Magnetic and structure transition of Mn3-xFexO4 solid solutions under high-pressure and high-temperature conditions

Magnetic and structure transitions of Mn3–xFexO4 solid solutions under extreme conditions are clarified by neutron time-of-flight scattering diffraction and X-ray Mössbauer measurement. The ferrimagnetic-to-paramagnetic transition temperature (100 °C) of Mn2FeO4 spinel is different from the tetragonal-to-cubic structure transition temperature (180 °C). The structure transition temperature decreases with increasing pressure. The transition is not coupled with the magnetic transition. Synchrotron X-ray Mössbauer experiments have revealed the pressure effects on the distribution of Fe2+ and Fe3+ at the tetrahedral and octahedral sites in the spinel structure. Ferrimagnetic MnFe2O4 and Mn2FeO4 spinels show sextet spectral features with hyperfine structure elicited by internal magnetic fields. Cubic MnFe2O4 spinel and tetragonal Mn2FeO4 transform to high-pressure orthorhombic postspinel phase above pressures of 18.4 GPa and 14.0 GPa, respectively. The transition pressure decreases with increasing Mn content. The postspinel phase has a paramagnetic property. Mn2O10 dimers of two octahedra are linked via common edge in three dimentional direction. The occupancy of Fe2+ in the tatrahedral site is decreased with increasig pressure, indicating more oredered structure. Consequently, the inverse parameter of the spinel structure is increased with increasing pressure. The magnetic structure refinements clarify the paramagnetic and ferrimagnetic structure of MnFe2O4 and Mn2FeO4 spinel as a function of pressure. The magnetic moment is ordered between A and B sites with the anti-parallel distribution along the b axis. The nuclear tetragonal structure (aN, aN, cN) has the ferrimagnetic structure but the orthorhombic magnetic structure has the ferrimagnetic structure with the lattice constants (aM, bM, cM). The magnetic moment is ordered between A and B sites with the anti-parallel distribution along the bM axis.


Introduction
Important information about plate tectonics and geomagnetic reversals has been derived from measurements of remnant magnetization of spinels in basalts. Spinels are also the most fundamental magnetic compounds in industrial applications. Their magnetic properties, charge transfer and electrical resistivity changing under high-pressure conditions are significant research issues of intensive studies. The iron bearing spinels are the most fundamental magnetic compounds in industrial applications (Fei et al. 1999;Lavina et al. 1994;Jackson et al. 2005;Lin et al. 2013).
Structure analyses of the solid solution between Fe 3 O 4 and Mn 3 O 4 were conducted using thermal neutron diffraction by Hasting et al. (1956); Murasik et al. (1964). They are composed of mixed-charge cations in the tetrahedral (A) and octahedral (B) sites in AB 2 O 4 spinels. Iron-rich members of the Mn 3-x Fe x O 4 spinels have a magnetic structure of two-dimensional triangular Yafet-Kittel spin configuration reported by Yafet et al. (1952); Boucher et al. (1971); Gutzmer et al. (1995). Disorder of the cations in two sites has a great influence on magnetic properties such as saturation magnetization, exchange couplings and ferrimagnetic ordering temperatures.
