want to discuss now in detail. Under pressure, the *R*3*m* symmetry is preserved up to at least 5 GPa. However, Cu–O–Cu bond angles are non-monotonically affected. First, for *P* < 0.25 GPa, a linear increase is observed, followed by a decrease up to 5.1 GPa. The Cu–O bond distance was found to decrease linearly at the low pressure side of *P* < 0.25 GPa and to be pressure independent above. Figure 9a shows the pressure effect on the crystal structure of Herbertsmithite. Most importantly, the CuO4-plane tilts respectively to the Cl–Cu–Cl axis, inducing a trigonal distortion. Interestingly, the ratio of DM and Heisenberg interaction in Herbertsmithite is lowered under pressure. A quantum phase transition from the QSL ground state to an ordered AFM phase is observed at 2.5 GPa with *TN* = 6 K as a peak in susceptibility measurements (Figure 9b). In the AFM ordered state, *TN* is further decreased under pressure and explained by a decrease of Heisenberg interaction (15% from 2.5 GPa to 5.1 GPa). The AFM structure is of type <sup>√</sup><sup>3</sup> <sup>×</sup> <sup>√</sup>3 (see Figure 9c).

#### **6. Spin 1/2 Dimer Systems**

We also want to highlight pressure-dependent studies on the spin dimer system TlCuCl3 [111,112]. This magnetic insulator host dimerized *S* = 1/2 moments of Cu2<sup>+</sup> ions confined by strong AFM interaction. The formation of spin dimers leads to a quantum disordered phase at ambient pressure. Between the singlet ground state (*S* = 0) and the first excited triplet state (*S* = 1), there is a small gap of about 0.7 meV for spin excitations. Pressure [113–117], magnetic field [118], and impurity doping were shown to generate AFM order [119]. We are going to review the pressure-induced phase transition in detail. In a simple picture, the interdimer coupling can be increased by external pressure, closing the spin gap [120]. Rüegg et al. found a quantum phase transition (QCP) at *P* = 0.107 GPa and a power law increase of *TN* in the AFM phase [116]. Spin dimer formation can be destroyed by the suppression of quantum fluctuations or the reduction of thermal fluctuations, both leading to magnetic order. Figure 10 summarizes both phase transitions as probed by inelastic neutron scattering [117]. First, we focus on the QPT (Figure 10a). As the pressure is increased, the spin gap is suppressed and finally closed with a temperature-dependent pressure *pc*. In the ordered Néel state (right-hand side), two types of excitations are observed, namely the conventional Goldstone mode or spin wave (Figure 10a grey symbols) and, remarkably, the longitudinal Higgs mode (Figure 10a red symbols) [121]. Decreasing the pressure softens the Higgs mode, and finally as dimer-based quantum fluctuations destroy magnetic order, the system becomes gapped under *pc*. While, transverse excitation remains gapped (0.38 meV at *pc*) over the full pressure range, they can be well distinguished from the gapless longitudinal modes at *pc*. Now, we want to focus on the classical phase transition (Figure 10b). At high temperatures, thermal fluctuations gap all observed modes. Having the temperature as a tuning parameter and a fixed pressure of 0.175 GPa, the ordered state emerges below *TN* as the longitudinal mode becomes gapless at *TN*. Here, we see that quantum and thermal melting of the ordered phase are affecting the neutron spectra in a qualitatively very similar way. Finally, a full phase diagram covering quantum critical and classical critical region is shown in Figure 10c.

**Figure 10.** Quantum and classical phase transition from a dimer *S* = 1/2 state to magnetic order in TlCuCl3 observed by inelastic neutron scattering: (**a**,**b**) Evolution of mode energies for pressure and temperature as tuning parameters. At the quantum critical point, QPT takes place: (**a**) Transverse magnetic modes (T) or Goldstone mode of the ordered phase remains gapped while the longitudinal Higgs mode (L) is gapless at the QCP with a temperature-dependent *pc*. Taking temperature as the tuning parameter (**b**) and a fixed pressure, the ordered state emerges at a pressure-dependent *TN*. A qualitatively similar evolution of the mode gaps for classical and quantum phase transition is observed. The results are summarized in the phase diagram (**c**) showing the quantum disordered state (QD) and induced magnetic phase (RC-AFM). Quantum critical and classical critical regions are indicated as QC, and CC, respectively. Grey spheres show the power-law behavior of *TN*(*p*), while blues symbols (*TSL*(*p*)) denote the limit of classical scaling. Reproduced from Reference [117].

#### **7. Summary**

In summary, external pressure can be a very powerful tool to tune the electronic, magnetic, and structural parameters opening a new route in the investigations of QSLs and candidates. For instance, small perturbations to the crystal structure can drive the geometrical frustration factor towards a favourable state. More complicated but possible is a direct tuning of the exchange coupling (Cs2CuCl4). Moreover, unwanted magnetic interactions and fluctuations can be suppressed, leaving room for realization of a pure QSL state. However, it is often difficult to predict the influence of external pressure on magnetic properties of a candidate system. In fact, we have seen few systems where the pressure induces spin freezing rather than a liquid state (for instance, in Tb2Ti2O7 or Yb2Ti2O7) or an unfavourable modification of the crystal structure (*α*-RuCl3). Promising are candidates where a magnetic order vanishes before the structural transition as in the case of the iridate systems. Therefore, there is no easy answer for whether external pressure is always a pathway to introduce spin liquid physics in the candidate systems. Albeit that the end results are unpredictable, exotic states of matter in the vicinity of the QSL state can be investigated.

**Author Contributions:** T.B. wrote the manuscript. T.B. and E.U. discussed the content. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Deutsche Forschungsgemeinschaft through grant No. DR228/52-1. and the "Margarete von Wrangell Habilitation Programm" by the Ministry of Sciences, Research, and Arts in Baden Württemberg.

**Acknowledgments:** We thank Weiwu Li, Seulki Roh, Andrej Pustogow, Artem Pronin, and Martin Dressel for fruitful discussions. T.B. acknowledges funding from Deutsche Forschungsgemeinschaft through grant No. DR228/52-1. E.U. acknowledges the support by "Margarete von Wrangell Habilitation Programm" by the Ministry of Sciences, Research, and Arts in Baden Württemberg.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


c 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Review* **Mechanisms of Pressure-Induced Phase Transitions by Real-Time Laue Di**ff**raction**

**Dmitry Popov 1,\*, Nenad Velisavljevic 1,2 and Maddury Somayazulu <sup>1</sup>**


Received: 30 November 2019; Accepted: 11 December 2019; Published: 14 December 2019

**Abstract:** Synchrotron X-ray radiation Laue diffraction is a widely used diagnostic technique for characterizing the microstructure of materials. An exciting feature of this technique is that comparable numbers of reflections can be measured several orders of magnitude faster than using monochromatic methods. This makes polychromatic beam diffraction a powerful tool for time-resolved microstructural studies, critical for understanding pressure-induced phase transition mechanisms, by in situ and in operando measurements. The current status of this technique, including experimental routines and data analysis, is presented along with some case studies. The new experimental setup at the High-Pressure Collaborative Access Team (HPCAT) facility at the Advanced Photon Source, specifically dedicated for in situ and in operando microstructural studies by Laue diffraction under high pressure, is presented.

**Keywords:** Laue diffraction; high pressure; mechanisms of phase transitions

#### **1. Introduction**

White beam (polychromatic) Laue diffraction is a powerful experimental tool for studying mechanisms of pressure-induced phase transitions. Use of the full white beam spectrum allows for fast data collection, which then provides both spatially and time-resolved microstructural information to be gained simultaneously from a sample in Diamond Anvil Cell (DAC), with spatial resolution down to microns and time resolution down to seconds [1,2]. The alternative, using monochromatic beam diffraction, would not provide comparable time resolution, even with high X-ray energies, due to the need to rotate the sample while collecting X-ray images [3,4]. This makes total data collection time across the sample in a DAC substantially longer.

To some extent, the mechanisms of transitions can be determined by studying samples recovered at ambient pressure [5–7]. However, such samples may be substantially altered during the recovery process or undergo reversible phase transformations as pressure is released. In contrast, polychromatic beam diffraction makes it possible to determine the morphology, deformation and orientation relations of co-existing parental and product phases in real time in situ. Time-resolved measurements are vital for revealing details of phase transitions, which may be controlled by kinetics, and therefore require the fastest techniques of data collection.

Despite the fairly wide use of Laue diffraction for characterization of materials, including in situ studies of materials under external stress [8–10], the application of this technique for high-pressure DAC studies requires additional experimental development and consideration. The purpose of this review article is to summarize the currently available polychromatic beam diffraction experimental techniques at high pressure and data analysis capabilities at HPCAT, as well as to present some recent case studies.

#### **2. Experimental Facilities and Procedures**

There are multiple synchrotron beamlines dedicated to Laue micro-diffraction [10–13]. However, currently these facilities are not specifically optimized for measurements on materials at high pressures. The first experimental setup specifically dedicated to high-pressure Laue micro-diffraction was developed at the 16BMB beamline of the Advanced Photon Source (APS) [2] (Figure 1). This setup is mounted on a granite table in order to maintain mechanical stability and positioning of the x-ray beam spot on the sample. A fast PerkinElmer area detector (PerkinElmer Optoelectronics) is positioned with a detector arm and, therefore, can be oriented in either transmitted or 90◦ geometry. The X-ray polychromatic beam from the bending magnet is focused down to 2μm<sup>2</sup> with KB-mirrors. The highest limit of X-ray energy at the sample position is adjustable by changing the tilt of the mirrors. For measurements in transmitted geometry, the highest possible energy is typically set at ~90keV, while in 90◦ geometry, the highest energy limit is around 35keV. The sample for high-pressure studies in a DAC is mounted on top of a fast x/y table, which in turn is mounted on top of an elevation stage. These stages are used to collect a series of two-dimensional (2D) translational scans across the sample. With a vertical rotational stage, sample orientation can be optimized to obtain the highest number of reflections. A Si 111 channel-cut monochromator provides monochromatic beam switchable with the polychromatic beam in a matter of minutes. This monochromatic beam is mainly used to identify powdered product phases after destructive phase transitions, to calibrate sample to detector distance and detector tilt in transmitted geometry using the CeO2 standard. Detector calibration in 90◦ geometry is done using the Laue diffraction pattern from a Si single crystal and the known energy of one reflection on this pattern measured with the monochromator [14].

**Figure 1.** Outline of Laue diffraction setup dedicated to studies at high pressure available at 16BMB beamline of Advanced Photon Source [2].

Measurements in a DAC introduce some specific requirements to the sample environment (Figure 2). Strong Laue reflections from diamonds can damage the area detector. To protect the detector during data collection a detector mask is used: small pieces of lead are placed on a kapton foil in order to block the reflections from the diamonds. Positions of strong diamond reflections are pre-determined by collecting an X-ray image with strong absorbers inserted in the incident beam to reduce intensities of these reflections to the level at which they will not damage the detector. A metal grid is placed on the kapton foil during the collecting of this image; this introduces a clear 'imprint' on the background of the pattern. Using the grid as a reference the pieces of lead are placed to the positions on the kapton foil coinciding with the strong diamond reflections. Before the detector mask is positioned, the sample is aligned in the X-ray beam and co-linear with the axis of the rotational stage by doing absorption scans across the sample with photodiode. A movable lead shield is used to protect the detector during this process and is removed for data collection.

**Figure 2.** Sample environment of the Laue diffraction setup available at 16BMB beamline of Advanced Photon Source [2].

A series of 2D scans is collected across the sample undergoing a phase transition, while sample pressure is varied remotely using a gas membrane system. Microstructural changes during the transition are observed in real time using ImageJ software [15], and pressure can be fine-tuned based on the observed changes, such that the most important details of the transition are not lost. As the sample position may shift during pressure change, it has to be periodically re-centered on the rotation axis during data collection, in order to maintain a constant spatial sample-to-detector relationship. This procedure requires absorption scans across the sample at different angular positions of the sample [16,17]. Therefore, a detector mask is not sufficient to eliminate unwanted diffraction spots, and the movable detector shield is used instead. During the experiment, pressure is continuously monitored, and is also measured before and after the transition using an off-line Ruby fluorescence system [18] that is available inside the experimental hutch.

