Magnetic and structure transition of Mn_3-xFe_xO₄ solid solutions under high-pressure and high-temperature conditions

Abstract

Magnetic and structure transitions of Mn_3–xFe_xO₄ 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 (a_N, a_N, c_N) has the ferrimagnetic structure but the orthorhombic magnetic structure has the ferrimagnetic structure with the lattice constants (a_M, b_M, c_M). The magnetic moment is ordered between A and B sites with the anti-parallel distribution along the b_M 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 Fe₃O₄ and Mn₃O₄ 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 AB₂O₄ spinels. Iron-rich members of the Mn_3-xFe_xO₄ 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-Fe₃O₄. The stability field and the crystal structure of the HP magnetite, first, show a CaTi₂O₄-type structure with space group Bbmm (Cmcm) above 25 GPa, and second, defined to be CaMn₂O₄-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 Fe₃O₄ 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).

The Néel temperatures of Fe_3-xMn_xO₄ solid solutions at ambient pressure are: Fe₃O₄ (858 K), MnFe₂O₄ (563 K) and Mn₂FeO₄ (413 K) Mn₃O₄ (41.8 K). Mn_3-xFe_xO₄ spinel structure transforms to a high-pressure phase of orthorhombic CaMn₂O₄-type postspinel structure. The transition pressures of the Mn_3-xFe_xO₄ solid solution at ambient temperature are: Fe₃O₄ at 21.8 GPa, MnFe₂O₄ at 18.4 GPa and Mn₃O₄ at 10 GPa (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-xFe_xO₄ spinel solid solutions are composed of mixed charged cations of Mn²⁺, Mn³⁺, Fe²⁺ and Fe³⁺ in the A and B sites in the AB₂O₄ spinel structure. In the Mn_3-xFe_xO₄ 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-xFe_xO₄ 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 Mn₃O₄ of about – 250 °C was reported by Boucher et al. (1971); Ole ́s, et al. (1976); Chardon et al. (1986).

Curie temperatures in these spinels increase with increasing Fe content: 140 °C in Mn₂FeO₄ (synthetic ferrite), 290 °C in MnFe₂O₄ (jacobsite) and 585 °C in Fe₃O₄ (magnetite) (Nakagiri et al. 1986; Willerd et al. 1999).

In the present experiment, magnetic and structure studies of MnFe₂O₄ and Mn₂FeO₄ 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 CaFe₂O₄-type (Pmma), CaTi₂O₄-type (Cmcm) and CaMn₂O₄-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.

Table 1 Transformations of the oxide spinels are summarized in three types. of CaTi₂O₄, CaFe₂O₄ and CaMn₂O₄

X-ray structure analysis of Mn_3-xFe_xO₄ 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-xFe_xO₄, 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 Fe₃O₄ (h-Fe₃O₄) 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. Fe²⁺ and Fe³⁺ 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-xFe_xO₄ 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 MnFe₂O₄ and Mn₂FeO₄ were prepared by solid–solid reaction at ambient pressure. To prepare the samples used for X-ray Mössbauer experiment, isotope-enriched samples with 30% ⁵⁷Fe 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 six-axis 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):

$$I_{o} = s\left( h \right)A\left( h \right)L\left( h \right)m\left( h \right) \, \left\{ {|F_{N} \left( h \right)|^{2} + \, | \, F_{M} \left( h \right)|^{2} } \right\},$$

(1)

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

$$F_{N} \left( {h_{k} } \right) \, = Sg_{j} b_{cj} T_{j } \exp \, |2pi\left( {hx_{j} + \, ky_{j} + \, lz_{j} } \right)|,$$

(2)

where T_j is the temperature factor of j atom. γ indicates the γ-factor of the nuclear magneton.

(γ  = 1.913). b is the scattering length ( b_Mn = – 3.73 fm, b_Fe = 9.54 fm).

And magnetic scattering factor F_M(h) is

$$F_{M} \left( {h_{k} } \right) = ge^{2} / \, 2mc^{2} \surd \, 1 \, - \, < \cos^{2} h > x f\left( {h_{k} } \right)Sg_{j} b_{cj} T_{j} \exp |2pi\left( {hx_{j} + \, ky_{j} + \, lz_{j} } \right)|,$$

$$\gamma \square e^{{{2}/}} {2}m_{e} {\text{c}}^{{2}} = { 2}.{696 }\left( {fm} \right),$$

(3)

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 Fe²⁺ and Fe³⁺ 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_xFe_3-xO₄ 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 ⁵⁷Fe spectrum in Fe₂O₃. 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 spectra were determined with the reference of 26.26 T (330 kOe) of the ⁵⁷Fe in Fe₂O₃ spectrum.