Magnetite undergoes a phase transition to a high-pressure (HP) form, called h-Fe 3 O 4 . The stability field and the crystal structure of the HP magnetite, first, show a CaTi 2 O 4 -type structure with space group Bbmm (Cmcm) above 25 GPa, and second, defined to be CaMn 2 O 4 -type structure (Pbcm). Several experiments have been devoted to magnetite under high-pressure conditions by X-ray powder diffraction (Haavik et al. 2000;Kuriki et al. 2002;Dubrobinsky et al. 2003;Rozenberg et al. 2007;Reichmann et al., 2004). The Verwey transition temperature of Fe 3 O 4 decreases non-linearly with increasing pressure (Todo et al. 2001). A big change in resistivity at the Verwey transition temperature was observed at pressure below 6.5 GPa. The pressure dependence of electrical resistivity of magnetite was measured under 100 GPa (Muramatsu et al. 2016 (Fei et al. 1999;Ye et al. 2015;Yamanaka et al 2022;Paris et al. 1992). The present neutron diffraction and X-ray Mössbauer spectroscopy shed light on the magnetic and structure change under extreme conditions. Mn 3-x Fe x O 4 spinel solid solutions are composed of mixed charged cations of Mn 2+ , Mn 3+ , Fe 2+ and Fe 3+ in the A and B sites in the AB 2 O 4 spinel structure. In the Mn 3-x Fe x O 4 solid solution, the spinel phase changes from cubic-to-tetragonal structure with increasing Mn content at ambient pressure. (Van Hook et al., 1958;McMurdie et al. 1950;Wickham 1969, Yamanaka et al. 1973. Numerous investigations have been conducted on the temperature dependence of the cation distribution in Mn 3-x Fe x O 4 spinel solid solution. (Hasting 1956;Rieck et al. 1966). Their phase stabilities and structures under extreme conditions have been studied. (Xu et al. 2004;Kirby et al., 1996;Yamanaka et al. 2001). The Curie temperature of Mn 3 O 4 of about -250 °C was reported by Boucher et al. (1971);Ole ś, et al. (1976); Chardon et al. (1986).
In the present experiment, magnetic and structure studies of MnFe 2 O 4 and Mn 2 FeO 4 were conducted using neutron time-of-flight scattering diffraction under high-pressure condition at PLANET J-PARC (Hattori et al. 2015). Our previous Raman spectroscopic studies and synchrotron X-ray powder diffraction studies of various postspinels have proposed orthorhombic phases of CaFe 2 O 4 -type (Pmma), CaTi 2 O 4 -type (Cmcm) and CaMn 2 O 4 -type (Pbcm) structures as high-pressure polymorphs of different spinels (Yamanaka et al. 2008). Transformations of the oxide spinels are summarized in Table 1. These phases further transform to a new phase by martensitic transformation to a maximal isotropic subgroup structure.
X-ray structure analysis of Mn 3-x Fe x O 4 causes an ambiguity, because X-ray atomic scattering factors of Fe (26) and Mn (25) are extremely similar. Neutron diffraction, however, has an effective advantage for the precise diffraction studies of Mn 3-x Fe x O 4 , because of the big difference in the coherent scattering lengths of Mn (-3.73 fm) and Fe (9.54 fm). X-ray powder diffraction study at high pressures up to 40 GPa has been also performed by synchrotron radiation at Photon Factory using symmetric diamond anvil pressure cell (DAC) in this experiment.
Mössbauer spectroscopy (MS) study is the effective method to investigate the iron elctronic properties at high pressure. MS allows distingushing between ferric and ferrous ions. High and low spin states of Fe and their relative abundance in substances are clarified. MS studies of high-pressure Fe 3 O 4 (h-Fe 3 O 4 ) at ambient temperature have been carried out by Pasternak et al. (1994). The cation distributions in spinels at ambient conditions were reported by Mössbauer experiments and NMR studies (Yasuoka et al. 1967;Singh et al. 1981). Hyperfine-structure spectra changes of ferrites were reported as a function of pressure (Kobayashi et al. (2006).
The pressure dependence of the site occupancy and their magnetic structures were determined. In the present study, neutron diffraction at high pressure and high temperature has been conducted. The precise cation distribution has been elucidated by use of the significant difference in coherent scattering lengths between Mn and Fe. Furthermore. Fe 2+ and Fe 3+ distributions have been clarified by synchrotron X-ray Mössbauer experiments at increasing pressure. We also investigated the electrical resistivity measurement with increasing pressure up to 40 GPa to elucidate the enhancement of electrical conductivity from semiconductor to metal in Mn 3-x Fe x O 4 spinel and postspinel with increasing pressure (Yamanaka et al. 2022). The observed enhancement of electrical resistivity with increasing pressure is shown in Supplement file 1.

