High pressure and multiferroics materials: a happy marriage

The community of material scientists is strongly committed to the research area of multiferroic materials, both for the understanding of the complex mechanisms supporting the multiferroism and for the fabrication of new compounds, potentially suitable for technological applications. The use of high pressure is a powerful tool in synthesizing new multiferroic, in particular magneto-electric phases, where the pressure stabilization of otherwise unstable perovskite-based structural distortions may lead to promising novel metastable compounds. The in situ investigation of the high-pressure behavior of multiferroic materials has provided insight into the complex interplay between magnetic and electronic properties and the coupling to structural instabilities.

1. Introduction

Multiferroism can generally be defined as a phenomena in which two or more of the so-called `ferroic' order parameters (ferroelectricity, ferromagnetism and ferroelasticity) simultaneously coexist in a single phase material.

Among the different interactions, magneto-electric coupling is the most desirable property; it refers to either the induction of magnetization by an electric field or polarization by a magnetic field. The ultimate goal is a single phase multiferroic (MF), with strong coupling between magnetic and electronic order parameters and the potential to mutually manipulate them at high (ambient) temperature. Aside from the very promising technological applications (Nan et al., 2008), the fascinating fundamental physics of MF materials certainly deserves further investigation.

Unfortunately, these compounds are extremely rare in nature; the scarcity of magneto-electric MFs can be understood by investigating a number of factors, including symmetry and electronic properties. From the structural point of view, there are only 13 point groups that can give rise to multiferroic behavior. Moreover, ferroelectrics by definition are insulators, while itinerant ferromagnets need conduction electrons. There seems to be an intrinsic contradiction between the conventional mechanism of off-centering in a ferroelectric, related to transition metals with d⁰ electronic configuration and the formation of magnetic order which requires the presence of unpaired electrons.

Interestingly, Landau & Lifshitz (1959) in a volume of their Course of Theoretical Physics stated `Let us point out two more phenomena, which, in principle, could exist. One is piezomagnetism… the other is a linear coupling between magnetic and electric fields in a media… Both these phenomena could exist for certain classes of magnetocrystalline symmetry, but it seems that till present, they have not been observed in any substance'.

Yet in 2000, Nicola A. Hill published a paper (Hill, 2000) entitled: `Why are there so few magnetic ferroelectrics?', clearly addressing the complexity of these materials.

Even to probe the magneto-electric coupling is a complicated issue (Bibes, 2012); it can be measured indirectly by simply recording changes in either the magnetization near a ferroelectric transition temperature or the dielectric constant near a magnetic transition temperature (`magnetocapacitance' or `magnetodielectric' response). Direct measurements are more challenging, requiring either a magnetic response to an applied electric field [M(E)] or an electrical response to an applied magnetic field [P(H)].

All these complexities were too puzzling until recently, when the researchers found out that an additional electronic or structural driving force must be present for ferromagnetism and ferroelectricity to occur simultaneously.

Undoubtedly, the recent `explosion' in MF studies is enabled by a combination of theoretical and experimental factors. In particular for the latter, new synthesis techniques such as vacuum-based thin film deposition techniques (for hetero-structures) and high pressure/high temperature (HP/HT), allow new materials to be obtained by stabilizing metastable or highly distorted structures, which might support ME coupling. Indeed, the use of high-pressure techniques (both for the synthesis and the characterization) is providing important (and somewhat unexpected) results.

Multiferroism is still a relatively young field of research; although predicted in the late 1950s (Landau & Lifshitz, 1959) and the term coined in 1994 (Schmid, 1994), the attention raised exponentially only after 2003, the `golden year' for MFs, concomitant with the discovery of large ferroelectric polarization in epitaxial grown thin films of BiFeO<sub>3</sub> (Wang et al., 2003) and the discovery of strong magnetic and electric coupling in orthorhombic TbMnO<sub>3</sub> (Kimura et al., 2003) and TbMn<sub>2</sub>O<sub>5</sub> (Hur et al., 2004). New results are continuously reported and material scientists (and the high-pressure community) are working hard to contradict Landau and Lifshitz's statement and to prove Hill's paper to be outdated. A measure of the activity of the research on MF materials is the large number of publications; at the date of submission of the present papers, about 4050 papers (2440 from 2010) were published with the term `multiferroic' in the title and 4200 (1780 from 2010) with the term `magneto-electric' (source: Google Scholar).

Besides the massive literature available on MFs (Spaldin & Fiebig, 2005; Fiebig, 2005; Eerenstein et al., 2006; Khomskii, 2006; Rao & Serrao, 2007, and reference therein), this review paper is limited to discuss the role of HP in the study of magneto-electric MF materials, combining HP/HT synthesis (why HP synthesis is so often needed?) and HP characterization (what kind of information can be derived from HP characterization techniques?).

2. HP/HT synthesis of bulk MF materials

The tremendous rise in research on MF and magneto-electric materials pushed the material scientists to search for new materials and mechanisms leading to magneto-electric coupling and multiferroic behavior. Historically, HP/HT synthesis has proven to be very effective in producing a large number of new phases (Badding et al., 1995; McMillan, 2002, 2003; Brazhkin, 2007), for example in the fields of super-hard materials (Haines et al., 2001), superconductors (Bos, Penny et al., 2008) etc. For some of them (for example when high density is required, as in the super-hard materials), the role of applied pressure is intuitively easy to understand, while for other systems, often supporting complex electronic, magnetic or transport properties, one can guess that the stabilization of uncommon metastable phases/structures/coordinations offers a pathway to new properties. Indeed, MF materials belong to the latter category.

A detailed description of the possible mechanisms supporting the multiferroism can be easily taken from the literature (see, for example, references cited in Khomskii, 2009) and goes beyond the scope of the present paper; they can be summarized in Lone-Pair MF (Es., BiFeO₃; Neaton et al., 2005), Geometric Ferroelectric MF (Es.: hexagonal RMnO₃; Van Aken et al., 2004), Charge Ordering Ferroelectrics (Es.: LuFe₂O₄; Ikeda et al., 2005; or (Pr,Ca)MnO₃; van den Brink & Khomskii, 2008) or Spin Spiral Ferroelectrics (Es.: TbMnO₃; Kimura et al., 2003; or TbMn₂O₅; Mostovoy, 2006).

Already from this general list, one should ask: why does the perovskite-type structure play such an important role in the search for MF properties? Generally speaking, it is well known that it is a very common structure, showing an extraordinary variety of properties. Many different atoms can occupy in particular the cationic sites, allowing a wide tuning of their properties. Moreover, the majority of ferroelectric materials exhibit perovskite structure.

People working with high pressure (and particularly geologists) are familiar with perovskites; being a typical HP structure (dense packing, high coordination number, low inter-atomic distances etc.) it is commonly found in our planet starting from the mantle to the core–mantle boundary, where silicate perovskites represent the main mineral phases (Murakami et al., 2012). Interestingly, part of this depth corresponds to the thermodynamical conditions accessible to conventional HP apparatus (piston cylinder, belt apparatus, multi anvil, diamond anvil) used for the HP/HT synthesis and characterization reported in the present paper.

Thus, it is not surprising that the section of this work on HP/HT synthesis of new materials eventually exhibiting MF properties deals mainly with perovskite-based compounds.

As already pointed out, measurement of the properties of MFs, and in particular the direct magneto-electric coupling, is not trivial, even on high quality samples available in large quantities. This is usually not the case for HP synthesized metastable compounds, where the MF properties are generally detected (or hypothesized) in an indirect way, when the measurement (or the calculation) of the magnetic and ferroelectric transitions occur simultaneously.