Result and discussion

Pressure effect on the cooperative Jahn–Teller distortion of Mn₂FeO₄ spinel phase

Mn_3-xFe_xO₄ spinel structure transforms to high-pressure phase of orthorhombic CaMn₂O₄-type postspinel structure. Present neutron diffraction study reveals the phase diagram of Mn_3-xFe_xO₄ under high pressure at ambient temperature, which is presented in Fig. 1. Structure transition from tetragonal to cubic of Mn₂FeO₄ spinel under pressure at 20 °C is shown as a function of normalized unit-cell volume. Mn₂FeO₄ and MnFe₂O₄ spinel transform to postspinel at different pressures at 14.0 GPa and 18.4 GPa, respectively.

Fig. 1

Phase diagram of Mn_3-xFe_xO₄ 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)

Present neutron diffraction patterns of Mn₂FeO₄ at 2.2 GPa in the heating experiment disclose the tetragonal-to-cubic 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.

Fig. 2

Jahn–Teller effect degradation and appearance in Mn₂FeO₄ transition between tetragonal and cubic spinel spinels are shown. Neutron diffraction experiment of Mn₂FeO₄ 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

Mn³⁺ (3d⁴) prefers octahedral configuration in the strong ligand field. In the Mn_3-xFe_xO₄ solid solution, Mn-rich phases present lattice distortion due to the cooperative Jahn–Teller (JT) effects. At ambient pressure, Mn₃O₄ transforms from tetragonal (I4₁/amd z = 4) to cubic (Fd_3m z = 8) 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 Mn₂FeO₄ 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 Mn₂FeO₄. 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.

Fig. 3

Pressure dependence of the unit-cell volume of Mn₂FeO₄ and MnFe2O₄. Mn2FeO4 and MnFe₂O₄ transform to postspinel at pressures: 14.0 GPa and 18.4 GPa, respectively. Shadowed area indicates the two-phase mixture

The present transition case from tetragonal-to-cubic phase of Mn₂FeO₄ is extremely rare for the JT transition under compression. The following spinels: Fe₂TiO₄ (Yamanaka et al. 2013), FeCr₂O₄ (Kyono et al. 2011a, b), ZnMn₂O₄ (Choi et al. 2006), CuMn₂O₄ (Waskowska et al. 2001), CuFe₂O₄ (Kyono et al., 2015), ZnGa₂O₄ (Errandonea et al. 2009), NiMn₂O₄ (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 Mn₂FeO₄ 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 Mn₂FeO₄ is caused by localized orbital electronic states of Mn³⁺ under extreme conditions.

The result of the structure refinements of cubic MnFe₂O₄ and tetragonal Mn₂FeO₄ 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 and B–O together with AO₄ tetrahedral volume and BO₆ octahedral volume are presented in the tables.

The magnetic interaction is induced by supper exchange mechanism via oxygen. A–O and B–O bond distances and A–O–B bond angle are strongly related for the mechanism.

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 super-exchange model in the corner sharing octahedra is shown in Fig. 5. Super exchange for the electron hop** between Fe²⁺ and Fe³⁺ ion is more possible.

Fig. 4

Inter-cation distances A–A, B–B, and A–B in MnFe₂O₄ and Mn2FeO₄. The B–B distances in MnFe₂O₄ and Mn₂FeO₄ are much shorter than the A–A and A–B distances

Fig. 5

Super exchange for the electron hop** between Fe²⁺ and Fe³⁺ ion is more possible in the B site than the A site. The super-exchange between B and the adjacent B cations is easier to gain extremely low resistivity. With compression, B–B shorter distance promotes a higher conduction. The B–B super-exchange model is shown in the corner sharing octahedra

Cation ordering

MnFe₂O₄ and Mn₂FeO₄ 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, 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. Charge transfer in Fe²⁺, Fe³⁺, Mn²⁺ and Mn³⁺ is often observed in many experiments. Neutron diffraction studies show the change of the site occupancies at the A and B site and A–O and B–O distances at extreme high pressures. The bond distances at the A and B sites of Mn–O and Fe–O were evaluated through neutron diffraction study.

The site occupancies have a significant effect on electrical conductivity. The magnetic moments of the A and B sites in the MnFe₂O₄ and Mn₂FeO₄ spinel structures were also clearly observed. The inverse parameter i of the spinel structure in (Mn²⁺_iFe³⁺_1-i)[Mn³⁺_1-iFe²⁺_1-iFe³⁺_2i]O₄ could be precisely defined for MnFe₂O₄. 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 MnFe₂O₄ is presented as a function of pressure in Fig. 6.

