Pressure Induced Spin Crossover and Magnetic Properties of Multiferroic Ba3NbFe3Si2O14

Recently, the iron containing langasite-type crystal Ba3NbFe3Si2O14 has attracted great attention as a new magnetically induced multiferroic. In this work, magnetic, structural and electronic properties of the multiferroic Ba3NbFe3Si2O14 were investigated by several methods, including synchrotron X-ray diffraction, Raman spectroscopy and synchrotron Mössbauer source technique at high quasi-hydrostatic pressures (up to 70 GPa), created in diamond anvil cells. At room temperature, two structural transitions at pressures of about 3.0 and 17.5 GPa were detected. Mössbauer studies at high pressures revealed a radical change in the magnetic properties during structural transitions. At pressures above 18 GPa, the crystal transforms into two magnetic fractions, and in one of them the Néel temperature (TN) increases by about four times compared with the TN value in the initial phase (from 27 to 115 K). At pressures above 50 GPa, a spin crossover occurs when the fraction of iron Fe3+ ions in oxygen octahedra transits from the high-spin (HS, S = 5/2) to the low-spin (LS, S = 1/2) state. This leads to a new change in the magnetic properties. The magnetic ordering temperature of the LS sublattice was found to be of about 22(1) K, and magnetic correlations between HS and LS sublattices were studied.

At ambient conditions, BNFS has a trigonal crystal structure (space group P321, point group 32, Z = 1), where layers of oxygen tetrahedrons with Fe(3f ) and Si(2d) ions alternate with the layers containing Nb(1a) and Ba(3e) ions, which are located in oxygen octahedrons and Thompson cubes, respectively [1,10] (Figure 1). A theoretical description of the helical magnetic structure and the conditions for the existence of multiferroic properties in langasites are presented in [5,6]. The low-temperature magnetic transition causes a structural transition from the P321 phase to the P3 (or C2) polar phase, which favors the appearance of ferroelectricity [5,13].
To create materials of practical importance, an increase in the critical temperatures of magnetic and ferroelectric transitions (TN and TP) is a key problem. Modification of the crystal structure using chemical engineering or/and external pressure is the most promising way. Actually, this can be done either by applying an external pressure or by cationic substitution, which can create "internal" chemical pressure.
The effect of pressure on magnetoelectric properties in magnetic materials with triangular lattices was recently considered in [15,16]. Additional interest to this topic arose after the discovery of a huge increase in the value of Neel temperature ТN (from 27 to 120 K) in the langasite family compound Ba3TaFe3Si2O14 under high pressure above 20 GPa [17].
Meanwhile, new magnetic properties may appear in iron oxide materials under applied high pressures above 50 GPa, where spin-crossover effects are expected [18]. In particular, the transition of Fe 3+ and Fe 2+ ions from the high spin to the low spin state was observed experimentally in a number of iron oxide compounds with perovskite-like and garnet crystal structures [18].
Preliminary data on the study of the crystal structure and Mössbauer spectra in BNFS under high pressure were presented in Ref. [19]. The interpretation of the structural data was not entirely correct, since it was not clear whether the lattice symmetry and the unit cell change after structural Mössbauer spectroscopy studies of magnetic properties revealed that magnetic moments of iron ions in BNFS arrange in three-dimensional antiferromagnetic order with the Neel temperature T N of 27.1 K [3]. As found by neutron diffraction [11], below T N , Fe ions in 3f sites form a net of triangle magnetic clusters in the (ab) planes with a 120 • orientation of iron magnetic moments, which appear due to frustrated exchange interactions ( Figure 1). In addition, magnetic triangles of Fe moments form a helical arrangement along the c axis rotating from plane to plane with a period of about 7 unit cells [11,12]. Recently, the relationship between structural and magnetic chirality has been studied in detail in [13,14]. It was shown in [13] that, in the absence of helical axes in a noncentrosymmetric Ba 3 NbFe 3 Si 2 O 14 crystal (and in a similar Ba 3 TaFe 3 Si 2 O 14 compound), the formation of the spiral electron density of Fe(3f ) and O3(6g) atoms in neighboring cells can be responsible for the phenomenon of crystalline chirality. The direction of rotation of the spiral is determined by the orientation of the ellipsoids of atomic displacements and correlates with the sign of rotation of the plane of light polarization by the crystal. The helical magnetic structure in BNFS was also recently investigated by Mössbauer spectroscopy [12].
A theoretical description of the helical magnetic structure and the conditions for the existence of multiferroic properties in langasites are presented in [5,6]. The low-temperature magnetic transition causes a structural transition from the P321 phase to the P3 (or C2) polar phase, which favors the appearance of ferroelectricity [5,13].
To create materials of practical importance, an increase in the critical temperatures of magnetic and ferroelectric transitions (T N and T P ) is a key problem. Modification of the crystal structure using chemical engineering or/and external pressure is the most promising way. Actually, this can be done either by applying an external pressure or by cationic substitution, which can create "internal" chemical pressure.
The effect of pressure on magnetoelectric properties in magnetic materials with triangular lattices was recently considered in [15,16]. Additional interest to this topic arose after the discovery of a huge increase in the value of Neel temperature T N (from 27 to 120 K) in the langasite family compound Ba 3 TaFe 3 Si 2 O 14 under high pressure above 20 GPa [17].
Meanwhile, new magnetic properties may appear in iron oxide materials under applied high pressures above 50 GPa, where spin-crossover effects are expected [18]. In particular, the transition of Fe 3+ and Fe 2+ ions from the high spin to the low spin state was observed experimentally in a number of iron oxide compounds with perovskite-like and garnet crystal structures [18].
Preliminary data on the study of the crystal structure and Mössbauer spectra in BNFS under high pressure were presented in Ref. [19]. The interpretation of the structural data was not entirely correct, since it was not clear whether the lattice symmetry and the unit cell change after structural transitions. Based on the available powder data, we made one of the most probable assumptions about the transition of BNFS into the hexagonal phase after 17-18 GPa. To confirm this, structural studies were carried out on BNFS single crystals at high pressures [20]. It was found that at a pressure of 3.5 GPa, the structure of this crystal transforms from the P321 phase (Z = 1) into the intermediate polar P3 (Z = 3) phase; and at a pressure of 17.5 GPa, the second structural transition to the perovskite-like phase with the space group P62m (Z = 1) and hexagonal symmetry occurs, which was previously unknown.
In the present work, the structural data of BNFS polycrystals were processed based on the results obtained for single crystals. The full-profile analysis of powder diffraction patterns was carried out up to pressures of 60 GPa and the lattice parameters of the structures before and after phase transitions were refined. Previously, the full-profile analysis could not be carried out because the lattice symmetry and unit cell after phase transitions were unknown. Based on the new data, an equation of state for langasite BNFS was constructed up to pressures of 60 GPa.
In view of the search and study the magnetic and electronic properties of the langasite family compounds, in this work, the Ba 3 NbFe 3 Si 2 O 14 multiferroic was investigated by synchrotron Mössbauer source (SMS) technique at high pressures (up to 70 GPa) created in diamond anvil cells. The high-pressure Raman spectroscopy studies were also performed to establish correlations between the structural and magnetic properties in these crystals.