2.1. HP/HT synthesis of simple perovskite bulk MF compounds

The `simple' perovskite structure (ABO₃) consists of corner-sharing BO₆ octahedra, with B ions (usually magnetic, such as Mn or Fe) in the center of the octahedral site (coordination number: 6) and A ions at the center of a cube formed by eight BO₆ octahedra (coordination number: 12). The most common structural distortion derives from the mismatch of A—O and B—O bond distances, the Jahn–Teller (JT) distortions (elongation/compression) and the buckling (variation of the B—O—O angle) of the BO₆ octahedra. The application of an external pressure enhances the ability of the perovskite to accommodate different ionic sizes, vacancies and the above-mentioned structural distortions.

For example, in the manganites (RMnO₃) two crystal phases, hexagonal and ortho­rhombic, exist at ambient pressure. The ortho­rhombic structure (Pbnm) is stable for large R ions (La, Pr, Nd, Tb and Dy), while small R ions (Ho, Er, Yb, Lu, In and Sc) adopt the hexagonal structure (P6₃cm, at room temperature). However, orthorhombic RMnO₃ with small R ions, such as Ho and Lu, can be synthesized as metastable perovskites by HP/HT synthesis (Wood et al., 1973; Wu et al., 2014; Rodgers et al., 2006).

The simplest method to induce MF is to combine in the same phase a magnetic ion (ferromagnetism) in a non-centrosymmetric structure, enabling the insurgence of ferroelectricity. Ferroelectricity can be inducted by the asymmetrical coordination produced by the stereochemical effect of a `lone-pair' atom such as Bi³⁺ and Pb²⁺, representing frequent ingredients of the magneto-electric MF compounds.

BiFeO₃ is the prototype material, but it is unusual among the Bi-based perovskites in that it can be made under ambient conditions; most others require HP/HT synthesis. Since Bi₂O₃ melts at 824°C at ambient pressure, HP is necessary in most cases to achieve a high-temperature solid state reaction whenever oxides are used as reagents.

BiMnO₃ is an obvious MF magneto-electric candidate, requiring HP/HT synthesis (P = 4 GPa, T = 1273 K). BiMnO₃ deserves a special discussion; in spite of its `simple' perovskite structure, it is a very complex material and we refer to the massive work that has been done to unveil its peculiar structural properties (Belik, Iikubo et al., 2006), the HP/HT synthesis (P = 4 GPa, T = 1273 K), the complex phase diagram at ambient and high temperature (Montanari, Righi et al., 2005; Montanari, Calestani et al., 2005), and the magnetic and electric properties (Chou et al., 2009), some of those are also detailed in the second part of this paper on characterization. We emphasize the controversial determination of its MF properties, since a general consensus on the structure and the ferroelectric properties is still lacking (Goian et al., 2012).

The search for polar structure in potentially MF Bi-based perovskites has been studied in particular by Belik, who reported a series of BiMO₃ oxides with M = Al, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Ga, In and Rh (Belik, 2012). He also investigated the solid solutions of BiGa_xM_1−xO₃ (M = Cr, Mn and Fe) prepared at P = 6 GPa and T = 1700 K (M = Cr and Fe) and 1300 K (M = Mn) resulting in the formation of a large family of polar materials with Cm and R3c symmetries. Samples with Cm symmetry have structures similar to PbVO₃ and BiCoO₃, while R3c symmetry compounds are isostructural with BiFeO₃ and have comparable calculated spontaneous polarization (58 µC cm⁻² for BiGa_0.4Cr_0.6O₃). Noticeable calculated polarizations of 116 µC cm⁻² and 102 µC cm⁻² are reported for BiGa_0.4Fe_0.6O₃ and BiGa_0.3Mn_0.3O₃, respectively. On the contrary, the HP synthesized BiMnO₃-type BiScO₃ (P = 6 GPa, T = 1413 K) crystallizes in the space group C2/c (centrosymmetric and therefore non-ferroelectric) (Belik, Iikubo et al., 2006).

To provide further evidence of the complex and intriguing behavior of BiMnO₃, recently Chakrabartty et al. reported a photovoltaic effect exploiting its ferroelectricity (i.e. the photo-carrier separated by the electrical dipole rather than in a p–n junction as in a conventional solar cell); an external solar power conversion efficiency of ∼ 0.1% was achieved in Bi–Mn–O thin films grown onto an Nb-doped SrTiO₃ single-crystal substrate by pulse laser deposition (Chakrabartty et al., 2014).

Ferroelectric behavior associated with lattice distortion is found in single crystals of perovskite-type YMnO₃ obtained under HP quasi-hydrothermal conditions (P = 5.5 GPa) (Ishiwata et al., 2011). Polarization along the ab-plane was observed, accompanied by the discontinuous jump of the dielectric constant at T_N = 42 K, below which P shows a stepwise increase reaching ca 0.22 µC cm⁻² at 2 K, larger than the value for the polycrystalline sample (Taguchi et al., 2012).

By combining dielectric, specific heat and magnetization measurements and high-resolution neutron powder diffraction, Ye et al. (2007) investigated the thermodynamic and magnetic and structural properties of the metastable ortho­rhombic perovskite ErMnO₃ prepared at P = 3.5 GPa and T = 1373 K. The system shows T_N = 42 K and a corresponding sudden increase of the dielectric constant.

The monoclinic (P2₁/n) ScMnO₃ perovskite was synthesized by Chen et al. (2013) from the hexagonal phase at P = 12.5 GPa and T = 1373 K. Although indirect evidence of MF properties have already been obtained, the monoclinic phase shows a similar structure to the orthorhombic Ho and Lu analogues, stimulating further studies on possibly coupled electrical polarization and magnetism.

Pb²⁺ lone-pair asymmetrical coordination was exploited by Shpanchenko et al. (2004) to search for multiferroism in PbVO₃ synthesized at P = 4–6 GPa and T = 973–1023 K. The non-centrosymmetrical tetragonal P4mm structure of corner-shared VO₅ pyramids rather than octahedra due to a strong tetragonal distortion is found and diffraction data suggest a large ferroelectric polarization above 100 µC cm⁻² (Belik et al., 2005). Tetragonal perovskite PbMnO₃ was obtained by treating the hexagonal perovskite phase at P = 15 GPa and T = 1273 K (Oka et al., 2009), but surprisingly the structural analysis suggested that PbMnO₃ crystallizes in the centrosymmetric space group P4/mmm, unlike PbVO₃ and PbTiO₃ (Chaudhari & Bichile, 2013), with an antiferromagnetic ordering at T_N = 20 K.

Varga et al. (2009) reported the HP/HT synthesis of FeTiO₃ (P = 18 GPa, T = 1473 K), isostructural with acentric LiNbO₃. Piezoresponse force microscopy and magnetometry demonstrate the coexistence of ferroelectricity and (weak) ferromagnetism below T_N = 110 K.

Other interesting examples are ScCrO₃ and InCrO₃, synthesized at P = 6 GPa and T = 1500 K. They crystallize in the GdFeO₃-type perovskite structure (space group Pnma). Antiferromagnetic transitions occur at T_N = 73 K in ScCrO₃ and 93 K in InCrO₃ and dielectric anomalies were observed in both compounds at T_N, indicating magneto-electric coupling, contrary to YCrO₃ (Belik, Matsushita et al., 2012).

Aimi et al. (2011) studied the correlation between structure, magnetic and dielectric properties in MnMO₃ (M = Ti, Sn) synthesized in HP/HT conditions (P = 7 GPa, T = 973 and 1073 K, respectively); both the compounds possess a polar LiNbO₃-type structure at room temperature. Weak ferromagnetism due to canted antiferromagnetic interactions was observed at T_N = 25 K for MnTiO₃ and at T_N = 50 K for MnSnO₃, with anomalies in the dielectric permittivity indicating the correlation between magnetic and dielectric properties.

