Pressure-induced spin collapse of octahedrally coordinated ${\mathrm{Mn}}^{3+}$ in the tetragonal hydrogarnet henritermierite ${\mathrm{Ca}}_3{\mathrm{Mn}}_2{[\mathrm{SiO}}_4{]}_2{[\mathrm{O}}_4{\mathrm{H}}_4]$

The high-pressure behavior of natural henritermierite garnet with close to end-member composition ${\mathrm{Ca}}_3{\mathrm{Mn}}_2\left[{\mathrm{SiO}}_4{]}_2\right[{\mathrm{O}}_4{\mathrm{H}}_4]$ was studied at pressures up to 80 GPa using single-crystal synchrotron x-ray diffraction, Raman spectroscopy, and quantum-mechanical calculations based on density functional theory. An isosymmetric phase transition was observed in the pressure range between 55 and 70 GPa, which is associated with a gradual high-spin to low-spin electronic transition in ${\mathrm{Mn}}^{3+}$ and a pronounced reduction of the Jahn-Teller distortion of the ${\mathrm{Mn}}^{3+}{\mathrm{O}}_4({\mathrm{OH})}_2$ octahedra. In the high-pressure phase the Jahn-Teller distortion is totally suppressed and the ${\mathrm{Mn}}^{3+}$ is in a low-spin configuration. Experimental structural data before and after the phase transition are in excellent agreement with the theoretically predicted structural compression of the high-spin and low-spin phases, respectively. While the overall unit-cell volume is reduced by about $1.5\%$ across the phase transition, a collapse of about $4\text{–}5\%$ of the ${\mathrm{MnO}}_6$ octahedral volume is observed. The high-spin phase shows a bulk modulus $B=101$(1) GPa and its pressure derivative $B^{\prime }=4.5$(1). The bulk moduli of the coordination polyhedra are $B_{{\mathrm{MnO}}_6}=178$(2) GPa, $B_{\mathrm{Ca}1{\mathrm{O}}_8}=101.2$(5) GPa, $B_{\mathrm{Ca}2{\mathrm{O}}_8}=88.4$(8) GPa, $B_{{\mathrm{SiO}}_4}=337$(5) GPa, and $B_{{\mathrm{O}}_4{\mathrm{H}}_4}=29$(1) GPa for the high-spin phase. Mode Grüneisen parameters range between 0.34 and 0.94. The computed spin-pairing energy is $\approx 3.6$ eV at 0 GPa.

Figure 1

Crystal structure of henritermierite. ${\mathrm{MnO}}_6$ octahedra (purple), ${\mathrm{SiO}}_4$ tetrahedra (small, blue), and ${\mathrm{O}}_4{\mathrm{H}}_4$ tetrahedra (large, green) share corners in a three-dimensional framework. Ca atoms (yellow spheres) occupy triangular dodecahedral sites with eightfold coordination. $\mathrm{O}\text{–}\mathrm{H}$ bonds are shown for the ${\mathrm{O}}_4{\mathrm{H}}_4$ tetrahedra.

Figure 2

Bonding in henritermierite showing the connectivity between the ${\mathrm{O}}_4{\mathrm{H}}_4$ tetrahedron and the ${\mathrm{MnO}}_6$ octahedron. The O2–Mn–O2 axis is Jahn-Teller elongated. Distances are given in Å.

Figure 3

Compression of the (a) unit-cell volume and (b) unit-cell parameters of henritermierite obtained from single-crystal x-ray diffraction (XRD) (Exp) and from DFT calculations for the high-spin (HS) and low-spin (LS) configurations. At pressures between 55 and 70 GPa the HS-LS crossover zone is observed. Lines represent equation of state fits to the (a) $p-V$ and (b) $p-a$ and $p-c$ data of the HS phase and guides for the LS phase. Literature values (Lit) from single-crystal XRD [8] are included in the plots and fits.

Figure 4

Volume compression of the ${\mathrm{O}}_4{\mathrm{H}}_4$ and ${\mathrm{SiO}}_4$ tetrahedra in henritermierite obtained from experiment and literature [8]. At about 55 GPa the large and highly compressible ${\mathrm{O}}_4{\mathrm{H}}_4$ tetrahedron is compressed to a similar volume as the small and stiff ${\mathrm{SiO}}_4$ tetrahedron.

Figure 5

Polyhedral volume compression of the ${\mathrm{MnO}}_6$ octahedron in henritermierite obtained from experiment (Exp), literature (Lit) [8], and DFT calculations for the high-spin (HS) and low-spin (LS) configurations. An increased continuous volume drop is observed in the spin crossover zone between 55 and 70 GPa indicating a gradual spin transition. Lines represent equation of state fits to the data of the HS phase and a guide to the eye for the LS phase. Experimental data of the volume compression of the ${\mathrm{Fe}}^{3+}{\mathrm{O}}_6$ octahedron in andradite (stars) [9] are shown for comparison. Errors are smaller than the symbol size.

Figure 6

(a) Compression of the $\mathrm{Mn}\text{–}\mathrm{O}$ bond distances in henritermierite obtained from experiment (Exp), literature (Lit) [8], and DFT for HS and LS configurations. The Jahn-Teller distortion of the ${\mathrm{Mn}}^{3+}{\mathrm{O}}_6$ octahedron is reduced with pressure showing a pronounced reduction in the spin transition zone at $55\text{–}70$ GPa and a complete suppression in the LS phase above 70 GPa. (b) Pressure dependence of the edge length distortion (ELD) in ${\mathrm{MnO}}_6$. The reduction of the ELD is well reproduced by theory for the HS and LS phases. Lines are guides to the DFT-HS (dash-dotted lines) and DFT-LS (dashed lines) data.

Figure 7

Compression of the (a) $\mathrm{Ca}2\text{–}\mathrm{O}$ bonds and (b) $\mathrm{Ca}1\text{–}\mathrm{O}$ bonds in henritermierite obtained from experiment (Exp), literature (Lit) [8], and DFT. Lines are guides to the DFT-HS (dash-dotted lines) and DFT-LS (dashed lines) data. Errors are smaller than the symbol size.

Figure 8

Pressure evolution of the (a) hydrogen bond distances and (b) hydrogen bond angles from experiment (Exp), literature (Lit) [8], and DFT calculations for the high-spin (HS) configuration ($0\text{–}55$ GPa) and the low-spin (LS) configuration ($60\text{–}80$ GPa). Lines are guides to DFT data.

Figure 9

Selected Raman spectra of henritermierite single crystals at high pressures and across the spin transition zone ($55\text{–}70$ GPa).

Figure 10

Pressure-dependent shifts of the (a) high-frequency $\mathrm{Si}\text{–}\mathrm{O}$ stretching modes and (b) low-frequency Raman modes of henritermierite. Anomalies and distinct changes are observed in the spin crossover region between 55 and 70 GPa.

Figure 11

Volume dependence of the bulk modulus of calcium silicate and hydro garnets. The line represents a linear fit to the experimental data. Theoretical values include literature data by Nobes et al.  [53] for katoite, Friedrich et al.  [9] for andradite, this study for henritermierite, and Milman et al.  [45] for various garnet compositions. Experimental values include data by Zhang et al.  [15], Pavese et al.  [54] for andradite, Zhang et al.  [15] for grossular, Diella et al.  [55] for uvarovite, Olijnyk et al.  [56], Lager et al.  [13] for katoite, and this study for henritermierite.