Fig. 6

Inverse parameter as a function of pressure of Mn₂FeO₄

Mössbauer resonance experiment also shows Fe²⁺ and Fe³⁺ 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 MnFe₂O₄ cubic spinel at 0.25 GPa and 300 K in Fig. 7. The spectrum of the A site is assigned to Fe³⁺ in the tetrahedral site. The spectrum of the octahedral site (B) site is assigned to mixture of Fe³⁺ and Fe²⁺. These Fe³⁺ and Fe²⁺ cations in the B site are not individually separated because of the electron hop** between these cations.

Fig. 7

Mössbauer spectrum of MnFe₂O₄ at 0.25GPa. Mössbauer spectrum of MnFe₂O₄ cubic spinel at 0.25 GPa and 300 K is shown. 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 Fe³⁺ in the tetrahedral site. The spectrum of the B site is assigned to mixture of Fe³⁺ and Fe²⁺ in the octahedral site. Intensity spectra ratio of the A and B site is presented

Mössbauer spectra of MnFe₂O₄ 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.

Fig. 8

Mössbauer spectrum of MnFe₂O₄ at 10.0 GPa and 300 K. Mössbauer spectrum of MnFe₂O₄ cubic spinel at 12.5 GPa and 300 K. The spectra show very similar hyperfine structures of sextet patterns to the spectra at 0.25 GPa shown in Fig. 5

Under further compression at 17.0 GPa 300 K shown in Fig. 9, Mössbauer spectrum of MnFe₂O₄ cubic ferrimagnetic phase shows one doublet indicates the Fe³⁺ spectrum at the A site and one sextet shows the Fe²⁺ and Fe³⁺ spectrum at the B site. The former spectrum proves neither hyperfine structure and nor internal magnetic field. The spectrum of the hyperfine structure at the A site is not observed but the spectrum at the B site shows the internal magnetic field.

Fig. 9

Mössbauer spectrum of MnFe₂O₄ cubic ferrimagnetic phase at 17.0 GPa 300 K. One doublet indicates the Fe³⁺ spectrum at the tetrahedral site One sextet shows the Fe²⁺ and Fe³⁺ spectrum at the octahedral site are shown. The former spectrum proves neither hyperfine structure and nor internal magnetic field

Neutron diffraction study of MnFe₂O₄ and Mn₂FeO₄ 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 Mn₂FeO₄ at 18.0 GPa and 300 K have two doublets, as shown in Fig. 10. One indicates the sixfold octahedron indicating Fe³⁺ in the octahedral site (M2 site). Another doublet represents Fe²⁺ in the highly distorted eightfold large cation site (M1 site) with good reason of a large quadruple splitting. Two doublets of the Mössbauer spectra of postspinel indicate paramagnetic behavior. The result of Fe²⁺ and Fe³⁺ distributions in the ^VIIIM1 and ^VIM2 sites is expressed by the following cation distribution: ^VIII[Mn²⁺_0.746,Fe²⁺_0.256]^VI(Mn³⁺_0.628,Fe³⁺_0.372)₂O₄. There is no sextet spectra in the postspinel phases of Mn₂FeO₄ and MnFe₂O₄ proving they are paramagnetic at high pressures.

Fig. 10

Mössbauer spectrum of orthorhombic postspinel Mn₂FeO₄ spectra at 18.0 GPa. Two doublets are presented: Inner larger doublet indicates the sixfold octahedron, which is assigned to Fe³⁺ in the M2 site. Outer doublet represents Fe²⁺ in the highly distorted eightfold large cation site (M1 site) and postspinel is paramagnetic

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 MnFe₂O₄ and Mn₂FeO₄ 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.

Table 2 Mössbauer spectra analyses of MnFe₂O₄ (cubic spinel), Mn₂FeO₄ (tetragonal spinel) and postspinel (CaMn₂O₄ type) of Mn₂FeO₄

Two sextets of the spectra of MnFe₂O₄ 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 Mn₂FeO₄ and MnFe₂O₄ spinels under compression are related to their elastic properties. The compression behavior of Mn_3-xFe_xO₄ spinels can be described by third-order Birch–Murnaghan equation of state. The equation of state is given by

$$P\left( V \right) = \frac{{3B_{0} }}{2}\left[ {\left( {\frac{{V_{0} }}{V}} \right)^{7/3} - \left( {\frac{{V_{0} }}{V}} \right)^{5/3} } \right]\left\{ {1 + \frac{3}{4}\left( {B_{0}^{^{\prime}} - 4} \right)\left[ {\left( {\frac{{V_{0} }}{V}} \right)^{2/3} - 1} \right]} \right\},$$

(4)

where P is the pressure, V₀ is the reference volume, V is the deformed volume with respect to pressure,, B₀ is the bulk modulus, and B₀' 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

$$B_{o} = \, - V\left( {\partial P/\partial V} \right)_{P = 0} and B_{o}^{,} = \, \left( {\partial B/\partial P} \right)_{P = 0} .$$

(5)

The equations of state of MnFe₂O₄ and Mn₂FeO₄ show the difference in their transition pressures. Bulk modules of Mn_3-xFe_xO₄ spinel solid solutions are presented in Table 3.