A similar structure was obtained for PbNiO₃ by Inaguma et al. (2011) at P = 3 GPa and T = 1073 K. The obtained perovskite-type phase crystallizes in an orthorhombic GdFeO₃-type structure (space group Pnma) that irreversibly transforms to a LiNbO₃-type phase with an acentric space group R3c by heat treatment at ambient pressure. The magnetic susceptibility measurement shows that PbNiO₃ undergoes an antiferromagnetic transition with T_N = 205 K.

2.2. HP/HT synthesis of double perovskite bulk MF compounds

This paragraph covers the HP/HT synthesis of `double' perovskite MF oxides with the general formula A₂BB′O₆. The presence of two different magnetic cations on the B-site may lead to different types of interactions, favoring an increase in the magnetic ordering temperature and the enhancement of the properties.

Many combinations of ions bringing either magnetic or electric properties have been attempted in the last few years; Shimakawa et al. (2011) reported that bulk Bi₂NiMnO₆ (monoclinic structure, space group C2, synthesized at P = 6 GPa, T = 1073 K) exhibits ferromagnetic (T_c = 485 K) and ferroelectric properties (calculated P = 20 µC cm⁻²). Bi₂FeMnO₆, a potential MF bulk sample, was obtained by Delmonte et al. (2013) at P = 6 GPa at T = 1373 K, displaying complex magnetic behavior (magnetic transitions at T = 420 and 288 K) and a temperature-induced magnetization reversal. The crystal structure is orthorhombic (space group Pnam), with no cation order on the B site; anomalies in the thermal dependence of the lattice parameters are observed at the magnetic ordering at T = 288 K, indicating a spin-lattice coupling and possible magneto-electric coupling. Cationic disorder of the Bi-based double perovskite is also observed in Bi₂FeCrO₆, a recently proposed candidate MF, prepared in bulk form by HP/HT (Suchomel et al., 2007).

In contrast, a significant degree of ordering of Mn⁴⁺ and Ni²⁺ ions was observed in In₂NiMnO₆, prepared at P = 6 GPa and T = 1600 K, characterized by a monoclinic structure (space group P2₁/n) and magnetic T_N = 26 K. In spite of the interesting magnetic behavior (a field-induced antiferromagnetic–ferromagnetic transition at low T), no magneto-electric coupling has been detected (Yi et al., 2013). Liu et al. (2014) synthesized high-purity crystals of Y₂FeMnO₆ and Y₂CrMnO₆, crystallizing in the orthorhombic space group Pnma, using a flux method under pressure (P = 6 GPa, T = 1573 K). An antiferromagnetic transition occurs at T_N = 328 K in Y₂FeMnO₆, and a ferrimagnetic one at T_N = 74 K in Y₂CrMnO₆; in both cases, the presence of the dielectric anomaly near T_N portends a magneto-electric effect.

Other interesting structures have been recently reported; Mathieu et al. (2013) succeeded in the preparation of Mn₂FeSbO₆ at P = 3 GPa and T = 1273 K, a rare example of an antiferromagnetic double perovskite polymorph (the material also crystallizes as ferrimagnetic ilmenite) with the A site entirely occupied by Mn and Fe/Sb cationic order on the B sites. Theoretical calculations for the perovskite phase suggest a complex magnetic structure, holding an electronic polarization and possible magneto-electric properties. Aimi et al. (2014) reported the synthesis of a novel ferroelectric A-site ordered double perovskite CaMnTi₂O₆ at P = 7 GPa and T = 1473 K, with an uncommon polar space group P4₂mc and a ferroelectric–paraelectric order–disorder type phase transition at 630 K. Similar to the structure of CaFeTi₂O₆, the A-site Ca²⁺ is 10-coordinated while Mn²⁺ shows alternate tetrahedral and square-planar coordination. The square-planar coordination shifts along the c-axis and the usual Ti⁴⁺ ion displacement accounts for its polar structure. P–E hysteresis measurement demonstrated that CaMnTi₂O₆ is ferroelectric with a calculated polarization and an observed remnant polarization of 24 and 3.5 µC cm⁻², respectively.

Another promising MF compound is lead iron niobate Pb₂FeNbO₆, possessing simultaneously ferroelectric properties below T ≃ 380 K, antiferromagnetic order at T_N ≃ 150 K (Levstik et al., 2008). Single phases of the (1 − x)Pb₂FeNbO_6 − xPb₂FeSbO₆ solid solution were synthesized at 6 GPa and 1400–1500 K (Raevski et al., 2013).

2.3. HP/HT synthesis of complex (quadruple) perovskite bulk MF compounds

`Quadruple' perovkites are A-site ordered compounds, derived by the doubling of the conventional ABO₃ axes; their general formula can be written as AA′₃B₄O₁₂ to better visualize the site occupation of the different elements. The structure is based on a three-dimensional network of corner-sharing tilted octahedra, centered on the B site (usually occupied by a magnetic element in MF materials) stabilized under high pressure by the presence of a Jahn–Teller atom (Mn³⁺ or Cu²⁺) on the A′ site, forming an uncommon square-planar coordination due to large distortion of the A-site coordination.

Among the compounds belonging to this family, CaMn₇O₁₂ (or CaMn₃Mn₄O₁₂) possesses all the requirements for being a good magneto-electric MF compound: (i) a ferroelectric transition temperature (T_C = 90 K) much higher compared with other magnetic MF manganites, and (ii) high polarization values, 450 µC m⁻² at 8 K when using a poling field of 7 kV cm⁻¹ (Zhang, Dong et al., 2011). By neutron powder diffraction from CaMn₇O₁₂ single crystals, Johnson et al. (2012) found that the polarization (along the c-axis of the rhombohedral cell) reaches the remarkable value of 2870 µC m⁻² at low temperatures, one of the largest measured values in magnetic MFs (Johnson et al., 2012). CaMn₇O₁₂ can be synthesized at ambient pressure although, curiously, was first synthesized under high pressure (Bochu et al., 1974; P = 8 GPa, T = 1273 K).

Those impressive properties certainly sparked interest in MF materials belonging to this family of complex perovskites.

Following the consolidated strategy based on the Bi³⁺ substitutions, Mezzadri et al. (2009) reported the HP/HT (P = 4 GPa, T = 1273 K) synthesis of BiMn₇O₁₂ (or BiMn₃Mn₄O₁₂). As expected, the structural characterization of single-crystal samples shows a distorted and asymmetrical coordination around the Bi atom due to the presence of the 6s² lone pair, resulting in the non-centrosymmetric space group Im, leading to a permanent electrical dipole moment and ferroelectric properties. The dielectric constant shows anomalies, matching the antiferromagnetic transition temperatures (T_N = 22 and 55 K).

By means of neutron diffraction, Gauzzi et al. (2013) found a large uniform modulation of the antiferromagnetic structure of the Mn³⁺ ions; this modulation (absent in the isovalent compound LaMn₇O₁₂) is induced by the internal strain created by the polar Bi³⁺ ion, and accounts for a large magneto-electric coupling. Therefore, the peculiar quadruple perovskite structure preventing the release of the strain provides a new degree of freedom to achieve large magneto-electric couplings.

Locherer et al. (2012) reported the HP/HT synthesis (P = 7.5 GPa, T = 1173–1273 K) of the isostructural and heterovalent PbMn₇O₁₂ (or Pb(Mn³⁺₃)(Mn³⁺₃Mn⁴⁺)O₁₂ to appreciate the different mixed-valence occupation of Mn on the B-site); as for BiMn₇O₁₂, the basic mechanism supporting the FE is supposed to be the stereochemical effect of the 6s² lone pair of Pb²⁺ that induces a permanent electric dipole but, surprisingly, PbMn₇O₁₂ crystallizes in a centrosymmetric structure (space group: ). However, a sizeable coupling of magnetic, electrical and dielectric properties at T_N = 68 K indicates a MF behavior.