Experiment
Powder samples of MnFe 2 O 4 and Mn 2 FeO 4 were prepared by solid-solid reaction at ambient pressure. To prepare the samples used for X-ray Mössbauer experiment, isotopeenriched samples with 30% 57 Fe content were prepared. The sample preparation is detailed in the supplement file 2.
Neutron diffraction experiment was executed at BL-11 J-PARC (Japan Proton Accelerator Research Complex, Japan Atomic Energy Agency) under high-pressure using spallation neutron time-of-flight (TOF) facility. We used a Paris-Edinburgh (PE) press (VX4) for the experiments at pressures up to 40 GPa at room temperature (Hattori et al. 2019), and also a large-volume sixaxis multi-anvil press ATSUHIME at PLANET J-PARC (Sano-Furukawa et al. 2014) for the experiments at pressures to 10 GPa and high temperatures up to 2000 ˚C. Incident neutron wavelength is 0.3 Å-5.8 Å and beam size is 15 mm × 15 mm at maximum. We performed Rietveld analyses of neutron diffraction data to refine the nuclear structure and magnetic structure. The analysis is conducted using the program GSAS (Larson et al. 1994;Toby 2001). The integrated intensity I o is produced by combination of magnetic scattering factor F M (h) and nuclear scattering factor F N (h): where s: scale factor, A: absorption, L: Lorentz factor and m: multiplicity.
The nuclear structure factor F N (h) for neutron diffraction is expressed by where T j is the temperature factor of j atom. γ indicates the γ-factor of the nuclear magneton.
And magnetic scattering factor F M (h) is where µ is magnetic moment. The detailed derivation of the neutron diffraction refinement is presented in the Supplement file 3.
Neutron diffraction experiments cannot provide precise information about the distribution of Fe 2+ and Fe 3+ between the A and B sites in the Mn-ferrite spinel and the M1 and M2 sites of the postspinel structure under high pressure. We measured the synchrotron X-ray Mössbauer spectra of the Mn x Fe 3-x O 4 solid solution at SPring-8 BL-10XU (Hirao et al. 2020) under high pressure using micro-beam with the wavelength of 14.4 keV and diamond anvil cell (DAC). A symmetric diamond anvil cell was used to generate high pressure. Ne gas was used as a pressure transmitting media. Rh gasket of 200 µm thick was preindented to 80 µm. High-pressure measurement was performed by ruby-fluorescence scale.
We used the program MossA (Prescher et al. 2012) for the analysis of our Mössbauer spectra and determined the cation distribution as a function of pressure. Deviations from Lorentzian profile shape may have to be fitted using Voigtian (a convolution of Gaussian and Lorentzian functions). The full width half maxim (FWHM) of spectrum is related to the positional disorder of cations.
The isomer shift is referred to the spectrum from zero velocity of the 57 Fe spectrum in Fe 2 O 3 . The peak positions of the spectra were detected within an error of less than ± 0.05 mm/ sec. The internal magnetic fields of the hyperfine structure (1) (3) ◻e 2∕ 2m e c 2 = 2.696(fm), spectra were determined with the reference of 26.26 T (330 kOe) of the 57 Fe in Fe 2 O 3 spectrum.

Result and discussion
Pressure effect on the cooperative Jahn-Teller distortion of Mn 2 FeO 4 spinel phase Mn 3-x Fe x O 4 spinel structure transforms to high-pressure phase of orthorhombic CaMn 2 O 4 -type postspinel structure. Present neutron diffraction study reveals the phase diagram of Mn 3-x Fe x O 4 under high pressure at ambient temperature, which is presented in Fig. 1. Structure transition from tetragonal to cubic of Mn 2 FeO 4 spinel under pressure at 20 °C is shown as a function of normalized unit-cell volume. Mn 2 FeO 4 and MnFe 2 O 4 spinel transform to postspinel at different pressures at 14.0 GPa and 18.4 GPa, respectively.