For the measurements in 90◦ geometry, a panoramic DAC with X-ray transparent gasket is used. The incident beam passes through the diamond, while the diffracted beams pass through the gasket material. In transmitted geometry, both incident and diffracted beams pass through diamonds. For the measurements in this configuration typically DACs with total opening of ~60◦ are used. The DACs are tilted vertically by ~25◦ with a sample holder, and the area detector is tilted vertically by 30◦. This configuration optimizes the amount of reciprocal space that can be accessed and allows us to collect sufficient number of reflections for indexing them.

Phase transitions may proceed very rapidly, and in order to observe details of phase transitions, pressure has to be changed in small steps. In the case of strongly displacive transitions, the initial parent single crystal sample breaks up into smaller crystals or powder-like crystalline aggregates. Due to this process, the sample becomes heavily deformed, which introduces additional difficulties in data analysis. In practice, one must therefore follow the process until this deformation sets in and makes

analysis difficult. Using Re gaskets in the transmitted geometry currently pressure rate can be as small as ~0.2 GPa/hour and can therefore allow us to appropriately capture the transition.

Measurements in diamond anvil cells require sufficiently small samples, typically smaller than 100 μm. Therefore, if the sample is bigger, a small part has to be separated from it. On the other hand, Laue diffraction is sensitive only to single crystals with sizes comparable to or larger than X-ray beams, so the original samples must be either single crystals or poly crystals with crystal size typically at least in the micron range. If the sample is too big to be put into a DAC but it is a single crystal with strong cleavage, it can be mechanically split into smaller crystals that still have good quality for the measurements. However, if the mechanical disintegration of the sample destroys the single crystals, an alternative approach may be considered using a laser micro-machining system [19]. The sufficiently small sample is carefully put in the center of gasket hole of a DAC using Axis Pro Micro Support micromanipulator (Supplementary Materials, Figure S1). Positioning of the sample right in the center of gasket hole is crucial to minimize diffraction signal from gasket material and to avoid sample-gasket interaction during pressure changes.

#### **3. Data Analysis**

Analysis of the high-pressure Laue diffraction data includes two major steps: indexation of diffraction patterns [14,20], and mapping of reflections. By systematic indexing of diffraction spots, single crystals can be identified, and therefore reflections from parent and daughter phases can be clearly distinguished. Furthermore, by going through systematic indexation, orientations of crystals can be determined, which in turn can be used to find orientation relations between coexisting parent and product phases. Relative orientations of single crystals can be determined from one Laue diffraction pattern with an angular precision down to ~0.02◦, which makes Laue diffraction a powerful tool for characterizing twining [21]. By application of the polychromatic beam diffraction, one can overcome a major challenge to recognize domain structures formed after phase transitions: the newly formed domains typically have pseudo symmetrical translational lattices with very low mismatch with respect to the lattice of parental phase [22]. As a Laue diffraction pattern is typically collected in a matter of a few seconds, such domain structures can be recognized in real time with a resolution reaching down to seconds. At the same time, determining twin relationships with the same level of precision using a monochromatic beam requires sample rotations in very small steps and correspondingly large data collection times.

Software for indexing and mapping of Laue reflections was developed in-house by the lead author of this paper D. Popov, in Python [23]. This program can be made available upon request, as it is developed for broader distribution. The indexation routine is tailored toward simultaneous indexation of reflections from multiple crystals or crystallites that can coexist on the same diffraction pattern. Two strong diffraction spots that could belong to the same crystal are selected first. Typically, two reflections from the same 'zone line' are selected, which is a good indication that reflections originate from the same crystal. Based on the positions of these diffraction spots and their indices, the orientation matrix of the crystal can be calculated [20]. However, in many cases, the indices are not known, and therefore the software is used to explore and converge on the possible indices for calculating the orientation matrix and indexing all other reflections using this matrix. Orientation matching to substantially bigger number of reflections than multiple orientations is first exhausted. The range of possible indices is determined based on 2θ angles of the selected two reflections and the highest limit of X-ray energy. After the diffraction spots from a crystal are determined, they are removed from further data analysis, and reflections from other crystals are indexed in the same repetitive way. The peak search function available in Fit2d [24] software is used for determining the positions of reflections.

The newly developed program can even detect a rather unlikely situation in which the same set of reflections can be indexed by multiple crystal orientations. In such a case, the data has to be recollected in order to obtain a broader set of reflections from the sample. A larger set of reflections can typically be obtained by using DACs with larger openings, varying sample orientation, and reducing the sample-to-detector distance. For example, one should avoid situations where only one 'zone line' from a crystal is present in the diffraction pattern, since, in those cases, there are two possible orientation variants that satisfy the diffraction condition. These two orientations are related by a mirror plane perpendicular to the zone axis.

Crystal orientation is determined from reflections picked up on X-ray images using a peak search algorithm which may not be able to recognize all diffraction spots. More reliably, all the reflections from a single crystal can be visually recognized. For this purpose, positions of all possible reflections from a single crystal are predicted and shown on X-ray image, by the new program, based on orientation matrix, highest X-ray energy limit, and some lower limit of d-values (Figure 3a). Software Dioptas [25], widely implemented in the high-pressure area, is used to visualize X-ray images with marks of predicted reflection positions and to look through series of such diffraction patterns collected during a 2D scan.

**Figure 3.** Results of identification and mapping of two ω-Zr crystals using Laue diffraction data collected at 34IDE beamline of APS with X-ray beam focused down to 500×500nm<sup>2</sup> at pressure of 5.16GPa. (**a**) Predicted positions of reflections from the two crystals of ω-Zr (shown by different colors, slightly shifted to the right not to overlap with the observed reflections) on a Laue diffraction pattern assuming X-ray energy limit of 30keV and the smallest d-values of 0.55Å (positions shown in red) and 0.65Å (positions shown in yellow). (**b**) Composite frame of area denoted by red rectangle in (**a**) presenting a map of (121) reflection. Composite frames of areas around some other reflections from the same crystal are presented in the Supplementary Materials (Figure S2).

For mapping the single crystal, the new program combines all images collected during the 2D scan of the crystal into a composite frame in the same order as those images were collected during the scan (Figure 3b). Such composite frames reproduce the shapes of single crystals and, at the same time, variations in the shapes and positions of diffraction spots across the sample are also clearly visible, indicating deformation of the crystals. The composite images are currently visualized with Fit2d.

In general, the microstructural changes during phase transitions are continuous, and as such, in order to analyze the 2D scans, one has to distinguish between changes that could be attributed to spatial inhomogeneity of the sample and those caused by temporal changes during the transition. Typically, there is variation in the diffraction spot positions across both the parental and product single crystals caused by their deformation. At the same time, rotation of the crystals due to deformation of the entire sample during a translational scan causes such a variation as well. Pressure increase may slightly mis-orient the DAC during a translational scan, also resulting in variation of diffraction

spot positions across the single crystals. The shapes of diffraction spots may also vary across parent crystals coexisting with product phase due to the inhomogeneity of their deformation. However, if the crystals are deformed during a 2D translational scan, they exhibit the same kind of variation. Maps of reflections across the sample are defined by crystal morphology, but the maps can also be affected by decreasing parent fraction or growth of product phase during the scan. The variations due to sample inhomogeneity are distinguished by comparing concurrent translational scans in order to find reproducible features. For instance, the composite frame presented in Figure 3b was extracted from a scan repeated twice. The composite frame from the second scan is identical, indicating that there were no observable changes in the sample within the time interval of 12 h required to collect both of the scans. Therefore, the composite frame clearly reproduces the shape of the crystal, and no changes to its morphology are indicated. More composite frames of reflections from the same crystal are presented in Supplementary Materials (Figure S2).

#### **4. Examples**

The mechanism of the α → β transition in Si was studied using Laue diffraction [1]. In Figure 4, maps of coexisting parent and product phases at the onset of transition are presented (Figure 4a), along with map of the rest of parent α-Si single crystal (Figure 4b).

**Figure 4.** Maps of the parent and product phases across the α → β phase transition in Si [1]. Time intervals of the 2D scans since the beginning of the data collection routine are shown. The pressure values have been interpolated based on the pressures measured before and after the transition. Step size was 5 μm. (**a**) Composite frames of reflections from three slightly mis-oriented crystals of α-Si (shown in different colors) and β-Si. The blue rectangle denotes the overlap area with the map presented in (**b**). (**b**) Map of the rest of parent α-Si crystal when the transition was nearly over.

Microstructural changes that evolve over longer time periods in comparison to typical acquisition times of one translational scan can be better analyzed and viewed by combining composite frames from consecutive scans. As examples, movies (Movie S1a,b) compiled from composite frames shown in Figure 4 are presented in the Supplementary Materials. Movie S1a captures the splitting of the original single crystal of α-Si at the onset of transition into three crystals that are slightly mis-oriented with respect to one another, while the newly formed β-Si is located at the interface of these crystals. In Movie S1b, the disintegration of the rest of parental single crystal is shown.

The results of study of the mechanism of the α → β phase transition in Si [1] presented in Movie S1a indicate that the interface between the parental and product phases is highly incoherent. While the α-phase produced very sharp reflections, the β-phase produced highly broadened 'streaky' reflections, indicating that crystals of this phase were heavily deformed. Most likely, this is due to the large volume collapse accompanying this transition, which then resulted in large lattice mismatch between the parent and daughter phases. The areas of β-Si were strongly elongated domains formed parallel to a <110> direction of the parent α-Si phase. This may also indicate that the nucleation of the product phase could be controlled by defects introduced along the cleavage planes during the sample preparation. It is interesting to note that the single crystals of α-Si were slightly bent as the β-phase started growing. This is indicated by the systematic shift of positions of reflections from α-Si across the sample reproducible on the composite frames from adjacent translational scans. Toward the end of the transition, the rest of the parental single crystal also exhibited the same kind of deformation (Movie S1b). The remaining α-Si crystal was strongly elongated parallel to the same <110> direction as the β-Si areas on the onset of transition.

Another example is our recent study of zirconium (Zr) metal. Zr has previously been observed to exhibit unusual grain enlargement across the α → ω phase transition [26]. The parent phase is a nano-crystalline aggregate, while the product phase is much grainier. The relative change in grain size structure was inferred from the 'spotty' diffraction lines recorded with a monochromatic beam on the daughter ω-phase of Zr in comparison to the continuous diffraction lines from the parent α-phase of Zr. The grain enlargement in Zr is observed under high pressure and room temperature conditions, as opposed to typical grain enlargement processes that are required to occur at elevated temperatures to overcome the activation barriers for diffusion. Currently, both the driving force and the mechanism of this phenomenon remain unknown. Measurements with a polychromatic beam that is 500 <sup>×</sup> 500 nm2 size demonstrated that the newly formed ω-Zr crystals may have an irregular morphology (Figure 3b).

Using Laue diffraction, the grain enlargement process in Zr was studied in real time [27]. Initially, we did not observe any Laue reflections from the fine-grained parent α-phase. As Zr started to undergo a transition to ω-phase, we started to observe the appearance of strong diffraction spots. The intensities of these reflections increased gradually along with increasing pressure. Mapping of the ω-Zr reflections clearly demonstrated that the ω-Zr crystals nucleated and grew in the nano-crystalline matrix of α-Zr. In the Supplementary Materials, a movie combined from maps of an ω-Zr reflection is presented as an example (Movie S2). The sizes of the newly formed ω-Zr crystals gradually increased along with the increase in pressure, while the intensities of the ω-Zr reflections gradually decreased towards the edges of the crystals away from the nucleation points. These observations indicate a grain enlargement mechanism that involves formation and movement of highly angular grain boundaries, distinguishing the enlargement from a recovery process in which stored energy of dislocations is released without movement of the grain boundaries. In the case of recovery, intensities of ω-Zr reflections on the composite frames would increase simultaneously over a single grain area. This is followed by gradual sharpening of the ω-Zr reflections. The observed ω-Zr reflections stayed at the same level of broadening during the grain enlargement process indicating that there was no substantial texture development involved in this process. The majority of ω-Zr reflections exhibited only positive shifts of their intensities, indicating that ω-Zr crystals mainly grew at a cost to α-phase, and not at cost to each other, as would be the case if the enlargement process had a similar nature to the widely known grain coarsening process.