This family of compounds is not fully explored yet; new promising properties are awaited, possibly also in non-`lone-pair' materials, for their complex structure leading to unusual magnetic properties, such as in LaMn₇O₁₂ (Prodi et al., 2009) and isostructural samples with decoupling of the magnetic contribution of the A′–B sites, as in LaMn₃Cr₄O₁₂ and LaMn₃Ti₄O₁₂ (Long et al., 2009).

2.4. HP/HT synthesis of distorted-perovskite bulk MF compounds

Among the numerous structures derived from various distortions of the perovskite structure, iron fluorides with tetragonal tungsten bronze (TTB) structure, having the general formula K_xFe_x²⁺Fe³⁺_1−xF₃, deserve a special mention. The structure can be described as a perovskite-like network of Fe²⁺O₆ octahedra surrounded by pentagonal non-perovskite sites. K_0.6Fe_0.6²⁺Fe³⁺_0.4F₃ single crystals have been grown by hydrothermal synthesis (P = 1.3 Kbar, T = 950 K) and below magnetic transitions (T_N = 118 K) the system, characterized by an ordered arrangement of Fe²⁺/Fe³⁺, is suggested to be a rare example of complete MF, being simultaneously ferrimagnetic, ferroelectric and ferroelastic (Mezzadri et al., 2008). In this case, the main role of the (limited) applied pressure is to reach the conditions suitable for hydrothermal synthesis.

A selection of perovskite-based materials, their structural properties, HP/HT syntheses conditions and the corresponding magnetic (T_N, T_C) and electric (polarization) transitions is summarized in Table 1.

Table 1
HP/HT synthesis and magneto-electric properties in MF materials with perovskite-based structure

Material	Synthesis conditions	Space group	Magneto-electric properties	Notes
BiMnO3	P = 4 GPa	?	TN = 100 K	Still controversial!!
	T = 1273 K	(Belik, Iikubo et al., 2006; Belik, 2012; Montanari, Righi et al., 2005; Montanari, Calestani et al., 2005; Chou et al., 2009; Goian et al., 2012)		Centro-/non-centrosymmetric?
BiGaO3	P = 6 GPa	Pcca	P > 100 µC cm^−2	Calculated P for BiGa1 − xMxO3, M = Cr, Mn, Fe (space group: R3c)
	T = 1473 K	(Belik, Rusakov et al., 2012)
YMnO3	P = 5.5 GPa	P21nb	TN = 42 K	Increase of dielectric constant @ TN
	T = 1273 K	(Wood et al., 1973)	P = 0.22 µC cm^−2
ErMnO3	P = 3.5 GPa	Pbnm	TN = 42 K	Sudden increase of dielectric constant @ TN
	T = 1373 K	(Ye et al., 2007)
ScMnO3	P = 12.5 GPa	P21/n	TN = 51 K	Not (yet) direct evidence of M–E coupling
	T = 1373 K	(Chen et al., 2013)
PbVO3	P = 5 GPa	Pnma	P = 100 µC cm^−2	VO5 pyramids
	T = 1023 K	(Shpanchenko et al., 2004)	(Varga et al., 2009)
PbMnO3	P = 5 GPa	P4/mmm	TN = 20 K	Centrosymmetric structure, non-FE
	T = 1023 K	(Oka et al., 2009)
FeTiO3	P = 18 GPa	R3c	TN = 110 K	Evidence of M–E coupling @ TN
	T = 1473 K	(Varga et al., 2009)
ScCrO3	P = 6 GPa	Pnma	TN = 73 K (SCO)	Anomaly in dielectric constant @ both TN
InCrO3	T = 1500 K	(Belik, Matsushita et al., 2012)	TN = 93 K (ICO)
MnTiO3	P = 7 GPa	R3c	TN = 25 K	Anomaly in dielectric constant @ TN
	T = 973 K	(Aimi et al., 2011)
MnSnO3	P = 7 GPa	R3c	TN = 50 K	Anomaly in dielectric constant @ TN
	T = 1073 K	(Aimi et al., 2011)
PbNiO3	P = 3 GPa	R3c	TN = 205 K	LiNbO3-like acentric structure
	T = 1073 K	(Inaguma et al., 2011)
Bi2NiMnO6	P = 6 GPa	C2	TC = 485 K	Evidence of M–E coupling
	T = 1073 K	(Shimakawa et al., 2011)	P = 20 µC cm^−2
Bi2FeMnO6	P = 6 GPa	Pnam	TN = 288 K	Reversal magnetization
	T = 1373 K	(Delmonte et al., 2013)		Evidence of M–E coupling
In2NiMnO6	P = 6 GPa	P21/n	TN = 26 K	Complex magnetic behavior
	T = 1600 K	(Yi et al., 2013)		No evidence of M–E coupling
Y2FeMnO6	P = 6 GPa	Pnma	TN = 328 K	Evidence of M–E coupling dielectric anomaly @ TN
	T = 1573 K	(Liu et al., 2014)
Y2CrMnO6	P = 6 GPa	Pnma	TN = 74 K	Evidence of M–E coupling dielectric anomaly @ TN
	T = 1573 K	(Liu et al., 2014)
Mn2FeSbO6	P = 3 GPa	P21/n	TN = 60 K	Possible M–E coupling by theoretical calculation
	T = 1273 K	(Mathieu et al., 2013)
CaMnTi2O6	P = 7 GPa	P42mc	TN = K	A-site ordering
	T = 1400 K	(Aimi et al., 2014)	P = 24 µC cm^−2
Pb2FeNdO6	P = 6 GPa	P42mc	TN = 150 K	Evidence of M–E coupling (Levstik et al., 2008)
	T = 1500 K	(Raevski et al., 2013)
CaMn7O12	P = 8 GPa	R3	TC = 90 K	Can be synthesized @ AP
	T = 1273 K	(Bochu et al., 1974)	P = 2870 µC m^−2 (Johnson et al., 2012)
BiMn7O12	P = 4 GPa	Im	TN = 22 K	Evidence of M–E coupling (Gauzzi et al., 2013)
	T = 1273 K	(Mezzadri et al., 2009)	TN = 55 K
PbMn7O12	P = 7.5 GPa		TN = 68 K	Evidence of M–E coupling
	T = 1273 K	(Locherer et al., 2012)
KxFex^2+Fe^3+1−xF3	P = 1.3 Kbar	Pba2	TN = 118 K	Complete MF
	T = 1053 K	(Mezzadri et al., 2008)		Hydrothermal synthesis

Due to unavoidable limitations of the HP/HT syntheses, such as the scarce amount of obtainable material, alternative methods have been developed to mimic the effect of the external pressure: thin film epitaxial stabilization and chemical substitutions.

2.5. Beyond HP/HT synthesis of MF materials: thin film epitaxial stabilization

This approach, desirable for device fabrication, implies the deposition of the single phase (i.e. non-hetero-structures formed by a multilayers architecture) in the form of a thin film on strained substrates. Interesting results have been achieved for several (potential) magneto-electric MF materials as a viable alternative to HP/HT synthesis to obtain Bi-based perovskites, such as BiMnO₃ (Moreira dos Santos et al., 2004; Sharan et al., 2004; Eerenstein et al., 2005), BiAlO₃ and BiGaO₃ (Belik, Wuernisha et al., 2006) on different substrates.

Analogously, fully epitaxial thin films of PbVO₃ were deposited by a pulsed laser deposition on a number of single-crystal substrates including NdGaO₃ (100) (Kumar et al., 2007) and LaAlO₃ (001) (Oh et al., 2014). PbVO₃ has been proposed as a good candidate to be a magneto-electric MF compound, having an antiferromagnetic ordering (T_N ≃ 200 K) and a ferroelectric polarization as large as 152 µC cm⁻².