Present neutron diffraction patterns of Mn 2 FeO 4 at 2.2 GPa in the heating experiment disclose the tetragonal-tocubic transition temperature at 180 °C. The cooling experiments show the back transformation from cubic structure to the tetragonal structure at 140 °C. The tetragonal-to-cubic transition is reversible and shows hysteresis, as shown in Fig. 2.
Mn 3+ (3d 4 ) prefers octahedral configuration in the strong ligand field. In the Mn 3-x Fe x O 4 solid solution, Mnrich phases present lattice distortion due to the cooperative Jahn-Teller (JT) effects. At ambient pressure, Mn 3 O 4 transforms from tetragonal (I4 1 /amd z = 4) to cubic (Fd_3m z = 8) Fig. 1 Phase diagram of Mn 3-x Fe x O 4 under high pressure at ambient temperature is presented by powder neutron diffraction study. Symbol of red stars indicate the X-ray Mössbauer experiment with increasing pressure in the present study at SPring-8. Plotted data with variable chemical compositions at ambient conditions are from Wickham et al. (1969) and Yamanaka ey al. (1973) at 1170 °C (McMurdie et al. 1950) with vanishing JT effect. The phase has an elongated structure along the c-axis with c/a > 1.
The tetragonal-to-cubic transition temperature of Mn 2 FeO 4 is 160 °C at 3 GPa and 180 ℃ at1GPa by the temperature dependence of c/a. These experiments prove the transition temperature decreases with increasing pressure. P-T boundary between the tetragonal and cubic phases has a negative slope. The distortion of the elongation along the c-axis disappears in the cubic Mn 2 FeO 4 . The lattice distortion may be reduced with increasing temperature and finally the lattice constant ratio becomes c/a = 1. resulting in the transformation to the cubic symmetry (c = a).
The two-phase mixtures with postspinel are found in the transition region (Fig. 3). The normalized unit-cell volumes of the three phases of cubic, tetragonal spinel and orthorhombic postspinel are shown in the figure. Both spinels have two-phase mixture regions with high-pressure postspinel phase.
The present transition case from tetragonal-to-cubic phase of Mn 2 FeO 4 is extremely rare for the JT transition under compression. The following spinels: Fe 2 TiO 4 (Yamanaka et al. 2013 (Åsbrink et al., 1988), transitions from cubic-to-tetragonal spinel show the with increasing pressure. Many of them have the tetragonal distortion with flattened octahedral distortion along the c-axis (c/a < 1). The octahedral site of the tetragonal phase of Mn 2 FeO 4 is elongated along the c-axis and the lattice constant ratio c/a > 1 according to the crystal field stabilization energy (CFSE). Topological presentation is developed from the JT distortion. Pressure dependence of cooperative JT distortion in Mn 2 FeO 4 is caused by localized orbital electronic states of Mn 3+ under extreme conditions.
The result of the structure refinements of cubic MnFe 2 O 4 and tetragonal Mn 2 FeO 4 are presented in Supplement Table 1 and Supplement Table 2. The site occupancies are also presented in these tables. Their bond distances of A-O Fig. 2 Jahn-Teller effect degradation and appearance in Mn 2 FeO 4 transition between tetragonal and cubic spinel spinels are shown. Neutron diffraction experiment of Mn 2 FeO 4 at 2.2 GPa with increasing temperature confirms the tetragonal-to-cubic transition temperature at 180 °C. In the cooling experiments the cubic structure transforms back to the tetragonal structure at 140 °C. The tetragonal-to-cubic transition is reversible and shows a hysteresis of the transition The compressions of the inter-nucleus distances A-A, A-B and B-B are strongly affected to the supper exchange. The B-B distance is much smaller than the other two A-A and A-B distances (Fig. 4). Then, the super-exchange between the B and the adjacent B cation is easier to gain extremely low resistivity. With compression, B-B shorter distance promotes a higher conduction. The B-B superexchange model in the corner sharing octahedra is shown in Fig. 5. Super exchange for the electron hopping between Fe 2+ and Fe 3+ ion is more possible.