X-Ray Diffraction
The phase composition of Ba 3 Nb 57 Fe 3 Si 2 O 14 was controlled by X-ray powder diffraction and by the transmission Mössbauer spectroscopy. The X-ray diffraction pattern of BNFS shown in Figure 2a demonstrates a high quality compound, whose crystal structure belongs to the space group (sp. gr.) P321 with unit cell parameters a = 8.530(2) Å and c = 5.235(2) Å.
In applied pressure above 3 GPa, a set of diffraction peaks corresponding to a new phase with sp.gr. P3 was observed in the XRD patterns along with the peaks of the initial P321 phase. In a certain pressure range these two phases coexist, however above 12 GPa only the polar phase P3 remains (Figure 2b). With a further increase in pressure, the phase P3 persists up to 17.5 GPa, and then a new phase with sp. gr. P62m appears (Figure 2c). The P3 and P62m phases coexist in the pressure range of about 13-21 GPa, and then only the P62m phase remains as the pressure further increases up to 58 GPa ( Figure 2d).
Structural phase transitions at pressures of about 3.5 and 17-18 GPa are clearly detected, and this supports the data of single-crystal XRD studies of the BNFS compound performed recently in Ref. [20]. The effect of the coexistence of two phases in our BNFS sample, observed in the pressure region of structural transitions, can be explained by the powder nature of the sample and the pressure gradients at the sample in this experiment. Figure 3 shows the pressure behavior of the unit cell parameters a and c and the unit cell volume V. The second transition at 17.5 GPa leads to strong changes in the unit cell parameters and a sharp drop in the cell volume by about 8%. From the viewpoint of magnetic characteristics, an appreciable decrease in the parameter c during the structural transition at P ≈ 17.5 GPa should lead to a pronounced enhancement of the exchange coupling between iron ions located in neighboring (ab) planes.

X-Ray Diffraction
The phase composition of Ba3Nb 57 Fe3Si2O14 was controlled by X-ray powder diffraction and by the transmission Mössbauer spectroscopy. The X-ray diffraction pattern of BNFS shown in Figure 2a demonstrates a high quality compound, whose crystal structure belongs to the space group (sp. gr.) P321 with unit cell parameters a = 8.530(2) Å and c = 5.235(2) Å.  In applied pressure above 3 GPa, a set of diffraction peaks corresponding to a new phase with sp.gr. P3 was observed in the XRD patterns along with the peaks of the initial P321 phase. In a certain pressure range these two phases coexist, however above 12 GPa only the polar phase P3 remains (Figure 2b). With a further increase in pressure, the phase P3 persists up to 17.5 GPa, and then a new phase with sp. gr. phase remains as the pressure further increases up to 58 GPa (Figure 2d).
Structural phase transitions at pressures of about 3.5 and 17-18 GPa are clearly detected, and this supports the data of single-crystal XRD studies of the BNFS compound performed recently in Ref. [20]. The effect of the coexistence of two phases in our BNFS sample, observed in the pressure region of structural transitions, can be explained by the powder nature of the sample and the pressure gradients at the sample in this experiment. Figure 3 shows the pressure behavior of the unit cell parameters a and c and the unit cell volume V. The second transition at 17.5 GPa leads to strong changes in the unit cell parameters and a sharp drop in the cell volume by about 8%. From the viewpoint of magnetic characteristics, an appreciable decrease in the parameter c during the structural transition at P ≈ 17.5 GPa should lead to a pronounced enhancement of the exchange coupling between iron ions located in neighboring (ab) planes.