#### **5. Future Developments**

In the future, faster area detectors and translational stages will be implemented in order to improve the time resolution of this technique, while improvement of its spatial resolution will require smaller incident beams. Improvement of both spatial and time resolution will provide better details of the phase transition mechanisms and interface developments thereof. For example, implementation of X-ray polychromatic beams focused down below 100 nm [12] may provide details of the mechanism of the pressure induced grain enlargement observed across the α → ω phase transition in Zr.

A clear advantage of DAC compared to other stress generation devices is that the sample can be studied under hydrostatic compression or alternately under shear. Hydrostatic pressure using either He or Ne as a transmitting medium can be contrasted with studies with other media (such as silicone oil for example), thereby modifying the shear forces.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2073-4352/9/12/672/s1, Figure S1: Axis Pro Micro Support micromanipulator available in sample preparation laboratory of HPCAT, Figure S2: maps of reflections (indices are shown) from a crystal of ω-Zr, Movies S1a and S1b: series of composite frames of reflections from coexisting α- and β-Si [1] at the onset of α → β transition (S1a) and when the transition was nearly over (S1b), arrows of different colors in S1a denote reflections from different crystals of α-Si, rectangle in S1a denotes overlap area with S1b, Movie S2: series of composite frames of a reflection from an ω-Zr crystal growing during the α → ω transition [27], time intervals since starting of data collection are shown in the movies.

**Author Contributions:** Conceptualization, D.P. and N.V.; software, D.P.; writing—original draft preparation, D.P. and N.V.; writing—review and editing, M.S.

**Funding:** This research was funded by DOE-NNSA's Office of Experimental Sciences. The Advanced Photon Source was funded by the U.S. Department of Energy (DOE) Office of Science.

**Acknowledgments:** This work was performed at HPCAT (Sector 16), Advanced Photon Source (APS), Argonne National Laboratory. HPCAT operations are supported by DOE-NNSA's Office of Experimental Sciences. The Advanced Photon Source is a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. Part of this work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Review* **Pressure-Induced Phase Transitions in Sesquioxides**

**Francisco Javier Manjón 1,\*, Juan Angel Sans <sup>1</sup> , Jordi Ibáñez <sup>2</sup> and André Luis de Jesús Pereira <sup>3</sup>**


Received: 12 November 2019; Accepted: 26 November 2019; Published: 28 November 2019

**Abstract:** Pressure is an important thermodynamic parameter, allowing the increase of matter density by reducing interatomic distances that result in a change of interatomic interactions. In this context, the long range in which pressure can be changed (over six orders of magnitude with respect to room pressure) may induce structural changes at a much larger extent than those found by changing temperature or chemical composition. In this article, we review the pressure-induced phase transitions of most sesquioxides, i.e., *A*2O3 compounds. Sesquioxides constitute a big subfamily of *AB*O3 compounds, due to their large diversity of chemical compositions. They are very important for Earth and Materials Sciences, thanks to their presence in our planet's crust and mantle, and their wide variety of technological applications. Recent discoveries, hot spots, controversial questions, and future directions of research are highlighted.

**Keywords:** sesquioxides; high pressure; phase transitions

#### **1. Introduction**

The family of sesquioxides (SOs), i.e., compounds with *A*2O3 stoichiometry, is very important from an applied point of view, since SOs play a vital role in the processing of ceramics as additives, grain growth inhibitors and phase stabilizers. They also have potential applications in nuclear engineering and as hosts for optical materials for rare-earth (RE) phosphors. Besides, SOs with corundum-like structure, like corundum (α-Al2O3), hematite (α-Fe2O3) and eskolaite (α-Cr2O3), are relevant to Earth and planetology Sciences, because they are minerals present in the Earth's crust or in meteorites. Therefore, knowledge and understanding of phase transitions (PTs) occurring at high pressure (HP) in SOs is very important for Physics, Chemistry and Earth and Materials Sciences.

SOs are mainly formed by materials featuring an *A* cation of valence 3+, so that the two *A* cations compensate the total negative valence (6−) of three O atoms acting with valence 2−. Among the cations featuring 3+ valence, we find all group-13 and group-15 elements, some transition metal (TM) elements and all RE elements. Additionally, we can also find SOs where cations show an average 3+ valence. In this context, SOs with cations showing both 2+ and 4+ valences (both valences present in the *A*2O3 compound), are named mixed-valence (MV) SOs. The different compositions of these compounds provide a very rich environment ranging from molecular or zero-dimensional (0D), one-dimensional (1D) and two-dimensional (2D) solids to the conventional (bulk) three-dimensional (3D) solids; all of them showing radically different properties and behaviors under compression.

After more than 50 years of exploration of pressure-induced PTs in SOs, we present in this work a review of the PTs of SOs at HP, including those occurring at high temperatures (HTs), at low temperatures like room temperature (RT), and even at room pressure (RP). We have structured the present paper in five main sections that are devoted to RE-SOs, group-13-SOs, group-15-SOs, TM-SOs, and MV-SOs.

Finally, before attempting to present our results, we must comment that several reviews of the PTs in SOs at HP have been already published. We can cite the review on oxides of Liu and Basset in 1986 [1], of Adachi and Imanaka in 1998 [2], of Smyth et al. in 2000 [3], of Zinkevich in 2007 [4] and of Manjón and Errandonea in 2009 [5]. The present review goes beyond previous studies of SOs by expanding the number of families studied, by discussing the most recent results published in the last decade, and by suggesting pressure-based studies still to be performed.

#### **2. High-Pressure Phase Transitions in Sesquioxides**

#### *2.1. Rare-Earth Sesquioxides*

RE-SOs are highly interesting and versatile for different types of applications, since the atomic radius can be finely tuned along the lanthanide family, thus enabling a wide range of technological applications, including light emitters (lasers and improved phosphors), catalysts, and high-dielectric constant (high-k) gates.

RE-SOs, and in particular lanthanide SOs (Ln2O3; Ln = La to Lu, including Y and Sc), usually crystallize at room conditions in either the A-, B-, or C-type structures, depending on the RE atomic size. Large cations from La to Nd usually crystallize in the trigonal A-type structure (s.g. *P*3*m*1), medium-size cations from Sm to Gd tend to show a monoclinic B-type structure (s.g. *C2*/*m*), and small cations from Tb to Lu, including Sc and Y, tend to adopt a cubic C-type structure (s.g. *Ia*3). At HTs, two additional phases, hexagonal H (s.g. *P*63/*mmc*) and cubic X (s.g. *Im*3*m*) structures, have also been found in Ln2O3 [6]. Zinkevich has reviewed temperature-induced PTs in RE-SOs and found that a C→B→A sequence of PTs usually occurs upon an increase in temperature [4]. Since the density and cation coordination of the A-, B- and C-type structures increase in the sequence C-B-A, C→B, B→A, and even direct C→A transitions are expected on increasing pressure (upstroke), while inverse PTs are expected on decreasing pressure (downstroke) [7,8]. Curiously, it has been found that the cationic distances in the three structures of the RE-SOs at room conditions are similar to those in the bcc, fcc and hcp structures of the RE metals, thus suggesting that a relationship must exist between them [9,10].

The effect of HP on Ln2O3 has been extensively studied by many research groups, mainly by X-ray diffraction (XRD), Raman scattering (RS) and photoluminescence measurements. The HP behavior of C-type compounds has been studied in Lu2O3 [11–14], Yb2O3 [15–18], Tm2O3 [19,20], Er2O3 [11,21,22], Ho2O3 [23–26], Dy2O3 [27,28], Gd2O3 [11,29–36], Eu2O3 [11,37–43], Sm2O3 [11,32,44,45], Sc2O3 [46–48], Y2O3 [11,32,49–60], and recently on Tb2O3 [61]. Examples of pressure-driven C→B, B→A, direct C→A, and even C→A+B transitions have been shown to occur in a number of RE-SOs. As example, Lu2O3 was found to show either a C→B PT around 12 GPa without B→A PT up to 47 GPa [12,13], or a C→A+B PT above 25 GPa, with a recovery of a single B phase on downstroke from 47 GPa [14]. Similarly, Yb2O3 was found to exhibit a C→B PT above 13 GPa, and no further PT was found up to 20 GPa [15], but an A phase was found above 19.6 GPa that transforms into the B phase below 12 GPa [16]. The A phase in coexistence with the B phase was confirmed by RS measurements up to 45 GPa [17]. The C→B→A sequence of PTs was also found in Y2O3, the most studied RE-SO at HP, around 12 and 19 GPa [49], and has been confirmed in many studies [60]. In this context, it must be stressed that the pressure-induced PT sequence in Y2O3 has been shown to be affected by the nature of the sample, since different sequences of PTs have been observed in nanocrystals [33]. It must be stressed that direct C→A PT, with A→B PT on downstroke from 44 GPa, has been observed in Sm2O3 [44]. This sequence of PTs has also been observed in Gd2O3 [31]. Other PTs in RE-SOs have been found at HP and HT. In particular, an orthorhombic Gd2S3-type structure (s.g. *Pnma*) has been found in C-type Y2O3 above 8 GPa [57].

The HP behavior of B-type compounds has been also studied in Y2O3 [62], Eu2O3 [63], and Sm2O3 [64,65]. A reversible pressure-induced B→A PT has been observed in all B-type compounds. Additionally, the Gd2S3-type structure has been found in B-type Sc2O3 above 19 GPa upon laser heating [47]. Table 1 summarizes the experimental PT pressures observed in C- and B-type RE-SOs.

**Table 1.** Experimental data of the phase transition pressures (in GPa) for Ln2O3 and related sesquioxides having a C- or B-type phase at room conditions. The measurement technique (Tech.) and the pressure-transmitting medium (PTM) are also provided. Comp. stands for compound, MEW stands for the 16:3:1 mixture of methanol:ethanol:water and Polyethy. stands for polyethylene glycol.


The HP behavior of A-type compounds has been studied in Nd2O3 [67,68], Ce2O3 [69], and La2O3 [11]. A-type Nd2O3 has been observed to suffer a reversible PT above 27 GPa towards a monoclinic s.g. *P2*/*m* phase [67]. However, other work has suggested a 1st-order isostructural PT above 10 GPa [68]. This behavior is in contrast with that of Ce2O3, which seems to be stable in the A-type phase up to 70 GPa. Curiously, A-type Ce2O3 shows anomalies in the compressibility of the lattice parameters around 20 GPa, which could be related to an isostructural PT similar to that of Nd2O3. Finally, A-type La2O3 seems not to be stable above 4 GPa, following a PT to a hexagonal superlattice and eventually to a distorted monoclinic structure with a group–subgroup relationship with the hexagonal one [11].

It must be mentioned that RE-SOs and their pressure-induced PTs have also been investigated theoretically, and the simulations of the bandgap, volume, bulk modulus and its pressure derivative for the C, B and A phases, as well as their PT pressures, have been reported and found in rather good agreement with experiment [70–83]. Theoretical studies have found that the C→A and C→B PTs result in a decrease in the unit cell volume per formula unit at the transition pressure of the order of 10% ± 2%, in good agreement with experiments [81]. On the other hand, the B→A PT results in a decrease in the unit cell volume per formula unit at the transition pressure of the order of less than 2%, in good agreement with experiments [76]. Figures 1–3 show a comparison of experimental data (from Table 1) and theoretical data for the C→A, C→B and B→A PT pressures in bulk RE-SOs as a function of the atomic number of the lanthanide, ZLn, and of the ionic radius of the RE cation. In general, a good agreement between theoretical and experimental data can be found for all PTs. As regards the C→A PT, the pressure of the transition increases along the lanthanide series with the increase in atomic number, i.e., with the decrease in the ionic radius. It must be noted that no work has reported the C→A PT for Sc2O3, and that the reported C→A PT in materials with a small ionic radius, like Lu2O3 and Yb2O3, are doubtful. Regarding the C→B PT, the pressure of the transition also increases along the lanthanide series with the increase in atomic number or the decrease in the ionic radius. Unfortunately, no theoretical data exist for the C→B PT along the whole RE-SOs series; consequently, theoretical data for the C→A PTs are plotted for comparison with experimental data of the C→B PTs. It must be noted that the C→B PT is not observed in Sm2O3 and Eu2O3, since these two SOs undergo a direct C→A PT. Finally, as regards the B→A PT, the pressure of the transition once again increases along the lanthanide series with the increase in atomic number or the decrease in the ionic radius. As observed, no experimental data for the B→A PT has been reported in Sc2O3, Lu2O3 and Tm2O3. This will require new experiments up to 40 GPa in Lu2O3 and Tm2O3 and above 80 GPa in Sc2O3.