Table 3 Bulk modulus of Mn_3-xFe_xO₄ spinel solid solutions are presented

MnFe₂O₄ and Mn₂FeO₄ are characterized by cation disorder and are more compressible than the end-members of the solid solution. MnFe₂O₄ is less compressible than Mn₂FeO₄.

High-pressure polymorph postspinel phase

Magnetite undergoes a phase transition to a high-pressure (HP) form, called h-Fe₃O₄ above 25 GPa and defined to be postspinel of CaMn₂O₄ (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 Mn₂FeO₄ 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 ^VIIIM1 site volume is much larger than the ^VIM2 site. The ^VIIIM1 site of Mn₂FeO₄ and MnFe₂O₄ postspinel is mostly occupied by Mn²⁺, which increases with increasing pressure. The ^VIM2 site of MnFe₂O₄ is occupied by mainly Fe and only small amount of Mn. On the other hand, the ^VIM2 of Mn₂FeO₄ is half-occupied by Mn. The phase of Mn₂FeO₄ is composed of an almost ideal ordered structure of ^VIII[Mn²⁺]^VI(Mn³⁺_0.5Fe³⁺_0.5)₂O₄. The atoms in the ^VIM2 site are located on the edge-sharing plane perpendicular to the c-axis, as shown in Fig. 11. Mn₂O₁₀ dimers of two octahedra in the structures are linked via common edges.

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

Magnetic structure of Mn₂FeO₄ and MnFe₂O₄ spinel

Present magnetic structure analysis of Mn₂FeO₄ and MnFe₂O₄ 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-to-cubic transition with increasing pressure. The site symmetry 0.2 m. of the octahedral (B) site in the tetragonal symmetry of I4₁/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 ferrimagnetic-to-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.

Fig. 12

Difference in the transition temperature between the magnetic (ferrimagnetic-to-paramagnetic) and structure (tetragonal-to-cubic) transition of Mn₂FeO₄. Magnetic transition temperature is 100 °C and structure transition temperature is 180 °C

The present magnetic refinement shown in Table 4 confirms the site occupancies at the A and B sites of Mn₂FeO₄ 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: Mn²⁺ (5.92 µB), Mn³⁺ (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 MnFe₂O₄ was determined by thermal neutron diffraction (Levy 2015). Spin moments of the A and B sites of the iron substitution on the magnetic property were clarified at temperatures 10 K and 295 K (Baron et al. 1998).

Table 4 Magnetic moment and site occupancy at the A and B sites of tetragonal Mn₂FeO₄ spinel

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 I4₁/amd are examined for the observed intensities. The magnetic space group of I4₁/am’d’ is the most reliable subgroup of the space group symmetry of I4₁/amd. Rietveld refinement of Mn₂FeO₄ at 2.2 GPa 20 ℃ tetragonal I4₁/amd with the paramagnetic structure model is χ² = 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 χ² = 2.157 and R(F²) = 0.117. The lattice constants (a_M, b_M, c_M) of Mn₂FeO₄ 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 Mn₂FeO₄ spinel are summarized in Table 4. The site occupancies of Mn at the tetrahedral and octahedral sites of Mn₂FeO₄ and MnFe₂O₄ 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.

Fig. 13

Paramagnetic Mn₂FeO₄ tetragonal structure at 2.2 GPa is shown in the left figure. Right figure shows anti-parallel magnetic spin moments along the c_M axis of the ferrimagnetic Mn₂FeO₄ orthorhombic structure at 2.2 χ²R(F²) = 0. 117). Only cations are presented in the figure. They are similar positions in the paramagnetic tetragonal structure. Ferrimagnetic lattice has a_M, b_M, c_M., and b_M is twice large b_N of the paramagnetic lattice

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-xFe_xO₄ 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-xFe_xO₄ 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 Mn₂FeO₄ is observed by the interaction between localized orbital electronic states of Mn³⁺ and the compression of the octahedral site. The transition temperature from tetragonal-to-cubic phase decreases with increasing pressure. The transition of Mn₂FeO₄ 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 Mn₂FeO₄ 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 Fe²⁺ in the tatrahedral site is decreased with increasig pressure, indicating more oredered structure. The inverse parameter is increased with increasing pressure.

(4) The cubic MnFe₂O₄ spinel and tetragonal Mn₂FeO₄ 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[Mn²⁺]^VI(Mn³⁺_0.5Fe³⁺_0.5)₂O₄, transformed from cubic Mn₂FeO₄ spinel.

(5) The magnetic 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.