Raman Spectroscopy
Room temperature Raman spectra of Ba3Nb 57 Fe3Si2O14 at pressures up to 25 GPa for

Raman Spectroscopy
Room temperature Raman spectra of Ba 3 Nb 57 Fe 3 Si 2 O 14 at pressures up to 25 GPa for compression and decompression cycles are shown in Figure 4. The pressure behaviour of the positions of Raman peaks clearly demonstrates the appearance of two successive transitions under the compression run ( Figure 4a). The first of them, at about 3-4 GPa, exhibits itself as a merger of some peaks, as well as in the appearance of a strong shoulder at 550 cm −1 . This anomaly is consistent with the observation of a structural transition according to XRD and Mössbauer spectroscopy data. The second transformation occurs at about 17.5 GPa, where the Raman spectrum drastically changes. The sharp peaks completely disappear and only a few weak and very broad maxima are observed (Figure 4a). According to XRD, this is related to the second structural transition, which is accompanied by a decrease in the unit cell volume by about 8% (Figure 3).
Molecules 2020, 25, x FOR PEER REVIEW 5 of 17 some peaks, as well as in the appearance of a strong shoulder at 550 cm −1 . This anomaly is consistent with the observation of a structural transition according to XRD and Mössbauer spectroscopy data. The second transformation occurs at about 17.5 GPa, where the Raman spectrum drastically changes. The sharp peaks completely disappear and only a few weak and very broad maxima are observed ( Figure 4a). According to XRD, this is related to the second structural transition, which is accompanied by a decrease in the unit cell volume by about 8% (Figure 3). The pressure behavior of the Raman peak positions ( Figure 5) more clearly demonstrates the appearance of successive transitions at ~3 and 17.5 GPa. The transition at 17.5 GPa occurs abruptly and with a large hysteresis.   During decompression, pronounced peaks appear only when the pressure is decreased to 3 GPa (Figure 4b). This demonstrates a very large hysteresis, which was also observed in the XRD measurements. This is indicative of a first order type of the structural phase transition at 17.5 GPa with a large energy barrier between the low-and high-pressure phases. When decompression to ambient pressure, the shape of the Raman spectrum returns to the initial sharp peaks characteristic of the low-pressure crystalline structure (Figures 4b and 5b). This observation confirms the diffuse-like transition of the first order type with a strong reconstruction of the crystal structure.
The results of the Raman experiment strongly support the existence of the first and second phase transitions and help locate more precisely the critical pressures of transitions.

Magnetic Properties of BNFS at Pressures in the Range 0-40 GPa
The magnetic and electronic properties of BNFS at high pressures up to 70 GPa and cryogenic temperatures were studied by synchrotron Mössbauer spectroscopy (SMS) technique. As shown in Figure 6, the SMS spectra of BNFS, recorded at the lowest temperatures in this experiment (3.0-4.9 K) are split into six main resonance lines demonstrating magnetic ordering of Fe ions at all pressures in the range from ambient to 45 GPa.
As was established by neutron diffraction [11] and Mössbauer spectroscopy [12] studies, below T N and at ambient pressure, iron magnetic moments lying in the (ab) planes (in the 3f crystal sites) exhibit helical rotation with a propagation helicoidal vector along the c axis with a period of about 7c (c is the value of the unit cell parameter along the c axis) [11,12]. In this case, the Mössbauer spectrum, in general, should consist of a combination of 7 subspectra corresponding to the different orientation iron magnetic moment relative to the main axis of the electric field gradient (EFG) [12]. Obviously, the transformation of the spectra shapes under the applied pressure, shown in Figure 6, is related to the modification of the helical magnetic structure by pressure.
The average values of the hyperfine parameters obtained from the Mössbauer spectrum at ambient pressure and helium temperatures are: the isomer shift is δ = 0.345(5) mm/s and the magnetic hyperfine field at iron nuclei H hf is about 45.77(5) T. These parameters correspond to the high spin state of Fe 3+ ions (3d 5 , S = 5/2) in tetrahedral oxygen sites and imply essential covalence in Fe-O bonds. The value of the quadruple shift at 4.2 K is ε = −0.66 mm/s, which is in agreement with the quadrupole splitting of ∆ = 1.3 mm/s observed in the paramagnetic state at room temperature.
As temperature increases, the magnetic splitting of the Mössbauer spectra decreases, and the six-line magnetic spectra gradually transform into a quadrupole doublet indicating a transition to the paramagnetic state ( Figure 7). The value of the Neel temperature T N can be estimated from the temperature dependence of the magnetic hyperfine field at iron nuclei H hf (Figure 8), and at ambient pressure the obtained value for BNFS is T N = 27.2(1) K.