**Figure 1.** Experimental (solid symbols) and theoretical (empty symbols) data for the C→A phase transition pressures in Ln2O3 and related sesquioxides as a function of (**a**) the atomic number, ZLn, and (**b**) the ionic radius. Experimental data are from Table 1, while theoretical data are from reference [81]. Ionic radii of Shannon for cation 6-fold coordination were considered.

**Figure 2.** Experimental (solid symbols) and theoretical (empty symbols) data for the C→B phase transition pressures in Ln2O3 and related sesquioxides as a function of (**a**) the atomic number, ZLn, and (**b**) the ionic radius. Experimental data are from Table 1, while theoretical data correspond to those of the C→A phase transition in reference [81], since no theoretical data for the C→B phase transition are known to our knowledge. Ionic radii of Shannon for cation 6-fold coordination were considered.

**Figure 3.** Experimental (solid symbols) and theoretical (empty symbols) data for the B→A phase transition pressures for Ln2O3 and related sesquioxides as a function of (**a**) the atomic number, ZLn, and (**b**) the ionic radius. Experimental data are from Table 1, while theoretical data are from reference [76]. Ionic radii of Shannon for cation 6-fold coordination were considered.

In summary, there are many HP studies in cubic C-type RE-SOs that allow us to conclude that this structure undergoes a pressure-induced irreversible 1st-order PT either to a hexagonal A-type structure or to an intermediate monoclinic B-type structure. It is also observed that the A-type structure of RE-SOs usually reverts to the B-type structure on decreasing pressure, but the B-type structure remains metastable at room conditions and does not revert to the C-type structure unless it is conveniently heated. The irreversibility of the C→A and C→B PTs means that there is a considerable kinetic energy barrier between the C-type and the A- and B-type structures, due to the reconstructive nature of these PTs. On the other hand, the reversibility of the B→A PT is consequence of the weak 1st-order nature of this PT, as expected, because A- and B-type structures obey a group-subgroup relationship. In this context, HP studies of B-type RE-SOs show a pressure-induced reversible weak 1st-order PT to the A-type structure. It must be noted that some PTs for RE-SOs with a small RE ionic radius have yet to be reported. Besides, a pressure-induced PT to the Gd2S3 structure has been found from some C- and B-type RE-SOs at HT. Finally, we must comment that HP studies on trigonal A-type RE-SOs are quite scarce and do not allow us to conclude which is the typical HP phase of A-type RE-SOs. Consequently, more work has to be done in A-type RE-SOs, either studying C- or B-type RE-SOs at higher pressures or studying in better detail RE-SOs crystallizing in the A phase at room conditions, in order to understand the behavior of the trigonal structure and its pressure-induced PTs.

#### *2.2. Group-13 Sesquioxides*

Group-13-SOs are highly interesting compounds, due to their chemical and physical properties, which enable their application as catalyst, lasers and light emitting materials [84]. HP studies in group-13-SOs have been conducted on the five compounds. Al2O3, also known as alumina, is by far the most studied compound [85–99], followed by In2O3 [100–109], Ga2O3 [107,110–114], and B2O3 [115–121]. Finally, Tl2O3 has been the least studied compound [122].

The interest in alumina comes from its high stability, making it interesting for HP science applications, especially as windows in shockwave experiments [123]. However, its main application occurs when alumina is doped with a small amount of Cr3<sup>+</sup>. Al2O3:Cr<sup>3</sup>+, also known as ruby, presents fluorescence lines that are pressure-dependent and is used as a pressure standard in static HP experiments using anvil cells [124]. Corundum (α-Al2O3) is a mineral of alumina that is found in abundance in the earth mantle incorporated into enstatite (MgSiO3) [99]. Given that both minerals might adopt similar structures at ultra-HPs, their study is interesting from a geophysical point of view. In fact, the most stable phase of alumina at room conditions is the corundum structure (s.g. *R*3*c*), where coordination of all Al atoms is six-fold and of O atoms is four-fold [94]. The unit cell has two formula units, with O atoms forming a slightly distorted, hexagonal, close-packed structure [88,125]. The same structure is also found in other SO minerals, such as hematite (Fe2O3), eskolaite (Cr2O3), karelianite (V2O3), and also Ti2O3 and Ga2O3 [125]. In this structure, cations occupy positions (0, 0, *z*) and oxygens occupy positions (*x*, 0, <sup>1</sup> <sup>4</sup> ) and, if both *z* and x coordinates were 1/3, the corundum-type structure would have a perfect hexagonal close-packed packing [125].

β-Al2O3 is another very interesting polymorph of alumina from a technological application point of view. This material is a non-stoichiometric compound (Na2Ox ·Al2O3, 5 ≤ x ≤ 11) and not a simple variation of alumina [126,127]. Due to its layered crystalline structure, β-Al2O3 has a high ionic conductivity and has been studied for solid state battery applications [126,127]. We have not found any HP study of this material.

Theoretical studies of corundum predicted a pressure-induced PT to the Rh2O3-II structure (s.g. *Pbcn*) between 78 and 91 GPa [87,92,96,98] and a second PT to an orthorhombic perovskite (Pv) structure (s.g. *Pbnm*) at 223 ± 15 GPa [87,92,96,98,128]. Other theoretical studies predicted that the post-perovskite (PPv) CaIrO3-type structure (s.g. *Cmcm*) would be more stable than the Pv structure at pressures higher than 150 GPa [85,99,129]. However, RT measurements performed up to 175 GPa under hydrostatic and non-hydrostatic conditions showed no PT [88,89]. The PT to the Rh2O3-II structure was only observed at HP (>95 GPa) and HT (>1200 K) [86,97] once the energy supplied by temperature allows the overcoming of the kinetic barrier of this 1st-order PT [86,89,96,97,128]. The Rh2O3-II structure is directly related to corundum structure; nevertheless, it presents a great distortion in the AlO6 octahedron [97]. Lin et al. reported that the Rh2O3-II-type Al2O3 (Cr3<sup>+</sup> doped) remains stable up to 130 GPa and 2000 K [97]. However, studies using shock waves have shown that a decrease by one order of magnitude in resistivity occurs at 130 GPa [123] that it is coincident with an increase in the density of Al2O3 [130], thus indicating a possible PT. This hypothesis was supported by the discovery of a PPv CaIrO3-type polymorph of Fe2O3 [131] and MgSiO3 [132]. In 2005, Oganov and Ono were finally able to synthesize the PPv CaIrO3-type phase of Al2O3 at ~ 170 GPa and 2500 K [94,129]. They showed that the Rh2O3-II → CaIrO3-type PT is a 1st-order PT with ~ 5% of volume decrease [94,129]. The possibility of obtaining this structure at HP and HT was important to understand the physical properties of the elements present in the D" layer of the earth mantle [129]. This layer is basically composed of a solid solution of MgSiO3, Fe2O3 and Al2O3. Since, under the HP and HT conditions of the Earth mantle, all these materials are isostructural, their solubility may be facilitated [94].

When synthesized as nanoparticles smaller than 20 nm, alumina tends to crystallize into a cubic structure known as a phase γ (s.g. *Fd*3*m*) [133]. HP experiments at room temperature observed an amorphization of γ-Al2O3 around 5 GPa [133]. On the other hand, it was also observed that the γ-Al2O3 → *R*3*c* PT, which occurs at RP near 1473 K, decreases to ~ 1023 K when γ-Al2O3 is pressurized at 1 GPa [134]. In addition, HP-HT experiments have revealed other phases of alumina, like polymorphs of RE-SOs B- and C-type, as well as polymorphs λ and μ [135,136]; however, no HP studies on these phases have been reported to our knowledge.

The search for new high hardness materials, such as Al2O3, has attracted the attention of many research groups for SOs, including indium oxide (In2O3) and gallium oxide (Ga2O3) [106]. In2O3 is a semiconductor with high potential for many transparent oxide applications, including touch and photovoltaic devices, thermoelectric and gas sensors [137]. At room conditions, In2O3 crystallizes in the cubic bixbyite structure (s.g. *Ia*3), also known as the C-type RE-SO structure (c-In2O3) [106]. In this structure there are two types of In atoms (they are surrounded by oxygen in the octahedral and trigonal prismatic coordination) located at positions 8*b* and 24*d* and one type of O located at position 48*e* [138]. In the 1960s, a PT from c-In2O3 to a metastable corundum-like rhombohedral phase (rh-In2O3; s.g. *R*3*c*) was reported at HP and HT (6.5 GPa and 1000 ◦C) [106,139,140]. This PT was also observed through shockwave compression experiments between 15 and 25 GPa [141]. Some HP-XRD studies of both bulk and nanoparticle samples claimed that the c-In2O3 → rh-In2O3 PT occurs at RT when the sample is exposed to pressures between 12 and 25 GPa [103,104]. This result is controversial since other studies using HP-XRD and HP-RS measurements did not clearly observe this PT up to 30 GPa [100,101]. On the other hand, García-Domene et al. reported that bulk c-In2O3 actually undergo a PT to an Rh2O3-II-type structure (o1-In2O3; s.g. *Pbcn*) orthorhombic phase at pressures above 31 GPa at RT [101]. This structure was also obtained at 7 GPa after laser heating at 1500 ◦C [106]. This result is consistent with the prediction of theoretical calculations that the Rh2O3-II-type phase is the most stable In2O3 structure between 8 GPa and 36 GPa [101]. On top of that, looking for a possible CaIrO3-type PPv phase in In2O3, Yusa et al. observed another PT from Rh2O3-II-type to α-Ga2S3-type structure (s.g. *Pnma*) above 40 GPa and 2000 K [107]. A reduction of 7%–8% in volume was observed, unlike the reduction of 2% expected for a Rh2O3-II-type → CaIrO3-type transition [107].

Releasing the pressure after obtaining the Rh2O3-II-type structure in In2O3, García-Domene et al. demonstrated that, at 12 GPa, o1-In2O3 undergoes a PT to a previously unknown phase [101]. The combination of experimental and theoretical results helped to conclude that, upon decreasing the pressure to 12.1 GPa, the In2O3 recrystallizes in a distorted bixbyite-like structure (o3-In2O3; s.g. *Pbca*), isostructural to Rh2O3-III [101,108]. Decreasing the pressure below 1 GPa, o3-In2O3 undergoes another PT to the metastable rh-In2O3 structure. The metastable rh-In2O3 phase at room conditions remains stable up to 15 GPa and above this pressure shows a reversible PT to o3-In2O3, which is stable up to 25 GPa [101]. The observation of the *Pbca* phase took place only when decreasing pressure using original bulk c-In2O3 samples was related to kinetic barriers in the c-In2O3 → o3-In2O3 PT, that cannot be overcome at RT during upstroke [101]. Similar studies in c-In2O3 nanoparticles performed up to 44 GPa did not clearly show these PTs [100,104,105]. Qi et al. reported that, when compressing 6 nm c-In2O3 nanoparticles, an irreversible PT to the rh-In2O3 phase occurs between 20–25 GPa [104]. Nowadays, it is now possible to synthesize In2O3 nanoparticles at room conditions with the rh-In2O3 metastable phase at relatively low temperatures (250 to 500 ◦C) [142–144]. Sans et al. studied rh-In2O3 nanoparticles (10–30 nm) up to 30 GPa using XRD and RS measurements [109]. XRD measurements did not show any PT up to 30 GPa, but RS measurements showed peaks of the o3-In2O3 phase above 20 GPa [109]. One reason for this discrepancy was attributed to the sensitivity of RS measurements to local structural changes, which is responsible for the observation of PTs at lower pressures in RS compared to XRD measurements [109]. Another reason might be related to the use of less hydrostatic pressure-transmitting medium in RS (MEW) than in XRD (Ar) measurements [109].