Cation ordering
MnFe 2 O 4 and Mn 2 FeO 4 compounds are composed of the mixed-charge elements and their ionic radii are similar. According to the effective ionic radii (Shannon et al. 1969) and cation site preference (Duniz et al. 1957(Duniz et al. , 1960, positional change of these cations may be possible at high pressure. The distortions of the tetrahedral and octahedral sites make cation exchange possible by compression. The cation exchange is common at high temperature and thermal atomic vibration is a strong mechanism for the cation positional change. . At high pressure, just before the transition pressures of the respective samples, they more closely adopt the normal spinel structure with i = 1. The inverse parameter of MnFe 2 O 4 is presented as a function of pressure in Fig. 6.  Mössbauer resonance experiment also shows Fe 2+ and Fe 3+ positional change in the A and B site at high pressure. Mössbauer spectra indicate two hyperfine structures of sextet patterns indicating ferrimagnetic moment of the A and B sites of MnFe 2 O 4 cubic spinel at 0.25 GPa and 300 K in Fig. 7. The spectrum of the A site is assigned to Fe 3+ in the tetrahedral site. The spectrum of the octahedral site (B) site is assigned to mixture of Fe 3+ and Fe 2+ . These Fe 3+ and Fe 2+ cations in the B site are not individually separated because of the electron hopping between these cations.
Mössbauer spectra of MnFe 2 O 4 cubic spinel at 10.0 GPa and 300 K are shown in Fig. 8 and they indicate two hyperfine structures of sextet patterns indicating ferrimagnetic moment of the A and B sites, which is a very similar spectra of the spectra in Fig. 7. Internal magnetic field observed from the both sextets at A and B sites are not changed between two pressures, 0.25 and 10.0 GPa.
Under further compression at 17.0 GPa 300 K shown in Fig. 9, Mössbauer spectrum of MnFe 2 O 4 cubic ferrimagnetic phase shows one doublet indicates the Fe 3+ spectrum at the A site and one sextet shows the Fe 2+ and Fe 3+ spectrum at the B site. The former spectrum proves neither hyperfine structure and nor internal magnetic field. The spectrum of The spectra indicate two hyperfine structures of sextet patterns indicating ferrimagnetic moment of the A and B sites. The spectrum of the A site is assigned to Fe 3+ in the tetrahedral site. The spectrum of the B site is assigned to mixture of Fe 3+ and Fe 2+ in the octahedral site. Intensity spectra ratio of the A and B site is presented  Mössbauer spectrum of MnFe 2 O 4 cubic ferrimagnetic phase at 17.0 GPa 300 K. One doublet indicates the Fe 3+ spectrum at the tetrahedral site One sextet shows the Fe 2+ and Fe 3+ spectrum at the octahedral site are shown. The former spectrum proves neither hyperfine structure and nor internal magnetic field the hyperfine structure at the A site is not observed but the spectrum at the B site shows the internal magnetic field.
Neutron diffraction study of MnFe 2 O 4 and Mn 2 FeO 4 spinels indicates the ferrimagnetic cubic spinel structure at pressures up to 17.4 GPa and 14.0 GPa, respectively. Mössbauer spectra do not show any remarkable change up to 12.5 GPa. However, at 17.0 GPa the spectrum changes from sextet to doublet, proving neither hyperfine structure and nor internal magnetic field and magnetic moment of magnetic ions disappears, as shown in Fig. 9. Peak width of the sextet spectrum becomes broad at 17.0 GPa. The positional disorder of magnetic ions in the octahedral (B) site induces the peak broadening of the large FWHM in the spectrum.