Magnetic Properties of BNFS at Pressures in the Range 0-40 GPa
The magnetic and electronic properties of BNFS at high pressures up to 70 GPa and cryogenic temperatures were studied by synchrotron Mössbauer spectroscopy (SMS) technique. As shown in Figure 6, the SMS spectra of BNFS, recorded at the lowest temperatures in this experiment (3.0-4.9 K) are split into six main resonance lines demonstrating magnetic ordering of Fe ions at all pressures in the range from ambient to 45 GPa.  Under the applied pressure, the temperature evolution of the Mössbauer spectra does not changed essentially with increasing pressure from ambient to 17 GPa (Figure 7), while the T N value slightly increases to about 32.0 K. However, at pressures above 18 GPa, the temperature evolution of the Mössbauer spectra change significantly ( Figure 7). Along with the transition of the main fraction of the sample into the paramagnetic state at about 30 K, some part of the sample remains in magnetically ordered state even at rather high temperatures. This indicates the separation of the sample into two fractions with different magnetic properties.
From the temperature dependence of the magnetic hyperfine field H hf at, the temperature of the onset of magnetic ordering in a new magnetic phase can be estimated at about 110-115 K ( Figure 8).
Obviously, the appearance of a new magnetic phase with high value of T N is associated with a structural transition at pressure of 17.5 GPa, which was observed according to XRD and Raman spectroscopy studies. At this transition, Fe cations can change the local oxygen arrangement and/or redistribute between tetrahedral and octahedral oxygen sites.
At ambient conditions, iron ions in BNFS occupy 3f oxygen tetrahedra ( Figure 1). The local nearest neighbors of Fe 3+ are Si 4+ and Nb 5+ , which occupy the tetrahedral 2d sites and octahedral 1a sites, respectively (Figure 1). At high pressures, redistribution of Fe 3+ ions can occur either between two types of tetrahedral 3f and 2d sites in the (ab) plane or/and between tetrahedral 3f and octahedral 1a sites in the nearest layers along the c axis. the quadrupole splitting of ∆ = 1.3 mm/s observed in the paramagnetic state at room temperature.
As temperature increases, the magnetic splitting of the Mössbauer spectra decreases, and the six-line magnetic spectra gradually transform into a quadrupole doublet indicating a transition to the paramagnetic state ( Figure 7). The value of the Neel temperature TN can be estimated from the temperature dependence of the magnetic hyperfine field at iron nuclei Hhf (Figure 8), and at ambient pressure the obtained value for BNFS is TN = 27.2(1) K. Under the applied pressure, the temperature evolution of the Mössbauer spectra does not changed essentially with increasing pressure from ambient to 17 GPa (Figure 7), while the TN value slightly increases to about 32.0 K. However, at pressures above 18 GPa, the temperature evolution of  Obviously, the appearance of a new magnetic phase with high value of TN is associated with a structural transition at pressure of 17.5 GPa, which was observed according to XRD and Raman spectroscopy studies. At this transition, Fe cations can change the local oxygen arrangement and/or redistribute between tetrahedral and octahedral oxygen sites.
At ambient conditions, iron ions in BNFS occupy 3f oxygen tetrahedra (Figure 1). The local nearest neighbors of Fe 3+ are Si 4+ and Nb 5+ , which occupy the tetrahedral 2d sites and octahedral 1a sites, respectively (Figure 1). At high pressures, redistribution of Fe 3+ ions can occur either between two types of tetrahedral 3f and 2d sites in the (ab) plane or/and between tetrahedral 3f and octahedral In particular, when iron ions partially occupy the 2d tetrahedral sites, replacing Si, a very strong magnetic interaction can appear between the Fe(3f ) and Fe(2d) ions in the (ab) plane, since the Fe(3f )-O2(6g)-Fe(2d) bond distances and the bond angle are very effective for strong superexchange interaction [10,20]. In addition, under high pressure, Fe ions can partially be redistributed between tetrahedral 3f and octahedral 1a sites in the nearest layers along the c axis ( Figure 1). This will initiate the Fe(3f )-O-Fe(1a) superexchange interaction.
The high pressure XRD studies of BNFS revealed a drastic decrease in the lattice parameters a and c during the structural transition at a pressure of about 17.5 GPa (Figure 3). A decrease in the c parameter should substantially increase the exchange interaction between Fe ions in adjacent (ab) planes, leading to a further increase in the Neel point.
On the other hand, the applied pressure can initiate the displacement of oxygen atoms around the Fe ions. Our recent X-ray diffraction studies of the single crystal established two modifications of crystal structures of BNFS, which are stable in the pressure ranges of 3.5-17.0 GPa and 17.5-32.5 GPa [19]. At pressures above 3.2 GPa, BNFS undergoes a continuous phase transition from the P321 phase into an intermediate structure with space group P3. The creation of the polar P3 phase in BNFS leads to the appearance of ferroelectric properties, and such a crystal can be considered as the pressure-induced multiferroic.
A smooth decrease in the Fe-O5 distance during this transition results in the addition of a fifth oxygen to the environment of the iron ion. Figure 9 shows   ( Figure 2d). This new modification can be considered as a perovskite-like structure [19]. In this case, a direct bond Fe-O-Fe is formed between Fe atoms in the nearest (ab) planes, and each Fe atom in the structure acquires the octahedral coordination of oxygen atoms (Figure 9). The appearance of new direct Fe-O bonds leads to a strong increase in the values of the superexchange interactions between Fe 3+ cations that can result in growing of the Neel temperature

