High-pressure magnetic, electronic, and structural properties of $M\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_4$ ($M=\mathrm{Mg},\mathrm{Zn},\mathrm{Fe}$) ferric spinels

Magnetic, electronic, and structural properties of $M\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_4 (M=\mathrm{Mg},\mathrm{Zn},\mathrm{Fe})$ ferric spinels have been studied by ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopy, electrical conductivity, and powder and single-crystal x-ray diffraction (XRD) to a pressure of 120 GPa and in the 2.4–300 K temperature range. These studies reveal for all materials, at the pressure range 25–40 GPa, an irreversible first-order structural transition to the postspinel $\mathrm{CaT}{\mathrm{i}}_2{\mathrm{O}}_4-$ type structure (Bbmm) in which the HS $\mathrm{F}{\mathrm{e}}^{3+}$ occupies two different crystallographic sites characterized by six- and eightfold coordination polyhedra, respectively. Above 40 GPa, an onset of a sluggish second-order high-to-low spin (HS-LS) transition is observed on the octahedral $\mathrm{F}{\mathrm{e}}^{3+}$ sites while $\mathrm{F}{\mathrm{e}}^{3+}$ occupying bicapped trigonal prism sites remain in the HS state. Despite an appreciable resistance decrease, corroborating with the transition to the LS state, $\mathrm{MgF}{\mathrm{e}}_2{\mathrm{O}}_4$ and $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$ remain semiconductors at this pressure range. However, in the case of $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$, the second-order HS-LS transition on the $\mathrm{F}{\mathrm{e}}^{3+}$ octahedral sites corroborates with a clear trend to a gap closure and formation of a semimetal state above 50 GPa. Above 65 GPa, another structural phase transition is observed in $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ to a new Pmma structure. This transition coincides with the onset of nonmagnetic $\mathrm{F}{\mathrm{e}}^{2+}$, signifying further propagation of the gradual collapse of magnetism corroborating with a sluggish metallization process. With this, half of $\mathrm{F}{\mathrm{e}}^{3+}$ sites remain in the HS state. Thus, this paper demonstrates that, in a material with a complex crystal structure containing transition metal cation(s) in different environments, a HS-LS transition and delocalization/metallization of the $3d$ electrons does not necessarily occur simultaneously and may propagate through different crystallographic sites at different degrees of compression.

Figure 1

Mössbauer spectra of (a) $\mathrm{MgF}{\mathrm{e}}_2{\mathrm{O}}_4$ and (b) $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$ recorded at room temperature and various pressures. For $\mathrm{MgF}{\mathrm{e}}_2{\mathrm{O}}_4$, two $\mathrm{F}{\mathrm{e}}^{3+}$ components at the spinel phase correspond to the tetrahedral and octahedral sites. At 29 GPa, two paramagnetic components appear in the central part of the spectrum. The abundance of the new phase increases with pressure, reaching 100% above 40 GPa. For $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$, the spectra up to 24 GPa consist of only one doublet, corresponding to $\mathrm{F}{\mathrm{e}}^{3+}$ in the spinel octahedral sites. Above 25 GPa, two new $\mathrm{F}{\mathrm{e}}^{3+}$ sites appear (dashed and dash-dot-dotted lines) corresponding to the components of the HP phase.

Figure 2

The pressure evolution of the IS and the quadrupole splitting of (a) $\mathrm{MgF}{\mathrm{e}}_2{\mathrm{O}}_4$ and (b) $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$ at 300 K relative to a ${}^{57}\mathrm{Co}(\mathrm{Rh})$ source at 300 K. Note that, above 60 GPa, the PS1 component is replaced by the PS3 component characterized by a significantly reduced IS value. All lines are to guide the eye. Symbols: “$•$” represents the spinel, “$▴$” and “$\blacksquare$” the PS1 and PS2 components, respectively, “$⧫$” the PS3 component. Filled and empty shapes mark compression and decompression cycles, respectively. The pressure uncertainties are 5%.