Mössbauer spectra of the orthorhombic postspinel Mn 2 FeO 4 at 18.0 GPa and 300 K have two doublets, as shown in Fig. 10 In the Mössbauer spectra, the relative intensities of individual components possibly give a suggestion of the corresponding population. The intensities of the various peaks reflect the relative concentrations of cations. Observed site occupancies are estimated from the peak intensities of the Mössbauer spectra of MnFe 2 O 4 and Mn 2 FeO 4 at various pressures. The following data: (1) the isomer shift (δ), (2) the quadruple splitting (Δ) and (3) the magnetic hyperfine field (B hf ) are presented in Table 2. Peak intensity (Int) ratios of two or three spectra are also presented.
Two sextets of the spectra of MnFe 2 O 4 cubic spinel at pressures from 1 atm to 12.5 GPa do not show a big difference in their peak intensities in Table 2 but show a slight increase in the intensity ratio with increasing pressure. The hypothetical structure proposed from the intensity ratio of two sextet spectra of the MS experiment gives the cation distribution, which is somewhat different from the result of the neutron diffraction structure analysis.
The distortion of Mn 2 FeO 4 and MnFe 2 O 4 spinels under compression are related to their elastic properties. The compression behavior of Mn 3-x Fe x O 4 spinels can be described by third-order Birch-Murnaghan equation of state. The equation of state is given by where P is the pressure, V 0 is the reference volume, V is the deformed volume with respect to pressure,, B 0 is the bulk modulus, and B 0 ' is the derivative of the bulk modulus. The bulk modulus and its derivative are usually obtained from fits to experimental data and are defined as  Table 3.
MnFe 2 O 4 and Mn 2 FeO 4 are characterized by cation disorder and are more compressible than the end-members of the solid solution. MnFe 2 O 4 is less compressible than Mn 2 FeO 4 .

High-pressure polymorph postspinel phase
Magnetite undergoes a phase transition to a high-pressure (HP) form, called h-Fe 3 O 4 above 25 GPa and defined to be postspinel of CaMn 2 O 4 (Pbcm) structure. Postspinel is characterized by herringbone structure, shown in Fig. 11. The present X-ray Mössbauer spectra analyses and neutron diffraction experiments describe the cation distributions of Mn and Fe. The structure refinements of postspinel of Mn 2 FeO 4 at pressures up to 26.8 GPa are presented in Supplement Table 3. (The refinement of the quenched sample is also presented in the table.) The VIII M1 site volume is much larger than the VI M2 site. The VIII M1 site of Mn 2 FeO 4 and MnFe 2 O 4 postspinel is mostly occupied by (4)   Fig. 11. Mn 2 O 10 dimers of two octahedra in the structures are linked via common edges.

Magnetic structure of Mn 2 FeO 4 and MnFe 2 O 4 spinel
Present magnetic structure analysis of Mn 2 FeO 4 and MnFe 2 O 4 as a function of pressure is executed using the neutron diffraction intensity I o . Integrated intensity I o is a combination of both magnetic scattering factor |F M (h) | 2 and nuclear scattering factor |F N (h)| 2 by Eq. (1). Present Rietveld refinement based on the ferrimagnetic structure discloses the tetrahedral and octahedral symmetry of the tetragonal-tocubic transition with increasing pressure. The site symmetry 0.2 m. of the octahedral (B) site in the tetragonal symmetry of I4 1 /amd changes to the symmetry of._3m of the cubic symmetry of Fd_3m.