Spin Crossover and Magnetic Properties of BNFS at Pressures above 45 GPa
The appearance of fragments of a crystalline structure with iron ions in the octahedral oxygen sites was further supported by the Mössbauer spectroscopy studies of BFNS at pressures above 45 GPa. Figure 10 demonstrates the temperature evolution of the Mössbauer SMS spectra at pressures of 52, 64 and 69 GPa, which are above the pressure of the third transition observed in BFNS at about 42 GPa by optical absorption and XRD studies [20,21].
At the lowest temperature of 3.0-3.9 K, the SMS spectra of BNFS consist of two sets of the magnetically split lines with different values of the magnetic hyperfine fields Hhf at the iron nuclei. The first magnetic component with Hhf = 42 T is typical of Fe 3+ ions in the high-spin state (3d 5 , HS, S = 5/2) in tetrahedral oxygen sites as was observed at ambient and low pressures in the BNFS sample. The second magnetic component with the Hhf value of about 8-9 T corresponds to the low-spin Fe 3+ ions (LS, S = 1/2). The second structural transition at a pressure of about 17.5 GPa leads to the transformation of the crystalline structure with an increase in symmetry to the sp. gr. P62m (Figure 2d). This new modification can be considered as a perovskite-like structure [19]. In this case, a direct bond Fe-O-Fe is formed between Fe atoms in the nearest (ab) planes, and each Fe atom in the structure acquires the octahedral coordination of oxygen atoms (Figure 9). The appearance of new direct Fe-O bonds leads to a strong increase in the values of the superexchange interactions between Fe 3+ cations that can result in growing of the Neel temperature

Spin Crossover and Magnetic Properties of BNFS at Pressures above 45 GPa
The appearance of fragments of a crystalline structure with iron ions in the octahedral oxygen sites was further supported by the Mössbauer spectroscopy studies of BFNS at pressures above 45 GPa. Figure 10 demonstrates the temperature evolution of the Mössbauer SMS spectra at pressures of 52, 64 and 69 GPa, which are above the pressure of the third transition observed in BFNS at about 42 GPa by optical absorption and XRD studies [20,21]. Thus, we can conclude that the magnetic component with a low value of Hhf (typical of the LS state of Fe 3+ ) corresponds to iron ions in the octahedral sites of BNFS in the high-pressure phase. Further support of the occurrence of the LS state of Fe 3+ follows from the values of the isomer shift δ in the Mössbauer spectra at high pressures ( Figure 11). The δ value of the LS phase is temperature dependent and decreases from about 0.2 to 0.0 mm/s with increasing temperature from 3.5 to 295 K ( Figure 11). Meanwhile, the δ value of the HS phase is about 0.42-0.45 mm/s at the lowest temperature, and only slightly decreases with a temperature rise in accordance with the behavior of the second order Doppler shift. At the lowest temperature of 3.0-3.9 K, the SMS spectra of BNFS consist of two sets of the magnetically split lines with different values of the magnetic hyperfine fields H hf at the iron nuclei. The first magnetic component with H hf = 42 T is typical of Fe 3+ ions in the high-spin state (3d 5 , HS, S = 5/2) in tetrahedral oxygen sites as was observed at ambient and low pressures in the BNFS sample. The second magnetic component with the H hf value of about 8-9 T corresponds to the low-spin Fe 3+ ions (LS, S = 1/2).
As was shown in Ref. [17,22], a low spin state of Fe 3+ ions cannot be created in the tetrahedral oxygen sites at such pressures, since the energy of the LS term is much higher than the energy of the HS term [22]. A theoretical consideration of the possible spin crossover HS (S = 5/2) → LS (S = 1/2) induced by high pressure in a similar langasite compound Ba 3 TaFe 3 Si 2 O 14 [17] predicted a much higher pressure value of the spin-crossover transition for the tetrahedral iron sites (about 800 GPa) compared with the octahedral iron sites (about 70 GPa).
Thus, we can conclude that the magnetic component with a low value of H hf (typical of the LS state of Fe 3+ ) corresponds to iron ions in the octahedral sites of BNFS in the high-pressure phase. Further support of the occurrence of the LS state of Fe 3+ follows from the values of the isomer shift δ in the Mössbauer spectra at high pressures ( Figure 11). The δ value of the LS phase is temperature dependent and decreases from about 0.2 to 0.0 mm/s with increasing temperature from 3.5 to 295 K ( Figure 11). Meanwhile, the δ value of the HS phase is about 0.42-0.45 mm/s at the lowest temperature, and only slightly decreases with a temperature rise in accordance with the behavior of the second order Doppler shift. In addition, a very high value of the quadrupole splitting parameter Δ of about 1.7 mm/s, revealed in Mössbauer spectra at P > 50 GPa, is a characteristic of the LS state of Fe 3+ ions. Moreover, the reduction of the optical gap Eg observed in BNFS down to a value of 0.7 eV, typical of semiconductors, is also a signature of the HS-LS crossover in iron oxides [21].