Concerning the double perovskite structure, the tendency is toward MF hetero-structures, that is the combination of layers with different functionalities, by using sophisticated deposition techniques enabling the precise control of the interfaces as detailed in several topical review papers (Shpanchenko et al., 2004; Ramesh & Spaldin, 2007; Martin et al., 2008; Vaz, 2012).

To the best of our knowledge no MF properties have been reported for the quadruple-perovskite thin film, although for NdMn₇O₁₂, that can be synthesized as bulk at 8 GPa and 1000°C, 10 nm-thick metastable thin film has been successfully grown on Nd_1−xMnO₃ substrate by the pulsed laser method or by injection MOCVD (Bosak et al., 2000; Prellier et al., 2001; Gorbenko et al., 2002) and the isostructural CaCu₃Ti₄O₁₂ can be grown onto Pt/Ti/SiO2/Si substrates using a pulsed-laser (Fang & Shen, 2003).

2.6. Beyond HP/HT synthesis of MF materials: `chemical' pressure

This approach exploits the well known effect of the chemical substitution of atoms with different sizes, mimicking the application of external pressure [see Moritomo et al., 1997, for a comparison between chemical (internal) pressure and mechanical (external) pressure on perovskite manganites].

To mention a relevant (but not comprehensive) example, Catalan et al. (2009) reported the ambient pressure synthesis of bulk Ca-doped BiFeO₃ ceramics, for which T_N increases with Ca concentration (0.66 K per 1% Ca molar). The smaller ionic size of Ca compared with Bi results in a contraction of the lattice, simulating the external pressure at a rate of 1% Ca = 0.3 GPa. Thus, hydrostatic pressure increases the magnetic transition temperature of BiFeO₃ of 2.2 K GPa⁻¹ and the interesting conclusion is that pressure, either chemical or mechanical, may be used to enhance the magneto-electric coupling in MF materials.

The same principle can be applied to thin films; Izquierdo et al. (2014) combined the epitaxial strain and the chemical pressure to modify the magnetic response of Al-doped TbMnO₃ films grown under compressive/tensile strain using (001)-oriented SrTiO₃ and MgO substrates by RF-sputtering. The chemical pressure generated by Al doping, together with the substrate-induced strain, modify the subtle competition between magnetic interactions in the system (the films show a weak ferromagnetic phase coexisting with the expected `bulk' antiferromagnetic phase), hence an additional degree of freedom to control the magnetic ordering can be provided, for example, by varying the film thickness and/or using other substrates.

2.7. Effect of HP on electrical and magnetic measurements

Besides the HP/HT synthesis, the application of external pressure often plays an important role in the magneto-electrical characterization even on thermodynamically stable compounds. This effect is clearly reported by Retuerto et al. (2009), comparing the DC-magnetic susceptibility versus T and H of the double perovskite Sr₂FeMoO₆ synthesized at ambient pressure and at 2 GPa, the latter displays a higher saturation magnetization and a sharper ferromagnetic transition at T_C as high as 430 K, thanks to the HP-induced cationic ordering. Although Sr₂FeMoO₆, contrary to the isostructural compounds reported in §2.2, does not belong to the family of MF materials, it indicates that HP is an important tool to better probe their magnetic and electric properties.

Relevant examples include enhancements in the polarization and magnetic properties in BiFeO₃ ceramic prepared by HP/HT synthesis (Su et al., 2007), the improved multiferroic properties in bulk RMn₂O₅ (R = Tb, Dy, Ho) (dela Cruz et al., 2007) or Ru-doped BiFeO₃ thin films (Feng et al., 2010), or other phenomena such as the HP-induced polarization reversal in multiferroic YMn₂O₅ (Chaudhury, dela Cruz et al., 2008), the HP-induced spin-liquid phase of bulk YMnO₃ (Kozlenko et al., 2008) or the HP-induced increase in the microwave absorption properties of bulk BiFeO₃ (Wen et al., 2010).

3. In situ investigations of MF materials at HP

Pressure is an ideal tool to manipulate the electronic and magnetic structure and the atomic arrangement of a material (Hemley & Ashcroft, 1998; Hemley et al., 2009; Schilling, 2000; Struzhkin et al., 2000). Although some HP phases can be quenched to ambient conditions and be recovered for detailed experimental characterization (as reviewed in §2 of this article), the majority of pressure-induced structural, electronic and magnetic phase transitions are reversible. Therefore, it is paramount to investigate the high-pressure behavior of materials in situ. The advances in HP technology over the past 50 years at large scale facilities (e.g. synchrotron radiation facilities and neutron sources) and in the laboratory (Bassett, 2009; Liebermann, 2011) have provided us with a large number of experimental tools to investigate the response of materials in situ at high pressure and variable temperature.

3.1. Multiferroic materials with perovskite structure

The vast majority of investigations at high pressure have been conducted on compounds with perovskite-type structure or variations hereof (we stressed its pivotal role in the synthesis of MF materials in the previous section). The geometrical features of the perovskite structures can be manipulated by the application of high pressure; since there is a direct link between the atomic structure and the magneto-electric properties, dramatic changes in the multiferroic behavior can be expected at high pressure.

3.1.1. BiFeO₃ a prototype multiferroic material

As already mentioned, BiFeO₃ is a prototype MF material with perov­skite structure that shows magnetic and ferroelectric behavior with a strong polarization at T = 300 K (Teague et al., 1970; Wang et al., 2003; Catalan et al., 2009; Shvartsman et al., 2007; Lebeugle et al., 2007). Over the past years, BiFeO₃ has developed into the most popular model system for experimental and theoretical investigations of MF materials at HP. The pressure-induced changes in BiFeO₃ have been experimentally investigated by Raman spectroscopy (Haumont et al., 2006; Yang et al., 2009; Guennou, Bouvier, Chen et al., 2011), X-ray powder and single-crystal diffraction (Belik et al., 2009a; Haumont et al., 2009; Zhu et al., 2010; Zhang et al., 2013; Guennou, Bouvier, Chen et al., 2011; Guennou, Bouvier, Haumont et al., 2011; Mishra et al., 2013), neutron powder diffraction (Kozlenko et al., 2011), optical absorption spectroscopy (Gomez-Salces et al., 2012; Gavriliuk et al., 2008), resistivity measurements (Gavriliuk et al., 2008), Nuclear Forward Scattering (NFS) (Gavriliuk et al., 2005, 2008) and X-ray Emission Spectroscopy (XES) (Gavriliuk et al., 2008) as well as theoretically through first-principles calculations (Gonzalez-Vazquez & Iniguez, 2009; Shang et al., 2009; Feng et al., 2013; Qiang et al., 2013). BiFeO₃ displays a complex response to high pressure with a number of structural phase transitions in the pressure range up to 60 GPa (Belik et al., 2009a; Haumont et al., 2009; Zhu et al., 2010; Guennou, Bouvier, Chen et al., 2011; Kozlenko et al., 2011; Mishra et al., 2013). However, the number of phase transitions, the atomic structure and the symmetry of the HP phases remain controversial. Gavriliuk et al. (2008) observed no structural phase transition in the pressure range to 60 GPa. Zhu et al. (2010) proposed a structural phase transition at about 10 GPa, however, based on the low-resolution diffraction data no unit cell or space group were proposed for the HP phase. Kozlenko et al. (2011) proposed a phase transition at 3 GPa from R3c to an orthorhombic phase with the space group Pbam from neutron powder diffraction data. Haumont et al. (2009) reported two phase transitions at P ≃ 3.5 and 10 GPa and proposed a R3c → C2/m → Pnma phase sequence. Mishra et al. (2013) observed two phase transitions at P = 4.1 and 11 GPa with a proposed phase sequence of R3c → P222₁ → Pnma. Two phase transitions at P = 4 and 7 GPa on compression have been observed by Belik et al. (2009a) and an additional phase transition on decompression, stable in a narrow pressure range between 3.4 to 4.9 GPa. The resulting phase transition sequence is the following R3c → Pbam → Ibam → Cmmm proposing three different low-pressure phases with orthorhombic symmetry (Belik et al., 2009a). Guennou, Bouvier, Chen et al. (2011) conducted X-ray single-crystal diffraction experiments up to pressures of 60 GPa, reporting six structural phase transitions at P = 4, 5, 7, 11 and 38 GPa, respectively. The proposed phase sequence is R3c → O-I → O-II → O-III → Pnma → Pnmm → Cmcm. The limited reciprocal space coverage of the HP single-crystal diffraction data did not allow an unambiguous identification of the structure models or space groups of the low-pressure orthorhombic O-I, O-II and O-III phases. Gavriliuk et al. (2008) conducted XES, NFS and resistivity measurements up to P = 55 GPa. The results from the XES and NSF measurements suggest a spin crossover from high spin (HS) to low spin (LS) of Fe³⁺ in the region between 45 to 55 GPa and a reversible insulator to metal Mott transition above 55 GPa. The authors suggest that the insulator to metal transition is driven by the HS–LS transition of the Fe³⁺, by changing the effective correlation energy below the threshold for the insulator to metal transition. First-principles calculations (Gonzalez-Vazquez & Iniguez, 2009) confirm the HS–LS transition and the very complex structural-electronic magnetic interplay during the transformations observed experimentally by Gavriliuk et al. (2008). Furthermore, an additional transition to a metallic non-spin phase at pressures above 70 GPa was proposed (Gonzalez-Vazquez & Iniguez, 2009).