Regarding Ga2O3, its most stable structure at room conditions is the monoclinic phase (s.g. *C*2/*m*), known as β-Ga2O3 [145,146]. However, depending on the pressure, temperature and atmosphere conditions, it is possible to find Ga2O3 in the α, β, γ, σ and ε phases [111,147]. Compared to Al2O3 and In2O3, HP studies on Ga2O3 are scarcer. In 1965, Remeika and Marezio reported the synthesis of α-Ga2O3 (s.g. *R*3*c*), which is isostructural to α-Al2O3, by pressurizing β-Ga2O3 to 4.4 GPa, after heating to 1000 ◦C and quenching to room conditions [147]. Lipinska-Kalita et al. reported that, upon

pressing nanoparticles (~15 nm) of β-Ga2O3 homogeneously dispersed in a host silicon oxide-based glass matrix, it is possible to observe a PT to α-Ga2O3 at 6 GPa [111]. In that study, the β-Ga2O3 → α-Ga2O3 PT is not completed up to 15 GPa and it is not clear whether the PT is induced by glass matrix densification or is an intrinsic behavior of the β-Ga2O3 nanoparticles [111]. This work led Machon et al. to study the behavior of β-Ga2O3 microparticles by XRD and RS measurements with different pressure-transmitting media [113]. They observed a PT to the α phase above 20 GPa, unlike what was observed in reference [111]. A highly disordered α-Ga2O3 was recovered at RP after a fast decompression from 25 GPa and a mixture of α and β phases were recovered when decompression was performed slowly [113]. The β-Ga2O3 → α-Ga2O3 PT can be considered to be of 1st-order and involves a change in O2- ions packing from cubic to hexagonal, accompanied by a change in Ga3<sup>+</sup> coordination from four to six [111,113,148].

The β-Ga2O3 → α-Ga2O3 PT was not clearly observed in an experiment performed up to 65 GPa without pressure-transmitting medium [106]. Instead, XRD measurements at 65 GPa showed only a diffraction pattern similar to a material with low crystallinity or amorphous. After laser heating (~2300 K), a recrystallization to an orthorhombic phase Rh2O3-II-type (s.g. *Pbcn*) was observed [106]. This phase remained stable up to 108 GPa and 2500 K. During decompression, the Rh2O3-II-type → α-Ga2O3 PT was observed between 32 and 21 GPa, being the α phase metastable at RP [106]. These results differ from other published by Lipinska-Kalite et al. up to 70 GPa with (N2) and without pressure-transmitting medium [110]. In that study, a β-Ga2O3 → α-Ga2O3 PT was clearly observed, which starts at 6.5–7.0 GPa (3 GPa) and completes at 40 GPa (30 GPa) when measured with (without) pressure-transmitting medium [110]. Through XRD measurements, Lipinska-Kalita et al. observed no evidence of pressure-induced amorphization or deterioration of the diffractogram up to 70 GPa [110]. The β-Ga2O3 → α-Ga2O3 PT was also observed at 16 GPa in shockwave experiments [149]. Wang et al. conducted HP studies on β-Ga2O3 nanoparticles (14 nm) at RT and found the PT to α-Ga2O3 above 13.6 GPa [114]. Above this pressure, the α phase remains stable up to 64.9 GPa and stays metastable upon returning to RP [114].

Boron sesquioxide (B2O3) is one of the most important oxides in applications involving vitreous systems. In glass form, B2O3 has a low melting point (750 K) and a structure similar to vitreous SiO2 and H2O [117]. When pressing the glassy material, it is possible to observe a structural rearrangement around 3 GPa that was considered a low- to high-density vitreous PT [118]. Furthermore, starting from the glassy material, it is possible to obtain B2O3 crystals at HP and HT. At room conditions, the most stable structure of B2O3 is a trigonal structure (s.g. *P*3121) known as B2O3-I, where B is in the center of triangles of O atoms [115–117,119,121]. Despite its stability at room conditions, working with this material is not simple due to its strong hygroscopic behavior, capable of decomposing the sample in a few minutes [121]. Above 3.5 GPa and 800 K, B2O3-I undergoes a PT to an orthorhombic structure, known as B2O3-II (s.g. *Ccm*21), composed of distorted BO4 tetrahedra [116,120]. The B2O3-I → B2O3-II transition leads to an increase of B and O coordination from 3 to 4, and from 2 to an intermediate between 2 and 3, respectively, and a volume change of ~27% [117,120,150].

The last group-13-SO is thalium oxide (Tl2O3). This material is very interesting from a technological point of view as it has potential for interesting applications such as solar cell electrode, optical communication and HT superconductors [151–154]. Its most stable phase at room conditions is c-Tl2O3, a bixbyite body-centered cubic phase isostructural to c-In2O3. A corundum-like structure (s.g. *R*3*c*) was also observed at HP (6.5 GPa) and HT (500-600 ◦C) [140]. So far, only one paper reports the properties of the c-Tl2O3 at HP, probably due to the toxicity of this material [122]. Theoretical calculations predict a c-Tl2O3 → Rh2O3-II-type (s.g. *Pbcn*) PT at 5.8 GPa and a second Rh2O3-II-type → α-Gd2S3-type (s.g. *Pnma*) PT at 24.2 GPa [122]. However, ADXRD measurements at RT, performed using MEW as pressure-transmitting medium, showed only an irreversible pressure-induced amorphization at 25.2 GPa, which was a consequence of kinetic barriers that cannot be overcome at RT [122]. In addition, theoretical calculations predicted a mechanical instability of c-Tl2O3 above 23.5 GPa [122]. Future work involving HP and HT is needed to better understand the behavior of Tl2O3 at HP.

To finish this section, we summarize in Table 2 the phase transition pressures observed in group-13-SOs.

**Table 2.** Experimental data of the phase transition pressures (in GPa) for group-13 sesquioxides. The letters A, B, C, D, E, F, G, H, and I refer to the structures *R*3*c*, *Rh*2*O*<sup>3</sup> − *II*-type, *CaIrO*3-type, *Ia*3, α − *Ga*2*S*3-type, *Pbca*, *C*2/*m*, *P*3121, and *Ccm*21, respectively. Between parentheses are the transition temperatures (when necessary). SW stands for shockwave experiments and NP for nanoparticles.


#### *2.3. Transition-Metal Sesquioxides*

TM-SOs belong to a highly heterogeneous family of compounds, as their fundamental (electronic, magnetic) properties strongly depend on the number, and therefore on the spin state, of *d* electrons in the *A*3<sup>+</sup> cation. TM-SOs include, among others, the ubiquitous ferric oxide (Fe2O3), the commonly-used green pigment Cr2O3, or the relatively rare Ti2O3 oxide, found in the famous Allende meteorite as the mineral tistarite [155]. Thus, each of these compounds has its own particularities and, regarding the HP structural properties, its specific behavior upon compression.

Among all the TMs, excluding the *f*-block lanthanide and actinide series and including group-3 and group-12 elements, in this section we will only consider *A*2O3 compounds with at least one *d* electron. Thus, Sc2O3, Y2O3 and La2O3 are not included here, since they have been discussed together with the RE-SOs in Section 2.1. Among the rest of possible TM-SOs, only the following compounds have been found to be stable at room conditions: Ti2O3, V2O3, Cr2O3, Mn2O3, Fe2O3, Co2O3, Ni2O3, Rh2O3 and Au2O3. Other compounds, like Hf2O3 and Zr2O3, might be metastable at HP [156].

With the exception of Mn2O3, the most stable form of all TM-SOs at room conditions corresponds to the rhombohedral structure of the corundum. As can be seen in Figure 4a, the lattice parameters of the corundum-like structure adopted by most of TM-SOs are barely reduced by increasing the number of *d* electrons in the *A*3<sup>+</sup> cation. This result simply reflects the slight reduction in the atomic radius of the cations with increasing atomic number. However, as can be seen in Figure 4b, the *c*/*a* ratio of these compounds displays a well-known anomaly around Ti2O3 and V2O3 that deserves further attention. In particular, V2O3 has highly remarkable properties and behaves, upon compression, in a highly

different fashion than other corundum-type TM-SOs [157]. In turn, Mn2O3 crystallizes in the so-called bixbyite structure (s.g. 206, *Ia*3), which takes the name of the mineral form of Mn2O3. The absence of the corundum structure in Mn2O3 at room conditions has been attributed to the Jahn-Teller distortion associated with the *d*<sup>4</sup> Mn3<sup>+</sup> ion [158].

**Figure 4.** (**a**) Lattice parameters, a and c, of different corundum-type 3d-TM-SOs. The plot shows the similarity between the lattice parameters of these compounds. Corundum-type Ga2O3 (with 10 d electrons) is also included. (**b**) c/a ratio for different corundum-type TM-SOs. Al2O3 (with no d electrons) and Ga2O3 (with 10 d electrons) are also included. Note the well-known anomaly around Ti2O3 and V2O3.

Most TM-SOs have also been found to exhibit other stable or metastable polymorphs at room conditions, as well as at HP. Next, we focus on the rich and varied HP behavior of the different phases of TM-SOs, with special emphasis on Fe2O3, Mn2O3 and V2O3.

Iron oxides are highly important materials in a large variety of disciplines, including materials science, geology, mineralogy, corrosion science, planetology and biomedicine. In the particular case of iron SO (iron (III) oxide or ferric oxide), there exist several polymorphs that are stable or metastable at room conditions: α, β, γ, ε and ζ. First, we will briefly describe these phases at room conditions and, afterwards, we will discuss their HP behavior.

The most common phase of Fe2O3 is the α phase, which has the corundum structure and is ubiquitously found in nature as the mineral hematite. α-Fe2O3 is a wide-gap antiferromagnetic insulator, with a Morin transition around 250 K. It is weakly ferromagnetic from this temperature up to a Néel temperature around 950 K, above which it becomes paramagnetic. Besides temperature and doping, pressure is a highly convenient tool to modify the insulating/metallic state of this type of material. In particular, hematite can be considered as an archetypal Mott insulator [159] and is interesting from the point of view of metal-insulator PTs in highly correlated electron systems.

The mineral hematite is the main ore of iron and a very common phase in sedimentary rocks, where it occurs as a weathering or alteration product. It is, however, unlikely that Fe2O3 or any of its HP phases have much relevance in the Earth's lower mantle, where Fe3<sup>+</sup> is mainly incorporated into other minerals, like bridgmanite or garnet, with the possible coexistence of reduced iron-rich metal (Fe0) [160]. In contrast, it cannot be ruled out that Fe2O3 may be responsible for the presence of magnetic anomalies in the upper mantle arising from deep-subduction processes [161]. Thus, the HP behavior of hematite may still be highly relevant from a geophysical point of view, as it might play a key role in relation to the magnetic properties of recycled crust materials in subduction zones.

The γ phase of Fe2O3 is also found in the Earth's crust as the relatively common mineral maghemite, which is formed by weathering or low-temperature oxidation of magnetite and related spinel minerals. Maghemite, which is also a very common corrosion product, is metastable and transforms upon

heating into the α phase. γ-Fe2O3 has the same cubic spinel ferrite structure (s.g. 227, *Fd*3*m*) as magnetite (Fe2<sup>+</sup>Fe3<sup>+</sup>2O4), with 1/3 of Fe atoms tetrahedrally coordinated with oxygen (A sites), and 2/3 octahedrally coordinated with oxygen (B sites). Thus, maghemite can be considered as a Fe2+-deficient magnetite, with all A sites filled with Fe3<sup>+</sup> and only 5/6 of the total available B sites filled with Fe3+; i.e., with 1/6 of vacant (V) B sites, so it can be noted as (Fe3<sup>+</sup>) A(Fe3<sup>+</sup>5/3V1/3) BO4. γ-Fe2O3 exhibits soft ferrimagnetism at RT, with a Curie temperature around 950 K [162]. Most remarkably, ultrafine particles of γ-Fe2O3 exhibit super-paramagnetism, which is related to the thermally induced random flip of the magnetization in ferromagnetic nanoparticles. This phase is being intensively investigated in order to construct an appropriate theoretical framework for this phenomenon, which might set a limit on the storage density of hard disk drives.

A rare orthorhombic polymorph of Fe2O3, named ε-Fe2O3 (s.g. 33, *Pna*21), has also been found to be stable at room conditions. This phase seems to exist only in nanosized form and was first reported back in 1934 [163]. A few years later, it was synthesized and characterized by Schrader et al. [164]. The crystal arrangement of ε-Fe2O3 is considered as intermediate between the structures of the α and γ phases, with three octahedral FeO6 units (two of which are distorted) and a FeO4 tetrahedral unit. It is worth noting that this phase has recently been found in nature as the Al-bearing nanomineral luogufengite, which is an oxidation product of Fe-rich basaltic glass at HT [165]. It has also been found in ancient black-glazed wares from Jianyang county, China, produced during the Song dynasty (960–1279 AD) [166]. Recent studies have also shown that this polymorph is a non-collinear ferrimagnet [167]. Owing to its remarkable magnetic properties, such as giant coercive field, ferromagnetic resonance and magnetoelectric coupling [168], this phase is highly promising to develop a broad range of novel applications. Besides, the giant coercive field of lougufengite might explain the observed high-remanent magnezitation in some igneous and metamorphic rocks [169].