Discussion
Now, several very interesting conclusions about the magnetic behaviour of this compound can be obtained from the temperature evolution of the hyperfine parameters of the Mössbauer spectra.
1. First of all, from the area of the Mössbauer lines we can estimate the volume fraction of iron ions in the LS and HS states. In fact, this corresponds to the fraction of octahedral and tetrahedral sites occupied by iron ions in the high-pressure phases of BNFS at P > 52 GPa. Below, we will call them HS and LS sublattices.
2. From the temperature dependence of the magnetic hyperfine field Hhf, the values of magnetic ordering temperatures (Neel points) for iron ions in the high-spin and low-spin states can be obtained.
3. Specific magnetic properties of the material, which are due to interactions between iron ions in the HS (tetrahedral) and LS (octahedral) sublattices can be discovered. Figure 12 shows the temperature dependence of the magnetic fields Hhf in a BNFS sample at pressure of 51.8, 64.0 and 69.0 GPa. At highest pressures (64.0 and 69.0 GPa), the field Hhf in the HS sublattice gradually decreases from about 41 T to zero with increasing temperature from 3.5 to 22.0 K. In the LS sublattice, the field Hhf value is practically independent of temperature, remaining at the level of about 8.5 T, and drastically drops to zero at about 22.0 K ( Figure 12). Remarkably, that both HS and LS sublattices transit to a paramagnetic state at the same temperature, which implies a magnetic coupling and exchange interaction between these sublattices. Obviously, the magnetic transition temperature can be considered as the Neel point of the LS sublattice TN = (22.0 ± 1.0) K. In addition, a very high value of the quadrupole splitting parameter ∆ of about 1.7 mm/s, revealed in Mössbauer spectra at P > 50 GPa, is a characteristic of the LS state of Fe 3+ ions. Moreover, the reduction of the optical gap Eg observed in BNFS down to a value of 0.7 eV, typical of semiconductors, is also a signature of the HS-LS crossover in iron oxides [21].

Discussion
Now, several very interesting conclusions about the magnetic behaviour of this compound can be obtained from the temperature evolution of the hyperfine parameters of the Mössbauer spectra.
1. First of all, from the area of the Mössbauer lines we can estimate the volume fraction of iron ions in the LS and HS states. In fact, this corresponds to the fraction of octahedral and tetrahedral sites occupied by iron ions in the high-pressure phases of BNFS at P > 52 GPa. Below, we will call them HS and LS sublattices.
2. From the temperature dependence of the magnetic hyperfine field H hf , the values of magnetic ordering temperatures (Neel points) for iron ions in the high-spin and low-spin states can be obtained.
3. Specific magnetic properties of the material, which are due to interactions between iron ions in the HS (tetrahedral) and LS (octahedral) sublattices can be discovered. Figure 12 shows the temperature dependence of the magnetic fields H hf in a BNFS sample at pressure of 51.8, 64.0 and 69.0 GPa. At highest pressures (64.0 and 69.0 GPa), the field H hf in the HS sublattice gradually decreases from about 41 T to zero with increasing temperature from 3.5 to 22.0 K. In the LS sublattice, the field H hf value is practically independent of temperature, remaining at the level of about 8.5 T, and drastically drops to zero at about 22.0 K ( Figure 12). Remarkably, that both HS and LS sublattices transit to a paramagnetic state at the same temperature, which implies a magnetic coupling and exchange interaction between these sublattices. Obviously, the magnetic transition temperature can be considered as the Neel point of the LS sublattice T N = (22.0 ± 1.0) K. This analysis shows that the pressure value of 52 GPa can be considered as the onset point of the HS → LS transition in the Fe octahedral sites of the high-pressure phase of BNFS. This value is very similar to that found previously in other iron oxides with garnet (YIG), perovskite-like and orthorhombic crystal structures in such compounds as RFeO3, BiFeO3, Fe2O3, FeBO3 [18]. The magnetic correlation and the interaction between the LS-octahedral and HS-tetrahedral sublattices in BNFS are similar to the behavior of two iron sublattices in yttrium iron garnet Y3Fe5O12 [23]. In this garnet Fe 3+ ions occupy both octahedral [a] and tetrahedral (d) sites in a ratio of 40/60, that is {Y3}[Fe2](Fe3)O12. As was observed in Ref. [23], under a pressure of about 50 GPa, the HS → LS crossover occurs in Fe ions of the octahedral sites of the garnet, leading to magnetic collapse in both sublattices.