Figure 3

Mössbauer spectra of (a) $\mathrm{MgF}{\mathrm{e}}_2{\mathrm{O}}_4$ and (b) $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$ recorded at 47 GPa and various temperatures; spectra were fit with two $\mathrm{F}{\mathrm{e}}^{3+}$ sites PS2 and PS1 (dashed and dash-dot-dotted lines, respectively). A strong magnetic relaxation effect is observed below 200 K, and below 100 K, the hyperfine fields become saturated. Note a slight discrepancy between the experimental and calculated data at the central part of the spectra at 53 and 80 K.

Figure 4

Mössbauer spectra of (a) $\mathrm{MgF}{\mathrm{e}}_2{\mathrm{O}}_4$ and (b) $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$ recorded at 80 and 88 GPa, respectively, and various temperatures. The spectra below 50 K are characterized by the two components: the first is characterized by a static magnetic hyperfine interaction $H_{\mathrm{hf}}=45\mathrm{T}$ (HS PS2 component, dashed line), and the second by a spin-spin magnetic relaxation spectrum (PS3 component, dotted line), the typical feature of the LS state [31]. Note that the magnetic ordering temperature for the HS component drops from $\sim 100\mathrm{K}$ at 47 GPa (Fig. 3) to below 50 K here. The spectra of $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$ at 84 GPa, 5 and 3.08 K were collected using energy-domain MS carried out at the beamline ID18 at ESRF.

Figure 5

Unit-cell volume of the spinel and postspinel $\mathrm{CaT}{\mathrm{i}}_2{\mathrm{O}}_4$-type phases of (a) $\mathrm{MgF}{\mathrm{e}}_2{\mathrm{O}}_4$, (b) $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$, and (c) $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ as a function of pressure at room temperature; (d) pressure derivative of the unit-cell volume for $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ as a function of pressure. Circles ○ and stars ☆ represent the spinel and postspinel phases, respectively. The solid lines are fits to the second-order Birch-Murnaghan EOS of the spinel phases extrapolated to $\sim 50\mathrm{GPa}$, fitting results in the values of $K_0=170.5\left(8\right),174.1\left(2\right)$ [17], 198(9) GPa, and $V_0=591.0\left(2\right),602.8\left(4\right)$, and $589.0\left(2\right){\AA }^3$ for $M=\mathrm{Mg},\mathrm{Zn}$, and Fe, respectively. The third-order EOS for $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ results in $V_0=590\left(3\right){\AA }^3,K_0=182\left(29\right)\mathrm{GPa}$, and $K^{\prime }=5\left(2\right)$. The dashed line represents a fit to the postspinel phase of $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$ at the pressure range 25–40 GPa. Note a steeper decrease of unit-cell volume with pressure increase above 40 GPa, indicating a HS-LS transition on the octahedral sites. The inset shows the abundance of the quadrupole-split paramagnetic MS component as a function of pressure in $\mathrm{MgF}{\mathrm{e}}_2{\mathrm{O}}_4$ and $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$ (open and solid squares, respectively).

Figure 6

Mössbauer spectra of $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ recorded at various pressures and low temperatures (${\mathrm{N}}_2$ pressure medium). Note that, at its appearance, the postspinel phase is characterized by three equally abundant Fe components [14] [$\mathrm{F}{\mathrm{e}}^{2+},\mathrm{F}{\mathrm{e}}^{3+}\left(\mathrm{I}\right),\mathrm{F}{\mathrm{e}}^{3+}\left(\mathrm{II}\right)$: red dashed, olive dotted, and blue solid lines, respectively]. Above 40 GPa, an onset of a new quadrupole-split $\mathrm{F}{\mathrm{e}}^{3+}{\left(\mathrm{I}\right)}_{\mathrm{nm}}$ component is observed (magenta dotted line), replacing the $\mathrm{F}{\mathrm{e}}^{3+}\left(\mathrm{I}\right)$ component. Around 70 GPa, another unsplit $\mathrm{F}{{\mathrm{e}}^{2+}}_{\mathrm{nm}}$ component appears (green dashed line), gradually replacing the $\mathrm{F}{\mathrm{e}}^{2+}$ component. Components are shaded for grayscale viewing offline.