In contrast to ε-Fe2O3, β-Fe2O3 and the recently discovered "ζ-Fe2O3" phase [170] have not been found to occur in nature so far. These two rare polymorphs are metastable phases that have been obtained by synthetic methods and which only exist in nanocrystalline form. The beta phase exhibits the bixbyite structure, with trivalent Fe ions occupying two non-equivalent octahedral sites. It exhibits paramagnetic behavior at room conditions, with a Néel temperature just above 100 K. Antiferromagnetic ordering is observed below this temperature. Upon heating, β-Fe2O3 undergoes a PT to either the α or γ phases. In turn, "ζ- Fe2O3" displays a monoclinic structure (s.g. 15, *I*2/*a*) and was obtained by applying HP (>30 GPa) to β-Fe2O3 [169]. Surprisingly, this new phase (with a Néel temperature around 70 K) is metastable after releasing pressure, being able to withstand pressures up to ~70 GPa.

In spite of much effort to elucidate the structural, magnetic and electronic properties of α-Fe2O3 (hematite) at HT and HP [159,170–176], the HP behavior of the most important phase of Fe2O3 is still under debate. Only recently was a complete T-P phase diagram of α-Fe2O3 established [176]. According to that work, α-Fe2O3 transforms at RT to a HP phase above ~50 GPa, with an ~8.4% volume discontinuity. It is worth noting that in this work the HP phase was called "ζ-phase" and was indexed as triclinic (*P*1) [175]. This phase is not equivalent to the monoclinic s.g. *I*2/*a* phase stable at room conditions, also named "ζ-Fe2O3", which was produced by Tucek et al. [169]. It must be noted that the *P*1 phase was previously indexed as monoclinic (*P*21/*n*) in reference [175]. The fact that this HP phase is relabeled as "double perovskite" in reference [170] and treated as s.g. *P*21/*n* only adds confusion to the nomenclature of the different phases of such an important compound as Fe2O3.

As already mentioned, the single-crystal diffraction patterns of the *P*1 HP phase were initially indexed in a monoclinic unit cell [173], but were subsequently refined into a triclinic s.g. *P*1 structure [175]. However, previous works had assigned the HP phase (~50 GPa) of hematite to either a distorted corundum phase (Rh2O3-II-type structure, s.g. *Pbcn*) [159,170,172,177] or to a Pv structure (s.g. *Pbnm*) [129,178]. According to reference [175], the *P*1 structure of Fe2O3 is closer to a distorted (and not "double", as in reference [176]) Pv structure. However, a more recent study up to ~79 GPa has put into question the very existence of the distorted Pv phase [174], in agreement with

previous results [179]. The data and analysis of reference [159] indicate that the 1st-order PT around 50 GPa is accompanied by an insulator-to-metal transition with collapse of the magnetic properties. The structural PT would thus be very progressive [160,170], starting from the corundum-type structure and leading to a distorted Rh2O3-II-type structure. In contrast, Bykova et al. suggested that the Rh2O3-II-type structure only occurs below 50 GPa at HT and would be reconstructive, with a volume change of ~1.3% [173]. According to this work, the distorted Pv phase shows a PT at RT around ~67 GPa to a possibly metastable orthorhombic structure (s.g. 41, *Aba2*) or to a CaIrO3-type PPv phase (s.g. *Cmcm*) [175]. In fact, the *Aba2* to PPv PT was observed at HT (above 1600 K). After quenching the samples to RT, the PPv polymorph was found to be stable up to 100 GPa and down to 26 GPa; however, hematite was recovered below this pressure. In turn, the metastable *Aba*2 phase seems to be preserved at 78 GPa, up to 1550 K. This polymorph, also observed by Greenberg et al. [176] at RT, can be considered as a metastable HP phase at low temperature. It adopts a similar packing to the Rh2O3-II-type structure observed at low pressures, but, instead of octahedra, it consists of FeO6 prisms. Recent results obtained by Sanson et al. are compatible with the existence of the *Aba*2 polymorph [174]. However, these authors seem to rule out not only the *P*21/*n* HP phase, but also the *Pbnm* one.

Regarding the PPv structure, Ono et al. had previously reported a PT from hematite to the PPv structure above 30 GPa at HT [131]. Moreover, a new phase was found above 50 GPa to an unknown phase that was tentatively assigned to an orthorhombic or a monoclinic lattice. In relation to the magnetic and electronic properties of this phase, Shim et al. showed that the magnetic ordering of PPv-type Fe2O3 is recovered after laser heating at 73 GPa [179]. According to these authors, the appearance of the PPv phase gives rise to the transformation of Fe3<sup>+</sup> ions from a low-spin to a high-spin state, with Fe2O3 undergoing a semiconducting-to-metal PT. This effect might be relevant to understand the electromagnetic coupling between the Earth's mantle and the core. Previous research had already investigated with Mössbauer spectroscopy the high-spin to low-spin PT in α-Fe2O3, at HP associated to the structural PT [180,181].

Indeed, one of the main interests of studying hematite at HP, besides its crystal structure and phase diagram, has to do with its electronic properties and the nature of the HP-PT [171]. What drives the HP-PT in hematite? Is it the crystal structure, or the electronic structure? Note that one could expect that electronic PTs, such as the insulator-metal Mott PT observed at 50 GPa [159] or the high-spin to low-spin PT, are isostructural. According to this argument, the PT observed in hematite at ~50 GPa, accompanied by a large volume change, should drive the change in electronic properties. Badro et al. reached this conclusion and indicated that the electronic PT is isostructural and occurs after the crystal structure PT [171]. However, Sanson et al. have recently reached the opposite conclusion, i.e., that the structural PT is driven by the electronic transition [174]. These authors analyzed the local structure and observed no FeO6 octahedra distortion at HP, in disagreement with previous works [170]. A careful analysis recently performed by Greenberg et al. suggests that the pressure-induced insulator-to-metal PT in hematite arises from site-selective delocalization of electrons [176]. According to this study, such site-selective Mott transition ought to be characterized by delocalization (i.e., metallization) of Fe 3*d* electrons on only half of the sites in the unit cell. This work suggests that the interplay between crystal structure and electronic correlations may yield a complex behavior that could be also relevant to understand the HP behavior of other TM-SOs.

With regard to the rest of Fe2O3 phases stable at room conditions (γ, β and ε), the amount of published works regarding their HP behavior is sizably lower in comparison to hematite. The phase diagram of γ-Fe2O3 (maghemite) is relatively simple, since this phase readily transforms to α-Fe2O3 around 35 GPa [182]. Therefore, much of the effort regarding this phase has been in relation to the comparison of the compression behavior between bulk and nanocrystalline samples (see reference [183] and references therein). Further details about polymorphic PTs of nanosized Fe2O3, including doping, temperature and HP, can be found in reference [184]. In the case of maghemtite, Jiang et al. found that nanocrystalline γ-Fe2O3 transforms to hematite at ~27 GPa, below the PT pressure for bulk material [182]. As shown by Zhu et al., the γ-to-α PT might be initiated at the same pressure, around

16 GPa, both in bulk and nanocrystalline forms [183]. According to these authors, vacancies might play an important role in the structural PT. More recently, a combination of XRD and Mössbauer spectroscopy up to 30 GPa on vacancy-ordered maghemite has shown that the γ-to-α PT would be initiated at 13–16 GPa, giving rise to a particular texture in the transformed α-Fe2O3 material [185].

Finally, in relation to the Fe2O3 polymorphs, we must mention the recent HP study of ε-Fe2O3 by Sans et al. [186]. These authors found that this rare nanocrystalline phase, which is a promising magnetic material for a range of technological applications, is stable up to 27 GPa. Above this pressure, evidence for a PT, in which the tetrahedrally coordinated iron ions change towards quasi-octahedral coordination, was observed. Given that this phase has very high magnetic coercivity, it remains to be investigated whether its mineral form may play any relevant role in the magnetic remanence of mantle xenoliths, and in the magnetism of subducting slabs at depths corresponding to the mantle transition zone [161].

Manganese SO (Mn2O3) is unique among 3*d*-TM-SOs because its most stable phase at room conditions (α-Mn2O3) does not adopt the corundum structure. Instead, it crystallizes in the so-called cubic bixbyite structure that takes the name from the mineral form of this compound. In bixbyite, Mn3<sup>+</sup> occupies five different crystallographic sites, each of them surrounded by a highly distorted octahedron of O atoms. Such distortion originates from the Jahn-Teller effect, due to the lowering of overall energy as a consequence of a distortion-induced loss of degeneracy in the 3*d*-orbitals of the sixfold-coordinated Mn3<sup>+</sup> ions. As discussed by several authors, the Jahn-Teller distortion might explain the fact that Mn2O3 does not adopt the corundum structure at room conditions [158]. Also, it has been predicted that HP might suppress the Jahn-Teller effect, which would make Mn2O3 transform to a corundum-type polymorph and, afterwards, follow the usual sequence of pressure-induced PTs observed in the rest of TM-SOs [140]. α-Mn2O3 has been shown to be antiferromagnetic, with a Néel temperature of around 79 K [187] and has recently attracted considerable interest due to its potential use in chemical catalysis and magnetic devices, and also for energy conversion and storage applications.

Interestingly, the bixbyite structure actually occurs in doped samples and/or at temperatures slightly above RT. Indeed, it has been shown that Mn2O3 undergoes a subtle cubic-to-orthorhombic (*Pcab*) PT around RT and that the bixbyite structure is stabilized by the presence of impurities [188]. The low-temperature phase *Pcab* is just an orthorhombically distorted bixbyite structure. There exists another polymorph of Mn2O3 stable at room conditions, namely γ-Mn2O3. It is a tetragonal spinel-like polymorph (s.g. *I*41/*amd*), related to Mn3O4. This phase, which is ferrimagnetic below 39 K, can be viewed as the equivalent of maghemite in the case of the Fe2O3 system.

Several studies have investigated the HP phases of Mn2O3 [140,189–194]. It is now clear that α-Mn2O3 transforms at RT to a CaIrO3-type PPv-like structure above 16 GPa [190–194] with a large volume collapse of ~12%. Thus, no Pv polymorph is observed between the bixbyite and PPv structures at RT. As pointed out by Santillán et al. [190], this might be due to the similarity between the two structures (cubic bixbyite and PPv). Yamanaka et al. also reported a monoclinic HP phase of Mn2O3 that has not been confirmed by any other study [189]. More recently, synthesis performed with a multianvil apparatus and subsequent study of the recovered material has shown that, at HTs (between ~850 and 1150 K) the Pv structure, also called ζ-Mn2O3, can be synthesized and recovered at room conditions [193]. This polymorph is formed by a Pv octahedral framework with strongly tilted MnO6 octahedra. Its crystal structure was determined within the *a*= 4*ap* supercell, s.g. *F*1 (s.g. *P*1 in the standard setting, see reference [193]), where Mn cations are preferentially found in different sites depending on their valence state (Mn2<sup>+</sup>, Mn3+, Mn4+). This phase has been shown to be a narrow and direct bandgap semiconductor (0.45 eV) with remarkable hardness [195], and to exhibit a 3:1 charge ordering between two different sites, and a unique orbital texture involving a remarkable alternation of orbitals states [196].

A corundum-type polymorph of Mn2O3 (ε-Mn2O3) was also recovered at room conditions after applying intermediate pressures (15 GPa) and HT (> 1200 K) [193]. This phase, which is about 1% denser than the bixbyite polymorph, seems to confirm the existence of the undistorted, corundum-type

structure in the exotic Mn2O3. It should be noted that, in contrast to this phase and the ζ phase, the more usual HP PPv polymorph is not quenchable at room conditions. The multianvil apparatus experiments also show that reduction of Mn2O3 to Mn3O4 is observed below 12 GPa at HT (>1200 K) [193]. No HP studies of ε and γ phases are available to our knowledge.