The ratio of LS/HS = 40/60 in our langasite BNFS is the same as the ratio of occupation of [a] and (d) sites in the garnet. It can be supposed that some clusters with a garnet-like structure appear in BNFS at pressures above 42 GPa, where the structural and optical anomaly was detected by X-ray diffraction and optical absorption measurements [21]. The character of the magnetic interaction and the exchange coupling between the octahedral and tetrahedral sublattices in this langasite Ba3NbFe3Si2O14 at pressures above 52 GPa is similar to the behavior of garnet Y3Fe5O12 at high pressure.
Based on the structural, magnetic and electronic properties of Ba3NbFe3Si2O14 obtained, a magnetic phase P-T diagram was constructed ( Figure 13). It demonstrates the P-T regions of different magnetic and electronic phases and their correlation with the crystal structure at extreme conditions of high pressures and low temperatures. Since the hyperfine field H hf is directly proportional to the iron magnetic moment, the temperature behaviour of H hf in the LS sublattices is characteristic of a low-dimensional Ising-type magnetic system.
As follows from the area of Mössbauer resonance lines, the fractions of the HS and LS components at pressures 64 and 69 GPa are in a ratio of about 60/40. However, at a pressure of 51.8 GPa this ratio is about 80/20. This may indicate that not all Fe ions in octahedral sites transit to the LS state at this pressure, which may be due to the pressure gradient in the high-pressure cell.
Meanwhile, the magnetic properties of the BNFS sample at P = 51.8 GPa differ from those at pressures of 64 and 69 GPa. At higher pressures (64 and 69 GPa), the magnetic ordering in the HS and LS sublattices is simultaneously collapsed at the same temperature of about 22 K.
On the other hand, at a pressure of 51.8 GPa, the magnetic correlations in the LS sublattice disappear at a temperature of about 20 K, whereas, the HS sublattice transforms to the paramagnetic state at a much higher temperature of about 58 K ( Figure 12). Most probably, at a pressure of 51.8 GPa, not all Fe ions in the octahedral sites pass to the LS state (only half of them: compare 40% and 20%). The remaining part of the HS iron ions in the octahedral sites interacts with the HS iron ions in the tetrahedral sites leading to a relatively high magnetic ordering temperature of about 58 K.
As shown above, at pressures in the range 18-45 GPa, when all the Fe ions in the octahedral sites were in the HS state, the Neel temperature of the HS sublattice was about 115 K (Figure 8). At 51.8 GPa, when half of the octahedral HS Fe ions transferred to the LS state, the Neel temperature decreases from 115 to 58 K. This analysis shows that the pressure value of 52 GPa can be considered as the onset point of the HS → LS transition in the Fe octahedral sites of the high-pressure phase of BNFS. This value is very similar to that found previously in other iron oxides with garnet (YIG), perovskite-like and orthorhombic crystal structures in such compounds as RFeO 3 , BiFeO 3 , Fe 2 O 3 , FeBO 3 [18]. The magnetic correlation and the interaction between the LS-octahedral and HS-tetrahedral sublattices in BNFS are similar to the behavior of two iron sublattices in yttrium iron garnet Y 3 Fe 5 O 12 [23]. In this garnet Fe 3+ ions occupy both octahedral [a] and tetrahedral (d) sites in a ratio of 40/60, that is {Y 3 }[Fe 2 ](Fe 3 )O 12 . As was observed in Ref. [23], under a pressure of about 50 GPa, the HS → LS crossover occurs in Fe ions of the octahedral sites of the garnet, leading to magnetic collapse in both sublattices.
The ratio of LS/HS = 40/60 in our langasite BNFS is the same as the ratio of occupation of [a] and (d) sites in the garnet. It can be supposed that some clusters with a garnet-like structure appear in BNFS at pressures above 42 GPa, where the structural and optical anomaly was detected by X-ray diffraction and optical absorption measurements [21]. The character of the magnetic interaction and the exchange coupling between the octahedral and tetrahedral sublattices in this langasite Ba 3 NbFe 3 Si 2 O 14 at pressures above 52 GPa is similar to the behavior of garnet Y 3 Fe 5 O 12 at high pressure.
Based on the structural, magnetic and electronic properties of Ba 3 NbFe 3 Si 2 O 14 obtained, a magnetic phase P-T diagram was constructed ( Figure 13). It demonstrates the P-T regions of different magnetic and electronic phases and their correlation with the crystal structure at extreme conditions of high pressures and low temperatures.