Haumont et al. (2006) and Guennou, Bouvier, Haumont et al. (2011) find in their experimental results that stress and non-hydrostatic pressure conditions can not only lead to a significant shift in transition pressures, but also to stabilization of new phases. Guennou, Bouvier, Haumont et al. (2011) identified a new monoclinic phase at P ≃ 8 GPa under non-hydrostatic pressure conditions. In order to further understand the structural richness of BiFeO₃, Dieguez et al. (2011) conducted a systematic investigation of the stability of potential BiFeO₃ phases using first-principle methods. The results show a large number of metastable phases, which might explain the observation of a large number of HP and different phases reported.

The influence of impurities and defects on the HP behavior of BiFeO₃ has been investigated by Chen et al. (2012). Ba-doped BiFeO₃ (Bi_1−xBa_xFeO_3−0.5x) has been compressed to 18.7 GPa and significant changes in the compression behavior, the phase transition pressure and the phase sequence have been reported compared with pure BiFeO₃, observing a similar phase sequence, R3c → C2/m → Pnma, as Haumont et al. (2009).

3.1.2. Rare-earth manganite, RMnO₃ (R = Gd, Tb, Dy, Ho, La, Y, Lu, Tm, Sc, Dy)

Rare-earth manganites show a complex correlation between structural, electric and magnetic properties, which can be manipulated by exchanging the rare-earth ions. As of now, MF properties have only been reported for a subset of the rare-earth manganites and only a few have been characterized at high pressure.

The HP behavior of TbMnO₃ was investigated by X-ray diffraction and X-ray absorption spectroscopy (XAS). A continuous decrease in the Jahn–Teller distortion as well as a decrease in the tilt angles of the MnO₆ octahedra was observed with increasing pressure. XAS measurements show a shift of the Mn K-edge to higher energies while the pre-edge feature shifts to lower energies with pressure. Chen et al. (2009) interpret this as a broadening of the electronic band width of the e_g↑ orbitals in TbMnO₃.

Chou et al. (2013) investigated the response of the local and electronic structure of DyMnO₃ to pressure by Raman spectroscopy, XAS and XES measurements. A decrease of the Jahn–Teller distortion of the MnO₆ octahedra in combination with the gradual breakdown of the high-spin magnetism is detected at P = 32 GPa, suggesting a potential HS to LS transition above 32 GPa. No structural phase transitions were detected in the investigated pressure range.

GdMnO₃ has been investigated to pressures of 63 GPa by X-ray diffraction (Lin, Zhang et al., 2012) and to pressures of 53 GPa by X-ray diffraction and Raman spectroscopy measurements (Oliveira et al., 2012). A reversible first-order phase transition has been observed at P ≃ 50 GPa. Based on the diffraction data Lin, Zhang et al. (2012) interpreted the transition as an isostructural orthorhombic to orthorhombic transition. From X-ray diffraction and Raman spectroscopy measurements, Oliveira et al. (2012) conclude that it is an insulator to metal transition with a change in symmetry from orthorhombic (Pnma) to cubic (P2₁3).

Kozlenko and co-workers investigated the crystal and magnetic structure of hexagonal YMnO₃ (Kozlenko et al., 2008; Kozlenko, Kichanov, et al., 2010) and LuMnO₃ (Kozlenko, Kichanov et al., 2010) by simultaneous high-pressure and low-temperature neutron powder diffraction. The reduction of the in-plane splitting of the Mn—O bond with pressure has been identified as the potential reason for the observed enhanced spin fluctuations with increasing pressure in both compounds. Kozlenko, Kichanov et al. (2010) concluded that the reduction in Mn—O bond splitting with pressure implies a decrease in the magneto-elastic coupling strength.

Wang et al. (2010) investigated the high-pressure behavior of hexagonal TmMnO₃ by X-ray powder diffraction experiments up to P = 28.6 GPa. A hexagonal to orthorhombic transition was detected at 10.2 GPa.

ErMnO₃ crystallizes in the hexagonal space group P6₃cm. At P ≃ 20 GPa the structure undergoes an irreversible first-order transition to the orthorhombic phase with space group Pbnm (Lin, Liu et al., 2012).

The structural stability of RMnO₃ (R = Y, Ho, Lu) at HP has been investigated by X-ray diffraction, synchrotron IR spectroscopy, XAS and ab-initio quantum mechanical calculations (Gao et al., 2011). YMnO₃, HoMnO₃ and LuMnO₃ remain hexagonal up to P ≃ 20 GPa. Above 20 GPa the onset of a structural phase transition to orthorhombic symmetry has been observed. The IR measurements show that the O atoms are the most sensitive to pressure, with vibration modes mainly confined to the ab plane (Gao et al., 2011).