Among TM-SOs, vanadium oxide (V2O3) is one of the most interesting materials both from fundamental and applied points of view, due to its remarkable electronic and magnetic properties. This compound has a very rich phase diagram at RP and is often considered a paradigmatic example of metal to Mott-insulator transition in strongly correlated materials. Depending on temperature and doping with small amounts of Cr or Ti, V2O3 exhibits different phases including a paramagnetic metallic state, a paramagnetic insulating state or a low-temperature antiferromagnetic insulating state [197,198]. V2O3 adopts a corundum-type structure at atmospheric conditions and is found in nature as the rare mineral karelianite, first found in glacial boulders from the North Karelia region, in Finland. A metastable polymorph of V2O3 with bixbyite structure was obtained by synthetic methods [199]. This phase transforms into the stable corundum phase above 800 K, and is found to exhibit a paramagnetic to canted antiferromagnetic transitions at about 50 K.

The application of HP strongly modifies the phase diagram of corundum-type V2O3. Several studies have investigated the Mott-insulator transition in V2O3 and Cr-doped V2O3 at HP with a range of different experimental techniques [200–205]. Here, we would like to first focus on the link between the structural and electronic properties of V2O3. In particular, McWhan and Remeika [200] studied V2O3 and (V0.96Cr0.04)2O3 samples and found that the metallic state typically found in undoped V2O3 is recovered by compressing the Cr-doped sample. These authors also showed that the *c*/*a* ratio of the trigonal lattice is related to the insulating/metallic state as a function of Cr-doping level and as a function of pressure. In particular, they found that the *a* parameter of their Cr-doped sample, which was larger than that of undoped V2O3 at RP, dropped to the value of V2O3 at 4 GPa. In contrast, the *c* parameter was found to barely increase at HP in both samples, implying a remarkable increase in the *c*/*a* ratio in the Cr-doped sample as the metallic state was approached. In fact, they found a sharp increase in *c*/*a* ratio just at the insulator–metal transition. These authors also showed that undoped V2O3 becomes even more metallic at HP, with a suppression of the antiferromagnetic-insulating phase above 0.3 GPa.

More recently, Lupi et al. [198] studied with submicron resolution the Mott-insulator transition in Cr-doped V2O3. These authors found that, with decreasing temperature (which yields the antiferromagnetic insulator phase), microscopic domains become metallic and coexist with an insulating matrix. This seems to explain why the paramagnetic metallic phase is a poor metal. They attributed the observed phase separation to a thermodynamic instability around the Mott-insulator transition, showing that such instability is reduced at HP. Therefore, they concluded that the Mott-insulator transition is a more genuine Mott transition in compressed samples, which also exhibited an abrupt increase in the *c*/*a* ratio around the insulator-to-metal transition (i.e., around 0.3 GPa). This result confirms the close relationship between the structural properties of V2O3, the nature of the Mott-insulator transition and the role of HP in the modification of the electronic properties of this interesting compound.

In contrast to other TM-SOs, the compression of V2O3 is highly anisotropic (the *a* axis is nearly three times more compressible than the *c* axis) [206] and the unusual behavior of the *c*/a ratio is closely related to the Mott-insulator transition. It was also shown that the atomic positions in V2O3 tend to those of the ideal hcp lattice at HP, with large changes in interionic distances and bond angles upon compression [206]. Zhang et al. observed a pressure-induced PT to an unknown phase around 30 GPa [207]. Ovsyannikov et al. found two different PTs above 21 GPa and 50 GPa, respectively, and attributed the first HP phase to an Rh2O3-II-type orthorhombic structure [157]. With regard to the second HP phase, they conclude that it seems not to be related to the Th2S3- and α-Gd2S3-type structures predicted by Zhang et al. in V2O3, of around 30–50 GPa [208]. In conclusion, more work is needed to unveil the HP behavior of both the corundum and bixbyite polymorphs of V2O3.

Besides the compounds discussed above, other TM-SOs have been synthesized and/or exist in nature that crystallize in the corundum-structure at room conditions: the 3*d*-SOs Ti2O3, Cr2O3, and Co2O3, and the 4*d*-SO Rh2O3. There are also a few reports about the possible synthesis and characterization at room conditions of hexagonal Ni2O3 [209,210] and 5*d*-SO Au2O3 [211]. However, more work would be required to unambiguously demonstrate the stability of these two latter compounds at room conditions. Note that no natural occurrence of SOs with Ni or Co ions, both of which are more stable as divalent cations, has been found so far. On the other hand, no HP study is known for Au2O3.

The amount of HP investigations on the above mentioned materials is variable. Minomura and Drickammer [212] reported HP resistance measurements on several compounds at RT. They found a resistance maximum around 11 GPa in Ni2O3 that could be indicative of a PT. Unfortunately, no additional HP investigations can be found in the literature on this material. In the case of Co2O3, Chenavas et al. reported a low spin to high spin transition in quenched material, subject to 8 GPa and 850 ◦C, from a synthesis process involving different chemical reactions [213]. Therefore, the fundamental properties of both Ni2O3 and Co2O3 at HP have yet to be fully investigated.

Chromia (Cr2O3) is another important TM-SO, both from technological and fundamental points of view. This material with corundum structure occurs in nature as the uncommon mineral eskolaite. However, it is probably better known for its high stability and hardness, which makes it a commonly used green pigment and abrasive material. Cr2O3 is a typical antiferromagnetic insulator with a Néel temperature *TN* ~307 K, but it is remarkable as it shows an intriguing linear magnetoelectric effect that has attracted some research attention in relation to spintronic applications. Although the existence of HP polymorphs of Cr2O3 have not yet been well-established [214,215], it is clear that HP affects the magnetic properties of this compound. For instance, as recently shown by Kota et al., hydrostatic pressure may increase the *TN* of corundum-type Cr2O3, which could provide an enhancement of the magnetoelectric operating temperature in compressed samples [215]. However, there is an ongoing controversy in the literature in relation to the sign of *dTN*/*dP* (see reference [215] and references therein). With regard to its crystal structure at HP, no PT was found either by Finger and Hazen up to 5 GPa [206], or by Kantor et al. up to ~70 GPa [216]. In contrast, Shim et al. observed several changes around 15–30 GPa on pure synthetic Cr2O3 under cold compression that were compatible with a PT to a monoclinic V2O3-type (*I*2/*a*) structure [217]. According to these authors, a second PT could occur above 30 GPa at HT. The new HP-HT phase might be explained by either orthorhombic, Pv, or Rh2O3-II-type structures. In fact, the orthorhombic Rh2O3-II-type phase had been previously predicted to exist at ~15 GPa by first-principles calculations [218]. However, the recent results by Golosova et al. up to 35 GPa, also on synthetic Cr2O3, seem to rule out both PTs [219]. While these authors report a somewhat lower (1/*TN*)(*dTN*/*dP*) value in relation to reference [215] (0.0091 GPa−<sup>1</sup> vs. 0.016 GPa<sup>−</sup>1), their structural data point towards a slight anisotropy in the pressure behavior of the *c*/*a* axis at around 20 GPa, which could be of magnetic origin. Additional work is thus required to fully understand the HP behavior of chromia.

In the case of Ti2O3, which can be found in nature as the rare tistarite mineral, HP-XRD studies were first conducted by McWhan and Remeika [200] with the aim of comparing the results obtained for this compound with those of V2O3. Later on, Nishio-Hamane et al. reported a PT from corundum-type Ti2O3 to an orthorhombic Th2S3-type (s.g. *Pnma*) structure above 19 GPa and 1850 K, being the new polymorph metastably recovered at room conditions [220]. The same structure had been previously predicted at ultra HP for the case of Al2O3 [221]; hence, the synthesis of the Th2S3-type polymorph in Ti2O3 has been a remarkable finding, shedding new light on the fundamental properties of the TM-SOs family. In Ti2O3, the Th2S3-type structure was found to be ~10% denser than the corundum-type phase. Subsequently, Ovsyannikov et al. [222] synthesized polycrystalline Ti2O3 samples with Th2S3-type structure with the aim of studying its structural stability up to 73 GPa and 2200 K. The HP behavior of the structural, optical and electronic properties of this unusual, golden-colored polymorph of Ti2O3 were later thoroughly investigated [223,224], together with the T-P phase diagram of Ti2O3 [224].

With regard to 4*d*-SOs, there are a few reports on the existence of such compounds at room conditions, the most relevant of which is Rh2O3. Two low-pressure polymorphs of this material are known, namely Rh2O3-I and Rh2O3-III. While the stable phase at room conditions, Rh2O3-I, adopts a corundum-type structure, the Rh2O3-III polymorph crystallizes in an orthorhombic *Pbca* structure and is only stable at RP and HT (>750 ◦C) [225]. In addition, an HP phase, known as Rh2O3-II, was synthesized by Shannon and Prewitt at 6.5 GPa and 1200 ◦C [226]. This phase was found to adopt an orthorhombic *Pbna* structure, similar to that of corundum as it contains RhO6 octahedra that share their faces. In Rh2O3-II, however, only two edges of each octahedra are shared with other octahedra. In spite of the use of HP to synthesize Rh2O3-II, only a limited number of HP studies on this phase can be found in the literature. Zhuo and Sohlberg investigated theoretically the stability of this phase in comparison to Rh2O3-I and Rh2O3-III, which allowed them to predict the phase diagram of Rh2O3 [227]. According to their results, Rh2O3-II is stable below ~5 GPa and HT (>700 K), while the Rh2O3-III form is the main phase above 5 GPa, regardless of temperature. Unfortunately, no experimental HP studies dealing with the structural properties of any of the Rh2O3 phases have been published so far. Experimental work on this material, and, in particular, on the Rh2O3-III polymorph, due to its connection to the HP phases of other SOs, as described above, is still necessary.

Possible stable forms of other 4*d*-SOs, like Mo2O3 and W2O3, have been reported in relation to the growth of thin films or coatings (see bibliography in reference [228]). Recent DFT calculations predict that corundum-type Mo2O3 might be stabilized at 15 GPa, while a much higher pressure (60 GPa) is obtained by these authors for W2O3 [228]. Similar conclusions have been reached by other authors in relation to Hf2O3 and Zr2O3 using crystal prediction methods [157,229]. These two SOs might be metastable at HP. So far, however, there is no experimental evidence for the existence and stability of these SOs at HP. Much experimental and theoretical effort is still required to understand the stability and behavior of these two SOs upon compression, which could lead to the discovery of new HP phases with remarkable properties.

To finish this section, we summarize in Table 3 the phase transition pressures and HP phases observed in the best studied TM-SOs.

**Table 3.** Summary of the high pressure (HP) phases and phase transition (PT) pressures, PT (in GPa) reported for the best studied transition-metal sesquioxides (TM-SO) materials: Fe2O3, Mn2O3, V2O3 and Ti2O3. The fourth column shows the resulting phase obtained at HP starting from the phase displayed in the first column (DPv: distorted perovskite; PPv: post-perovskite; LH: laser heating).


#### *2.4. Group-15 Sesquioxides*

Group-15-SOs are relevant in a multitude of technological [230–232] and medical [233–235] applications, but the main interest in the study of the properties of these compounds resides in the physical–chemical interactions of their chemical bonds. The progressive increase in the strength of the stereoactive cationic lone electron pair (LEP) going up along the group 15 column, i.e., as the cation becomes lighter, dominates the formation and compressibility of the resulting crystallographic structures. In other words, the influence of the cation LEP determines the different existing polymorphs of group-15-SOs and it is possible to observe several trendlines of their behavior at HP. According to the literature, the group-15-SO polymorphs can be obtained from a defective fluorite structure where oxygen vacancy arrays are applied along different crystallographic directions [236,237]. These arrays define most of the polymorphs found at room conditions in these SOs. Nevertheless, the crystalline phases formed are quite different from the rest of SOs, mainly due to the above-mentioned influence of the LEP.