Materials and Methods
Polycrystalline samples of Ba3NbFe3Si2O14 were synthesized by a ceramic synthesis technology from precursor oxides and salts [9]. For Mössbauer studies, the iron used in the sample synthesis was enriched with 57 Fe isotope to 50%.
High pressure experiments were performed with diamond anvil cells (DAC). Polycrystalline compact samples were squeezed between diamonds and placed in the working volume of the rhenium gasket in the DAC. The cullet diameter of diamond anvils was about 200 μm, and the hole diameter in the gasket was about 80 μm. Helium and NaCl were used as the quasihydrostatic pressure-transmitting medium. The pressure was measured by the shift of the ruby fluorescence line [24] Several ruby chips were placed at different distances from the center of the gasket hole to evaluate the pressure gradient in the cell.

Materials and Methods
Polycrystalline samples of Ba 3 NbFe 3 Si 2 O 14 were synthesized by a ceramic synthesis technology from precursor oxides and salts [9]. For Mössbauer studies, the iron used in the sample synthesis was enriched with 57 Fe isotope to 50%.
High pressure experiments were performed with diamond anvil cells (DAC). Polycrystalline compact samples were squeezed between diamonds and placed in the working volume of the rhenium gasket in the DAC. The cullet diameter of diamond anvils was about 200 µm, and the hole diameter in the gasket was about 80 µm. Helium and NaCl were used as the quasihydrostatic pressure-transmitting medium. The pressure was measured by the shift of the ruby fluorescence line [24] Several ruby chips were placed at different distances from the center of the gasket hole to evaluate the pressure gradient in the cell.
X-ray diffraction patterns of Ba 3 Nb 57 Fe 3 Si 2 O 14 at high pressures up to 55 GPa were recorded using P02.2 Extreme Condition Beamline [25] (DESY, PETRA III, Hamburg, Germany). The synchrotron radiation with the wavelength λ = 0.289886 Å and spot size on the sample of 2 × 2.2 µm in DAC was used. The two-dimensional Perkin Elmer (XRD 1621) detector was set at a distance of 462.92 mm from the sample. The refinement of the unit cell parameters of the high-pressure phases was carried out as a result of a full-profile analysis by the Le Bail method [26] in the JANA2006 software [27].
Raman spectra at high pressures up to 25 GPa were obtained at room temperature using a Princeton Instruments Acton SP2500 monochromator/spectrograph (Teledyne Princeton Instruments, Trenton, NJ, USA) equipped with Spec-10 system with a nitrogen-cooled CCD detector. A krypton laser with a 647.1 nm line was used as an excitation source for the Raman signal.
The magnetic and electronic properties of BNFS at high pressures up to 70 GPa and in the temperature range from 3.0 to 295 K for each pressure point were studied by the synchrotron Mössbauer source technique (SMS) [28,29] in the European Synchrotron Radiation Facility Center (ESRF, Grenoble, France). Mössbauer absorption spectra were measured at the Nuclear Resonance beamline ID18. For the model processing of Mössbauer spectra, we used the MossA program specially developed for the analysis of synchrotron Mössbauer spectra (the MossA software package [30]). When approximating the spectra, the total transmission integral was calculated. The source line was approximated by the squared Lorentzian distribution, taking into account the peculiarities of synchrotron Mössbauer radiation [28], and for the absorber line this was done by the conventional Lorentzian one. The source line width was estimated from an experiment with a thin standard absorber of K 2 Mg 57 Fe(CN) 6 with a single line of known width. During the experiment, the source linewidth was monitored and evaluated before and after each measurement of the Mössbauer spectrum on the BNFS sample. The model used the following constraints: (1) At pressures above 50 GPa, for temperatures T < T N , the line width (FWHM) for the LS and HS magnetically split components was assumed to be the same and varied.
(3) Based on the fit of the spectrum at the lowest temperature of 3 K, the ratio of fractions of the HS and LS components was fixed in the entire temperature range. At pressures 64 and 69 GPa, it was HS: LS = 60:40, and at 51 GPa it was HS: LS = 80:20. At temperatures above T N , the spectra were fitted with two doublets (for the HS and LS components) with the corresponding area ratios.
For comparison, Figure 14 shows the BNFS Mössbauer spectra at 3.9 and 48 K for comparison on the same scale. It is clearly seen that the line width in doublets (at 48 K) is much less than the width of the magnetic spectrum at 3.9 K. Obviously, in terms of the width and asymmetry of the resonance lines, the magnetic sextet is much more suitable for fitting experimental spectra than the paramagnetic doublet. This indicates the magnetic nature of the line broadening.
with two doublets (for the HS and LS components) with the corresponding area ratios.
For comparison, Figure 14 shows the BNFS Mössbauer spectra at 3.9 and 48 K for comparison on the same scale. It is clearly seen that the line width in doublets (at 48 K) is much less than the width of the magnetic spectrum at 3.9 K. Obviously, in terms of the width and asymmetry of the resonance lines, the magnetic sextet is much more suitable for fitting experimental spectra than the paramagnetic doublet. This indicates the magnetic nature of the line broadening. Figure 14. Mössbauer spectra of BNFS at temperatures 3.9 and 48 K shown for comparison in the same scale. Obviousely, the line width in the doublets (at 48 K) is much smaller than the width of the magnetic spectrum at 3.9 K.

Conclusions
It is shown that in the langasite family Ba3NbFe3Si2O14 compound, external pressure strongly affects the crystal structure and leads to structural, magnetic and electronic transitions. At pressure above 3.2 GPa, BNFS undergoes a phase transition from the P321 phase into intermediate structure with space group P3. The creation of the polar P3 phase leads to the appearance of ferroelectric properties, and this crystal can be considered as a pressure-induced multiferroic. During the P321 → P3 transition the oxygen coordination of Fe ions gradually changes from FeO4 to FeO5. Figure 14. Mössbauer spectra of BNFS at temperatures 3.9 and 48 K shown for comparison in the same scale. Obviousely, the line width in the doublets (at 48 K) is much smaller than the width of the magnetic spectrum at 3.9 K.

Conclusions
It is shown that in the langasite family Ba 3 NbFe 3 Si 2 O 14 compound, external pressure strongly affects the crystal structure and leads to structural, magnetic and electronic transitions. At pressure above 3.2 GPa, BNFS undergoes a phase transition from the P321 phase into intermediate structure with space group P3. The creation of the polar P3 phase leads to the appearance of ferroelectric properties, and this crystal can be considered as a pressure-induced multiferroic. During the P321 → P3 transition the oxygen coordination of Fe ions gradually changes from FeO 4 to FeO 5 .
At pressures above 18 GPa, part of the iron ions passes from tetrahedral coordination to octahedral FeO 6 , and fragments with a perovskite-like structure with sp. gr. P62m appear. This entails an enhancement of exchange interactions, and the temperature of magnetic ordering in the octahedral Fe sites increases from about 30 K to 115 K.
At pressures above 45 GPa, further transformation of the structure occurs, and fragments with the coexisting FeO 4 and FeO 6 sites appear. The magnetic interaction between iron ions in these sites resembles the behavior of the octahedral and tetrahedral iron sublattices in the yttrium-iron garnet YIG. At pressures above 52 GPa, a spin crossover occurs in the Fe 3+ ions in the octahedral sites of BNFS and iron ions transit from the high-spin state S = 5/2 to the low-spin state S = 1/2. This causes a decrease in the value of the Néel point. The estimated value of the magnetic ordering temperature (T N point) for the LS phase of BNFS is about 22.0 ± 1.0 K. At higher pressures the magnetic ordering in the HS and LS sublattices collapses simultaneously at one temperature of about 22 K, which indicates a strong coupling between the FeO 4 and FeO 6 sites.