The diffraction peaks of 101 and 112 of tetragonal phase have a large contribution of magnetic scattering. The temperature evolution of the diffraction intensity of Mn2FeO4 at ambient pressure indicates that both peak intensities suddenly drop around 100 °C, which is displayed in Fig. 12. The magnetic transition temperature at 100 °C of ferrimagneticto-paramagnetic is different from the tetragonal-to-cubic structure transition temperature at 180 °C. The magnetic transition temperature is lower than that of the nuclear structure transition. The structure change is not coupled with magnetic transition. The isomer shift (IS), quadruple splitting (QS), relative intensity (Int) and internal magnetic field (BIF) of each site of MnFe 2 O 4 spinel are presented in the table spinel σ isomer (chemical) shift, ∆ quadruple splitting, Int intensity ratio of area ratio of two spectra. BIF hyperfine magnetic field The present magnetic refinement shown in Table 4 confirms the site occupancies at the A and B sites of Mn 2 FeO 4 postspinel under elevating pressure. Magnetic moment distribution of the spinel and postspinel structure requires the effective magnetic susceptibility of cations. Effective Bohr magneton is used from extant published data defined by previous experiments: Mn 2+ (5.92 µB), Mn 3+ (4.90 µB), Fe2+ (4.90 µB) and Fe3+ (5.92 µB) (Neel 1948). Iron-rich members of the Mn3-xFexO4 spinels have the magnetic structure of two-dimensional Yafet-Kittel triangular spin configuration. The magnetic structure of a powder sample of MnFe 2 O 4 was determined by thermal neutron diffraction (Levy 2015). Spin moments of the A and B sites of the 155.6(35) 3.266(6.71) χ 2 = 1.629 R = 0.9945

Fig. 11
Postspinel is constructed by herringbone structure of the M1 octahedra array. The dimer of octahedra is distributed in three-dimensional space. eightfold M2 cation has shared edges with M1 cation and chained in the direction of the b axis Fig. 12 Difference in the transition temperature between the magnetic (ferrimagnetic-to-paramagnetic) and structure (tetragonal-to-cubic) transition of Mn 2 FeO 4 . Magnetic transition temperature is 100 °C and structure transition temperature is 180 °C iron substitution on the magnetic property were clarified at temperatures 10 K and 295 K ( Baron et al. 1998).
The influence of iron substitution on the magnetic properties is clarified in both ordered and disordered ferrimagnetic spinel-phases. Magnetic cations of Mn and Fe are located at the crystallographically special position in the tetragonal and cubic structure. Positional parameters of these cations are variable and magnetic moments are also variable parameters besides thermal variables. The reliability factor for the refinement is enhanced by the inclusion of magnetic moment effect. Nuclear structure analysis without consideration of magnetic moment effect was not converged properly.
Several possible magnetic space groups in nine subgroups of the tetragonal spinel structure of I4 1 /amd are examined for the observed intensities. The magnetic space group of I4 1 /am'd' is the most reliable subgroup of the space group symmetry of I4 1 /amd. Rietveld refinement of Mn 2 FeO 4 at 2.2 GPa 20 ℃ tetragonal I4 1 /amd with the paramagnetic structure model is χ 2 = 10.51 and R(F2) = 0.211. We analyzed the diffraction intensities of the observed data in this study, because the quality of the data taken at high pressures in this study is not sufficient to discuss the detail of counted spins. The ferrimagnetic structure model based on the orthorhombic space group Pmma, (which is of an isomorphic subgroup of I41/amd) shows much better agreement of χ 2 = 2.157 and R(F 2 ) = 0.117. The lattice constants (a M , b M , c M ) of Mn 2 FeO 4 of the present orthorhombic ferrimagnetic structure are derived from the nuclear tetragonal structure ( a N , a N , c N ). The b M cell edge is twice larger than b N of the paramagnetic lattice, because the magnetic moment is ordered between A and B sites with the anti-parallel distribution along the b M axis. The Rietveld analysis is shown in Fig. 13. The distribution of the anti-parallel magnetic spins in A and B site are presented in the figure. Pressure dependence of site occupancy and magnetic moment of the ferrimagnetic Mn 2 FeO 4 spinel are summarized in Table 4. The site occupancies of Mn at the tetrahedral and octahedral sites of Mn 2 FeO 4 and MnFe 2 O 4 spinels are shown with increasing pressure. The cation distribution becomes close to the ordered normal spinel structure. Ferrimagnetic spin moment becomes smaller at higher pressure before the transformation to the high-pressure postspinel phase.