Figure 7

The spectra of $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ at 84 GPa and 2.4 K collected using energy-domain MS (He pressure medium). Note that only three equal abundant components are observed at this pressure, namely $\mathrm{F}{{\mathrm{e}}^{2+}}_{\mathrm{nm}}, \mathrm{F}{\mathrm{e}}^{3+}{\left(\mathrm{I}\right)}_{\mathrm{nm}}$, and $\mathrm{F}{\mathrm{e}}^{3+}\left(\mathrm{II}\right)$. This suggests that using the He pressure medium results in a complete electronic transformation on the octahedral sites at about 84 GPa. Meanwhile, $\mathrm{F}{\mathrm{e}}^{3+}$ ions occupying square antiprism coordinated sites remain in the HS state (blue solid line). The lack of any sign of a magnetic interaction for $\mathrm{F}{{\mathrm{e}}^{2+}}_{\mathrm{nm}}$ and $\mathrm{F}{\mathrm{e}}^{3+}{\left(\mathrm{I}\right)}_{\mathrm{nm}}$ components (green dashed and magenta dotted lines, respectively) above 84 GPa and down to 2.4 K suggests that these components emanate not from a paramagnetic, but rather from a nonmagnetic state. Components are shaded for grayscale viewing offline.

Figure 8

Example of Rietveld refinement of the postspinel phase of (a) $\mathrm{MgF}{\mathrm{e}}_2{\mathrm{O}}_4$ at 50.5(2) GPa, (b) $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$ at 51.0(5) GPa, and (c) $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ at 63.6(8) GPa and RT assuming a $\mathrm{CaT}{\mathrm{i}}_2{\mathrm{O}}_4$-type structure (SG Bbmm), and (d) F(calc) weighted (model biased) fitting of $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ at 79(1) GPa, assuming a Pmma post-postspinel type structure. Asterisks * mark the measured data, the solid line is the best fit to the data, and the dashed line shows the difference between the observed and calculated intensities (all background subtracted). Horizontal lines and X's show the expected diffraction peaks of the sample and neon, respectively. Here, ${\lambda }_{\mathrm{a},\mathrm{b}}=0.3738$ and ${\lambda }_{\mathrm{c},\mathrm{d}}=0.4152\AA$.

Figure 9

Reciprocal space reconstructions of HP-$\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ at 28.4(5) GPa corresponding to (a) $h$ 2 $l$ and (b) $h$ 1 $l$ planes, respectively. Sites on a blue lattice represent predicted positions of the reflections. Blue circles show systematic absences corresponding to B centering.

Figure 10

Powder XRD patterns of $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ at various pressures during compression. At 33 GPa, * mark the Ne pressure medium peaks, ↓ mark the disappearance of the spinel phase, and ↑ mark the appearance of the Bbmm postspinel phase. At 71.5 GPa, ↑ mark the appearance of the post-postspinel Pmma phase. Here, $\lambda =0.4152\AA$.

Figure 11

The pressure dependence of the resistance of (a) $\mathrm{MgF}{\mathrm{e}}_2{\mathrm{O}}_4$ and (b) $\mathrm{ZnF}{\mathrm{e}}_2{\mathrm{O}}_4$ recorded at 295 K. The solid ($▴$) and open ($▿$) triangles are data points obtained during the cycles of compression and decompression, respectively, of the $\mathrm{MgF}{\mathrm{e}}_2{\mathrm{O}}_4$ sample. Note the minor increase of $R$ up to 25 GPa in the spinel phase and more rapid decrease at the range 45–70 GPa. The vertical dashed lines set the boundary of the coexistence between the spinel and postspinel phases. The inset shows $R$($T$) and conductance $G$($T$) of the samples at various pressures.

Figure 12

The temperature dependence of the resistance of $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ at various pressures (part of these data were published previously in [14]). An incipient semimetal behavior is observed above 60 GPa followed by a sluggish metallization above 86 GPa.