3.1.3. BiMnO₃

A lot of work has been carried out on BiMnO₃ and HP characterization. The unit cell changes in BiMnO₃ with pressure were investigated by energy dispersive diffraction in the pressure range from ambient pressure to 27 GPa (Chi et al., 2008). The measurements showed no evidence of a structural phase transition. The DC magnetization was measured at pressures up to 1.6 GPa by Chou et al. (2008). T_C = 100 K at ambient pressure and the signal associated with ferromagnetic behavior decreases with pressure and disappears at P = 1.31 GPa. A second peak in the susceptibility has been detected at 1.17 GPa and has been interpreted as an onset of a structural phase transition (Chou et al., 2008). These measurements were followed up by magnetic hysteresis and AC susceptibility to high pressure and low temperature (Chou et al., 2009). Three magnetic phase transitions have been detected at ambient pressure and 98 K, 0.87 GPa and 93 K, and 72.5 K and 0.87 GPa. The ambient pressure and 100 K transition can be characterized as a long-range ferromagnetic transition, being suppressed at high pressure and therefore not observed. The transition is accompanied by an anomaly below 90 K, which is attributed to a spin-glass behavior. The second transition is attributed to a long-range soft ferromagnetic to a canted state, while the third is characterized as a canted antiferromagnetic transition. Chou et al. (2009) suggest that both the canted ferromagnetic and the canted antiferromagnetic transition are caused by the structural phase change from C2/c to P2₁/c, which has been observed by Belik et al. (2009b). This demonstrates the complex interplay between lattice distortion and spin configuration in multiferroic material. Belik et al. (2009b) reported two structural phase transitions at 0.9 and 8 GPa. The phase transition at 0.9 GPa has been characterized as a C2/c → P2₁/c transition, however, the structure of the new monoclinic HP phase could not be refined. At 8 GPa BiMnO₃ transforms to the non-ferroelectric GdFeO₃-type structure with Pnma symmetry. The GdFeO₃-type structure exhibits a strong Jahn–Teller distortion of the MnO₆ octahedra and long-range d(3y² − r²) e_g orbital ordering (Belik et al., 2009b). Kozlenko, Belik et al. (2010) conducted high-pressure neutron powder diffraction measurements on BiMnO₃ to 10 GPa and simultaneous high-pressure and low-temperature neutron diffraction experiments in the pressure region up to 2 GPa. The ferromagnetic ground state is suppressed at moderate pressures of 1 GPa at 90 K with a transition to an antiferromagnetic state with a propagation vector of k = (½ ½ ½) at 90 K. This change in magnetic state is accompanied by a monoclinic to monoclinic structural phase transition. The FM and AFM states coexist below pressures of 2 GPa (Kozlenko, Belik et al., 2010). Mei et al. (2010) explored the structural and elastic properties of BiMnO₃ by first principles calculations using LDA+U and GGA+U formalisms. The energies for the monoclinic (C2/c) phases and the orthorhombic (Pnma) phase were calculated as a function of pressure. The calculations, in contrast to the experimental results by Belik et al. (2009b), show that the orthorhombic phase is the stable structure at ambient pressure. A monoclinic to monoclinic phase transition is predicted at P = 10 GPa induced by a magnetic to volume instability in BiMnO₃. Recently, Kozlenko et al. (2014) determined the phase diagram of BiMnO₃ to a pressure of 50 GPa and investigated the phase relationships as a function of temperature and pressure in the range T = 300–900 K from ambient pressure to 4 GPa using X-ray diffraction and Raman spectroscopy. Two new high-pressure phases with C2/m symmetry, but distinctly different structural parameters, have been identified at moderate pressures and temperatures, as had been previously suggested based on the results from first-principles calculations (Mei et al., 2010). The transition to the high temperature orthorhombic phase is suppressed to room temperature at 8 GPa, consistent with reports from Belik et al. (2009b). Above 20 GPa BiMnO₃ undergoes a phase transition from Pnma → Imma, leading to a suppression of the long-range d(3y² − r²) e_g orbital ordering.

3.1.4. Cobaltite perovskites, ACoO₃

Ming et al. (2009) studied the structural stability, and the magnetic and electronic properties of BiCoO₃ by first-principles calculations up to 30 GPa. The calculations reproduce the C-type antiferromagnetic structure as a ground state. At P = 4 GPa a first-order isostructural transition is observed, accompanied by a HS–LS spin-crossover of Co³⁺ with an insulator to semi-metal transition. The authors conclude that in contrast to the excluded models for insulator to metal transitions, the spin-crossover effect at HP is the driving mechanism for the transition in BiCoO₃. Oka et al. (2010) investigated the HP behavior of BiCoO₃ by synchrotron and neutron powder diffraction and X-ray emission spectroscopy. A first-order tetragonal, PbTiO₃-type, to orthorhombic, GdFeO₃-type, phase transition has been observed at P = 3 GPa, in contrast to the proposed isostructural tetragonal to tetragonal transition by Ming et al. (2009). The transition is accompanied by a HS to LS transition with an intermediate spin state present at the transition as determined from XES data.

3.1.5. PbNiO₃

As already mentioned, two synthesized polymorphs of PbNiO₃ can be obtained by HP/HT synthesis, with a perovskite-type and a LiNbO₃-type structure (Inaguma et al., 2011). The unit-cell volume for LiNbO₃ and the perovskite-type polymorph suggest that the perovskite type might be a high-pressure polymorph of the LiNbO₃-type PbNiO₃. The LiNbO₃-type PbNiO₃ undergoes a pressure-induced phase transition to a GdFeO₃-type structure, space group Pnma, at about 3 GPa. In both polytypes the magnetic interaction of the Ni²⁺ is antiferromagnetically dominated by the Ni—O distances rather than the Ni—O—Ni angles. XPS measurements suggest Pb⁴⁺, Ni²⁺ valence states for both polymorphs. Hao et al. (2014) performed first principles calculation using the GGA, GGA+U and Heyd-Scuseria-Ernzerhof (HSE) approaches. The observed pressure-induced phase transition (Inaguma et al., 2011) from R3c to Pnma is reproduced, although at a slightly higher transition pressure of about 5 GPa. The orthorhombic HP phase shows a considerable anisotropy of the nearest-neighbor exchange couplings.

3.1.6. BiNiO₃

Azuma et al. (2007) investigated the high-pressure behavior of BiNiO₃ by neutron diffraction experiments in combination with electronic-state calculations using first principles with the LDA+U approach. At 4 GPa a pressure-induced phase transition from the to GdFeO₃-type structure, with space group Pbnm, has been observed. Calculation of the changes in electronic structure with pressure suggest that the pressure-induced phase transition is an insulator to metal transitions which occurs via simultaneous melting of the Bi charge disproportion and charge transfer from Ni to Bi.

3.2. MF materials with non-perovskite structure

Recently, the search for MFs has expanded to materials that crystallize in other structure types than the perovskite-type structure and to chemical compositions beyond `simple' oxides such as transition metal oxyhalides, germanates and silicates, transition metal orthotellurides and transition metal chalcogenides. These materials are relatively new and none of them require HP/HT synthesis, but a few have been investigated in situ at high pressure.

3.2.1. MnWO₄

MnWO₄ crystallizes in the wolframite structure (space group P2/c with Z = 2) and is ferroelectric showing incommensurate helical spin-density waves (Taniguchi et al., 2006). The pressure dependence of the dielectric properties up to pressures of 1.8 GPa has been measured by Chaudhury, Yen et al. (2008). Pressure suppresses the ferroelectric polarization in the ferroelectric phase suggesting that the stability of the ferroelectric phase is reduced by increasing the pressure. The structural changes in MnWO₄ with pressure have been investigated to 8 GPa and the compression mechanism has been derived from X-ray diffraction data (Macavei & Schulz, 1993). Ab initio quantum mechanical calculations (López-Moreno et al., 2009) confirm the experimentally determined compression behavior of MnWO₄ (Macavei & Schulz, 1993) and suggest no structural phase transition in the pressure range from ambient pressure to 31 GPa. The calculated magnetic moment decreases with pressure confirming the results from Chaundhury, Yen et al. (2008). Recently, Dai et al. (2013) determined the pressure and temperature behavior of MnWO₄ by Raman scattering. Changes in the Raman spectrum at P = 17.7 GPa at ambient temperature were interpreted as a monoclinic to triclinic structural phase transition.