Pressure dependence of magnetic structure was suggested by X-ray Mössbauer experiment. Deviations from ian profile may be induced from variations of local environments or fluctuations of parameters.

Conclusion
Magnetic studies of minerals are reliable witnesses of paleomagnetism by high-resolution studies of these structures. The magnetic structures are built during the cooling of molten rock and reflect the earth's magnetic field at the time of their formation. This record provides information on the past behavior of Earth's magnetic field and geomagnetic reversal. The magnetic properties are reset by the interaction  of the magnetic spin inside the Earth's magnetic field. The geomagnetic reversal is an indicator of magnetic field change in plate tectonics. However, the pressure effect of the plate tectonics still remains to be seen in the magnetic study of minerals. The present neutron diffraction and synchrotron X-ray Mössbauer spectroscopic study provide the comprehension of the magnetic and structure change under extreme conditions. Some of oxide spinels with transition elements have a ferrimagnetic property at ambient conditions. They transform to the postspinel structures under high-pressure condition. Cation distributions in Mn 3-x Fe x O 4 solid solutions under extreme conditions are significant research subjects not only for geophysical understands such plate tectonics and geomagnetic reversals but also for the basic magnetic ferrite industrial materials. Magnetic and structure transition studies are possible by neutron time-of-flight scattering diffraction at PLANET J-PARC. Besides the neutron diffraction, X-ray Mössbauer experiment is a significant and complementary study to investigate the magnetic property of Mn 3-x Fe x O 4 solid solutions from the hyperfine structure of Zeeman splitting. The present experiments disclosed the following new discoveries of magnetic properties: (1) The lattice distortion is not coupled with magnetic transition. The magnetic transition temperature from ferrimagnetic-to-paramagnetic of spinels is lower than the structure transition temperature from tetragonal-to-cubic structure transition. The structure transition temperature decreases with increasing pressure.
(2) Pressure dependence of cooperative Jahn-Teller distortion in Mn 2 FeO 4 is observed by the interaction between localized orbital electronic states of Mn 3+ and the compression of the octahedral site. The transition temperature from tetragonal-to-cubic phase decreases with increasing pressure. The transition of Mn 2 FeO 4 is an extremely rare case for the JT transition with increasing pressure. Generally many spinels show cubic-to-tetragonal transition at high pressure and the tetragonal distortion is of flattering octahedral distortion of c/a < 1, However, the tetragonal phase of Mn 2 FeO 4 shows the transformation from tetragonal-to-cubic and the octahedral site is elongated along to the c-axis and the lattice constant ratio is c/a > 1.
(3) Inverse parameter change under compression. X-ray Mössbauer measurement and nuetron diffraction study confirm that the occupancy of Fe 2+ in the tatrahedral site is decreased with increasig pressure, indicating more oredered structure. The inverse parameter is increased with increasing pressure.
(4) The cubic MnFe 2 O 4 spinel and tetragonal Mn 2 FeO 4 transform to the high-pressure orthorhombic postspinel phase at pressure 18.4 GPa and 14.0 GPa, respectively. The transition pressure decreases with increasing Mn content. The observed charge distribution of postspinel becomes an almost ideally ordered structure expressed by VIII [Mn 2+ ] VI (M n 3+ 0.5 Fe 3+ 0.5 ) 2 O 4 , transformed from cubic Mn 2 FeO 4 spinel. (5) The magnetic refinements clarify the paramagnetic and ferrimagnetic structure of MnFe 2 O 4 and Mn 2 FeO 4 spinel as a function of pressure. The magnetic moment is ordered between A and B sites with the anti-parallel distribution along the b axis.