Structural phases belonging to the cubic family are observed in group-15-SOs since the most usual structures of arsenic and antimony SO crystallizes in the s.g. *Fd*3*m*. They are obtained by applying an array model along the (111) direction to a defective fluorite structure. They have been experimentally found in c-As2O3 (whose mineral form is called arsenolite) and α-Sb2O3 (whose mineral form is called senarmontite). These SOs are also noted as As4O6 and Sb4O6, respectively, because this notation reflects the molecular arrangement of these two molecular or zero-dimensional solids. The molecular units *X*4O6 (*X*= As, Sb) are disposed in a closed-compact adamantane-type molecular cages, joined together by van der Waals (vdW), and chalcogen bonding among the closest arsenics belonging to different molecular units. In this case, the cations belonging to the same molecular unit form pseudo-tetrahedral units following the same disposition as their counterpart, the white phosphorus (P4). The molecular cages are stabilized by the cationic LEP oriented towards the outside of the cage, which confers great stability to the molecular unit. The HP behavior of both Sb4O6 and As4O6 dimorphs is quite different. They undergo different PTs [238–242], and both compounds show a pressure-induced amorphization driven by mechanical instability [238–240]. The origin of this instability is associated with the steric repulsion caused by the increase in the interaction between different molecular units when pressure increases [238]. It has been shown in a HP study using different pressure-transmitting media that the instability is enhanced by the loss of the hydrostatic conditions [241]. However, up to 15 GPa, both compounds behave differently. Whereas two 2nd-order isostructural PTs were observed in Sb4O6 at 3.5 and 12 GPa, respectively [242], no pressure-induced PT was reported in As4O6 [239,240]. The PTs exhibited by Sb4O6 at 3.5 and 12 GPa were suggested to be due to the loss of its molecular character and related to changes in the hybridization of Sb *5s* and O *2p* electrons, i.e., they are related to the decrease in LEP stereoactivity at HP [242].

At 15 GPa, Sb4O6 tends to form a new HP structure that can be defined by a distortion of the structural lattice due to the loss of the molecular character [238]. This HP phase crystallizes in a tetragonal structure (s.g. *P*4*21c*) similar to that of β-Bi2O3 [243] that will be described later. At HP (9-11 GPa) and HT (573–773 K), cubic Sb4O6 undergoes a 1st-order PT towards a new polymorph called γ-Sb2O3 [244]. This new phase crystallizes in an orthorhombic structure s.g. *P212121*, where the trigonal pyramid form given by the coordination of the Sb atom surrounded by O atoms in the cubic phase is changed by a tetrahedral unit in the orthorhombic phase, where the LEP acts as a pseudo-ligand. The tetrahedral units are arranged, forming chains or rods along the *a-axis* that show strong similarities with the <sup>β</sup>-Sb2O3 polymorph (s.g. *Pccn*), whose (Sb2O3)<sup>∞</sup> rods are aligned along the *c-axis*. Due to its rod-like structure, orthorhombic β-Sb2O3 is a quasi-molecular or acicular solid with two independent rods in the unit cell. In this structure, each Sb atom is bonded to three oxygen atoms, with their LEP oriented towards the void formed by the rod arrangement. Thus, this SO can be described by rods and linear voids oriented along the *c-axis*, being isostructural to the ε-Bi2O3 phase [245]. No HP study of ε-Bi2O3 is known so far.

HP studies of β-Sb2O3 revealed a 1st-order PT around 15 GPa [246,247]. Nevertheless, the nature of its HP phase is still under debate. Zou et al. tentatively assigned it to a monoclinic structure with s.g. *P21*/*c*. β-Sb2O3 also shows strong similarities with the tetragonal phase of bismuth SO (named β-Bi2O3), which crystallizes in s.g. *P*4*21c* [243]. In fact, β-Bi2O3 is a metastable polymorph obtained by heating

the most stable phase of the bismuth SO (α-Bi2O3) to 650 ◦C [248]. This material can be considered a defective fluorite structure, where an (100) array of vacants is applied [236]. This polymorph contains a linear channel, as well as β-Sb2O3, with the cation LEP oriented towards the center of this empty channel. β-Bi2O3 is very interesting from a physical–chemical point of view because it is a clear example of an isostructural 2nd-order PT. This structure is characterized by a Bi atom located at an 8e Wyckoff site and two O atoms located at 8e and 4d Wyckoff sites, with the Bi atom coordinated to six O atoms, forming a distorted pyramid. Above 2 GPa, several Wyckoff coordinates of β-Bi2O3 symmetrize, remaining fixed up to 12 GPa [243]. Thus, the six different Bi-O interatomic distances observed at RP in the polyhedral unit only become three different Bi-O bond lengths, thus reducing the eccentricity of the Bi atom drastically, up to 2 GPa. This PT is even more explicit when analyzing the compressibility of the unit cell volume below and above 2 GPa. Finally, a progressive broadening of the peaks leads to a pressure-induced amorphization above 12 GPa that is completed at 20 GPa [243].

α-Bi2O3 crystallizes in a monoclinic s.g. *P21*/*c* structure, where Bi atoms are located in two inequivalent crystallographic 4e sites and O atoms are located in three inequivalent 4e Wyckoff positions. One of the Bi atoms is penta-coordinated and the other is hexa-coordinated. This polymorph remains in the same structure up to 20 GPa, where a pressure-induced amorphization occurs [249]. The amorphization was explained by a frustrated PT towards the HPC-Bi2O3 polymorph, since the HPC-phase is thermodynamically more stable than the α-phase above 6 GPa, according to DFT calculations. This ongoing PT is likely inhibited by the kinetic barriers between both phases. The correlation between the amorphous phase and the HPC polymorph was revealed, thanks to the analysis of the diffraction pattern as a function of the interionic distances, using the process described in reference [250]. Results indicated average interatomic Bi-O distances closer to those of the HPC-Bi2O3 than to any other polymorph. HPC-Bi2O3 crystallizes in the hexagonal s.g. *P63mc* structure, and it is the HP phase of the HP-Bi2O3 phase, above 2 GPa [251]. In turn, HP-Bi2O3 with s.g. *P31c* was obtained from α-Bi2O3 at HP and HT (6 GPa and 880 ◦C) [252]. The strong polymorphism exhibited by Bi2O3 does not require the application of HP. It must be noted that α-Bi2O3 at HT (above 400 ◦C) shows a PT to R-Bi2O3 (s.g. *P21*/*c*) [252], which, despite belonging to the same s.g. as α-Bi2O3, has a completely different structure. No HP study of R-Bi2O3 is known.

In the same s.g. *P21*/*n,* related to the α- and R-Bi2O3 phases, one can find two additional As2O3 polymorphs, whose names are claudetite-I [253] and claudetite-II [254]. The naturally stable phase, claudetite-I, has been only characterized by HP-RS measurements to our knowledge, revealing a possible PT between 7–13 GPa and a lack of pressure-induced amorphization up to 40 GPa [255]. Claudetite-II is a synthesized quasi-layered material, similar to As4O6, where the molecular unit is an open shell forming AsO3E pseudo-tetrahedra (where E denotes the cation LEP) [256]. In this case, the LEPs of neighboring cations are oriented towards opposite neighboring layers. This particular structure shows several pressure-induced 2nd-order PTs around 2 and 6 GPa [257], given by two abrupt breakdowns of inversion centers that lead to doubling and hexaplicating the original unit cell, respectively. Additionally, a PT around 10.5 GPa leads to the non-centrosymmetric HP phase β-As2O3 (s.g. *P21*).

Another group-15-SO crystallizing in the monoclinic s.g. *P21*/*n* structure is the phosphorous SO (P2O3), which keeps the molecular character of cubic arsenic and antimony SOs, i.e., P4O6 [258]. Nevertheless, the symmetric distribution of the different P4O6 molecular cages is distorted in the case of monoclinic P2O3. The HP study of P2O3 exhibits strong difficulties, since it is only stable at low-temperatures, below RT. Thus, the HP behavior of this compound is still unknown.

To finish, we summarize in Table 4 the 1st- and 2nd-order PTs observed in group-15-SOs.


**Table 4.** Experimental and theoretical (DFT) data of the PT pressures (in GPa) for group-15-SOs. PIA stands for pressure-induced amorphization and MEW for methanol-ethanol mixture.

#### *2.5. Mixed-Valence Sesquioxides*

As mentioned in the introduction, there are *A2*O3 compounds where the *A* has two different valences, which constitute the subfamily MV-SOs. MV-SOs are highly interesting because they feature cations with different valences and consequently can be differently coordinated, thus resulting in a distortion in the structures of normal SOs. Examples of this kind of SOs are Sn2O3 and Pb2O3, where Sn and Pb cations show both 2+ and 4+ valences. While Pb2O3 has been known for almost a century [259] and crystallizes in the monoclinic s.g. *P21*/*a* [260], Sn2O3 has just recently been predicted [261] and experimentally found to crystallize in the triclinic s.g. *P*1 [262,263]. No HP studies on these two interesting but complex compounds have been reported to our knowledge.

#### **3. Conclusions and Future Prospects**

A great deal of work has been done on sesquioxides under compression and many pressure-induced phase transitions have been elucidated. In particular, the pressure-induced phase transitions of rare-earth sesquioxides and group-13 sesquioxides are quite well known, except for Tl2O3. The knowledge of pressure-induced phase transitions in transition-metal sesquioxides are not so well known, and those of group-15 sesquioxides have been recently studied, but still require more work. Finally, pressure-induced phase transitions in mixed-valence sesquioxides are completely unknown. It must be stressed that most of the high-pressure work done on sesquioxides corresponds to cubic, tetragonal, hexagonal, rhombohedral, and orthorhombic phases, while most of the high-pressure work still to be done on sesquioxides corresponds to complex monoclinic and triclinic phases. The study of these complex phases was rather difficult in the past, and is a challenge that must be accomplished in the 21st century with current and future experimental and theoretical techniques.

It must be noticed that the crystalline structures of the different subfamilies of sesquioxides and their pressure-induced phase transitions have some features in common. The archetypic structure of rare-earth sesquioxides is the C-type structure, which is isostructural to the bixbyite structure of several transition metal sesquioxides (Mn2O3) and group-13 sesquioxides (In2O3 and Tl2O3). On the other hand, the archetypic structure of group-13 and transition-metal sesquioxides is the corundum structure (Al2O3). In this context, it is remarkable that the pressure-induced transitions of C-type rare-earth sesquioxides, including Sc2O3 and Y2O3, are markedly different to those of C-type group-13 and transition-metal sesquioxides. In fact, these last compounds seem to have pressure-induced transitions that are closer to those of corundum-type structures of group-13 and transition-metal sesquioxides. On the other hand, the crystalline structures and pressure-induced phase transitions of group-15 sesquioxides are completely different to those of other sesquioxides, due to the stereochemically active lone electron pair of group-15 cations, which lead to more open-framework structures than those present in other subfamilies. Consequently, we can speculate that a similar behavior is expected to be observed in future experiments of mixed-valence sesquioxides under compression, since this subfamily is also characterized by having some cations with lone electron pairs.

Finally, it should be mentioned that we are not aware of studies of negative pressures in sesquioxides. In principle, it is possible to reach absolute negative pressures (of the order of a few GPa) [264] where novel structures might appear [265]. In fact, negative pressures have been found in several solids, such CaWO4 nanocrystals [266] and ice polymorphs [267]. Therefore, the application of negative pressures to materials is a route that can also be explored in sesquioxides, since it would lead to the expansion of the crystalline lattice, leading to the possible instability of the stable phase at room conditions in certain compounds, thus opening a new avenue to obtain novel and exotic metastable phases.

**Author Contributions:** F.J.M. contributed to the conceptualization and writing of the introduction, Sections 2.1 and 2.5 and conclusions; A.L.J.P. contributed to the writing of Section 2.2; J.I. contributed to the writing of Section 2.3 and J.A.S.T. contributed to the writing of Section 2.4 and the revision of the manuscript.

**Funding:** This research was funded by Spanish Ministerio de Ciencia, Innovación y Universidades under grants MAT2016-75586-C4-1/2/3-P, FIS2017-83295-P, PGC2018-094417-B-100, and RED2018-102612-T (MALTA-Consolider-Team network) and by Generalitat Valenciana under grant PROMETEO/2018/123 (EFIMAT). J. A. S. also acknowledges Ramón y Cajal Fellowship for financial support (RYC-2015-17482).

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

MDPI St. Alban-Anlage 66 4052 Basel Switzerland Tel. +41 61 683 77 34 Fax +41 61 302 89 18 www.mdpi.com

*Crystals* Editorial Office E-mail: crystals@mdpi.com www.mdpi.com/journal/crystals

MDPI St. Alban-Anlage 66 4052 Basel Switzerland

Tel: +41 61 683 77 34 Fax: +41 61 302 89 18