3.2.2. CuCrO₂

CuCrO₂ crystallizes in the delafossite-type structure (space group ) and shows multiferroic properties below T_N = 24 K, at which the magnetic moments ordered into a proper screw-type spiral structure (Seki et al., 2008; Kimura et al., 2008). The Cr³⁺ ions in the structure are arranged in triangular planes, which are stacked along the c axis. Spin frustration occurs on the triangular planes, leading to a degree of freedom of spin chirality in the magnetic screw-type spiral structure. The spin chirality allows a relaxation of the spin frustration and therefore has a stabilizing effect on the structure. A p–d hybridization model can be used to fully describe the ferroelectricity in conjunction with the screw spiral ordering (Arima, 2007). Aoyama et al. (2013) investigated the evolution of the crystal structure, magnetism and spin-driven ferroelectricity in CuCrO₂ up to pressures of 10 GPa. The temperature T_N of the transition to the spin-spiral ferroelectric ordering in CuCrO₂ increases with pressure. The magnitude of the dielectric anomaly at T_N is suppressed with increasing pressure and the spontaneous polarization is completely suppressed at about 8 GPa (Aoyama et al., 2013). Aoyama et al. (2013) attribute the ferroelectric antiferroelectric transitions to a shortening of the Cr-interlayer distances, which leads to an increase in the interlayer exchange integral with elevated pressure. The observed increase in the size of the field for the polarization reversal with pressure can be attributed to a rearrangement in the magneto-electric domains (Aoyama et al., 2013).

3.2.3. Ba₃TaFe₃Si₂O₁₄

Ba₃TaFe₃Si₂O₁₄, a member of the langasite family, crystallizes in the trigonal space group P321 with one formula unit per unit cell (Lyubutin et al., 2010). Gavriliuk et al. (2013) investigated the pressure and temperature behavior of Ba₃TaFe₃Si₂O₁₄ up to P = 38 GPa and down to T = 20 K by Nuclear Forward Scattering (NFS) and Raman spectroscopy. At P = 19.5 GPa a first-order pressure-induced phase transition has been observed. The transition is accompanied by a magnetic change with a fourfold increase in Néel temperature T_N from 27.2 to 120 K (Gavriliuk et al., 2013). The authors suggest a strong superexchange interaction caused by changes in the bond angles as an explanation for the strong pressure dependence of the Néel temperature.

3.2.4. Mn₂GeO₄

Recently, multiferroic properties have been reported in Mn₂GeO₄, a compound that crystallizes in the orthorhombic (space group Pnma) olivine-type structure (Creer & Troup, 1970). At low temperature, Mn₂GeO₄ undergoes three antiferromagnetic (AFM) phase transitions at T_N1 = 47 K > AFM1 > T_N2 = 17 K > AFM2 > T_N3 = 5.5 K > AFM3 (White et al., 2012; Volkov et al., 2013; Honda et al., 2012). The transitions are characterized by a change in the magnetic moments of Mn²⁺. The AFM1 phase shows mainly an alignment of the moments along the a axis with a slight canting along the c axis, making AFM1 a weak ferromagnetic phase. The spins are oriented along the b axis in the AFM2 phase. The AFM3 phase exhibits spontaneous magnetization and electric polarization along the c axis, characteristic for a MF phase. The ferroelectricity originates from the formation of an incommensurate (IC) spin-spiral structure and the spontaneous magnetization arises from a canting of a commensurate (C) magnetic structure (White et al., 2012). Honda et al. (2014) investigated the effect of pressure on the magnetism and the multiferroicity of Mn₂GeO₄. The transition temperatures of the magnetic transitions change monotonically with increasing pressure. The change in transition temperature T_N1 [dT_N1/dp = 0.046 (3) GPa⁻¹] can be described by a classical Heisenberg exchange Hamiltonian model assuming the size of the superexchange interactions scale proportionally to the power −10/3 of the volume (Honda et al., 2014). At 6 GPa the spin-driven ferroelectricty in the AFM3 phase disappears. High-pressure neutron diffraction experiments observed a shift of the IC magnetic peak towards a C position with increasing pressure (Honda et al., 2014). Therefore, the suppression of the spin-driven ferroelectricity in the AFM3 phase at 6 GPa is attributed to an IC-C phase transition.

3.2.5. FeTe₂O₅Br

A relatively new class of MF materials is the group of transition metal oxohalides (Choi et al., 2014). The incorporation of lone-pair cations and halides provides exchange pathways, which lead to magnetic frustration in these materials (Bos, Colin & Palstra, 2008; Lawes et al., 2003; Pregelj et al., 2009; Zaharko et al., 2006; Zhang, Kremer et al., 2011). FeTe₂O₅Br is not only a magnetically but also a geometrically frustrated system as well. The HP behavior of FeTe₂O₅Br has been investigated by Raman and optical absorption spectroscopy up to P = 7 GPa (Gnezdilov et al., 2011; Choi et al., 2014). Both, the Raman spectroscopy and the optical absorption measurements show evidence of a structural phase transition between 2.12 and 3.04 GPa. The HP phase exhibits an increased uniformity in the bonding forces, compared with the highly anisotropic ambient pressure phase. The anisotropic Fe(3d) orbitals start to overlap with the Br(4s) and O(2p) orbitals, changing from a two-dimensional electronic structure at ambient conditions to a three-dimensional electronic structure at HP.

3.2.6. HgCr₂S₄

HgCr₂S₄ belongs to the large group of thiospinels and crystallizes in the space group at ambient conditions (Hemberger et al., 2006; Weber et al., 2006). The compound exhibits both ferromagnetic and ferroelectric properties together with a pronounced magneto-capacitive coupling with a bond-frustrated magnetic ground state (Hemberger et al., 2006). The ferroelectricity in the chromium thiospinel family is caused by a dynamic disorder of the Cr³⁺ ions, which induces an off-center shift of the Cr³⁺ ions and a change in symmetry of the local structure to the polar space group (Gnezdilov et al., 2011). The HP behavior of HgCr₂S₄ has been investigated by a combination of X-ray powder diffraction measurements and band structure calculations based on the Linear-Muffin-Tin Orbital method (Efthimiopoulos et al., 2013). Two structural phase transitions have been observed at P = 20 and 26 GPa, respectively. At 20 GPa HgCr₂S₄ undergoes a reversible first-order cubic to tetragonal transition from the space group to I4₁/amd. The phase transition has an insulator to metal character and is accompanied by a change in the magnetic state to an antiferromagnetic one and the loss of ferroelectric properties. A second-order phase transition to an orthorhombic structure, most likely with Imma space group, has been reported at 26 GPa. Based on the diffraction data Efthimiopoulos et al. (2013) proposed a third phase transition at P ≃ 37 GPa. However, strong peak overlap between gasket, the ortho­rhombic phase and the potentially new HP phase prevented the detailed characterization of this phase.

4. Conclusions

The search for intrinsic magneto-electric MF compounds with the co-existence and coupling of magnetic and electric order in the same phase remains challenging despite large efforts in the scientific community. Most currently known intrinsic MF only exhibit very small magneto-electric coupling at low temperature, while for technological applications they are required to show large magneto-electric effects at ambient conditions. Therefore, it is paramount to broaden the search for MF materials to new classes of materials and to new synthesis techniques.

The HP/HT synthesis has proven to be a powerful tool for the stabilization of metastable HP phases with MF properties. The majority of these new phases crystallize in the perovskite or perovskite-related structure. The investigation of MF materials in situ at high pressure and temperature has provided valuable insight into the coupling between electric, magnetic and structural properties. Especially experiments at non-hydrostatic conditions can in the future lead to the identification of possible high-pressure MF phases that could be stabilized at ambient conditions as highly strained thin films.

Despite the promising results obtained so far, the currently employed high-pressure techniques have intrinsic shortcomings, such as comparatively long synthesis times, relatively small sample sizes and vast parameter space in pressure, temperature and composition that needs to be explored. However, these limitations can be overcome by a concerted effort between theory (e.g. structure prediction), which could potentially allow targeted synthesis at pressure and temperature, and the development of new HP synthesis and characterization approaches.

The availability of such new and more sophisticated synthesis and characterization techniques, combined with theoretical approaches, could lead to an enormous increase in our fundamental understanding of MF materials and potentially to widespread technological applications.