Title: Pressure-induced spin pairing transition of Fe$^{3+}$ in oxygen octahedra,
Abstract: High pressure can provoke spin transitions in transition metal-bearing
compounds. These transitions are of high interest not only for fundamental
physics and chemistry, but also may have important implications for
geochemistry and geophysics of the Earth and planetary interiors. Here we have
carried out a comparative study of the pressure-induced spin transition in
compounds with trivalent iron, octahedrally coordinated by oxygen.
High-pressure single-crystal Mössbauer spectroscopy data for FeBO$_3$,
Fe$_2$O$_3$ and Fe$_3$(Fe$_{1.766(2)}$Si$_{0.234(2)}$)(SiO$_4$)$_3$ are
presented together with detailed analysis of hyperfine parameter behavior. We
argue that $\zeta$-Fe$_2$O$_3$ is an intermediate phase in the reconstructive
phase transition between $\iota$-Fe$_2$O$_3$ and $\theta$-Fe$_2$O$_3$ and
question the proposed perovskite-type structure for $\zeta$-Fe$_2$O$_3$.The
structural data show that the spin transition is closely related to the volume
of the iron octahedron. The transition starts when volumes reach 8.9-9.3
\AA$^3$, which corresponds to pressures of 45-60 GPa, depending on the
compound. Based on phenomenological arguments we conclude that the spin
transition can proceed only as a first-order phase transition in
magnetically-ordered compounds. An empirical rule for prediction of cooperative
behavior at the spin transition is proposed. The instability of iron octahedra,
together with strong interactions between them in the vicinity of the critical
volume, may trigger a phase transition in the metastable phase. We find that
the isomer shift of high spin iron ions depends linearly on the octahedron
volume with approximately the same coefficient, independent of the particular
compounds and/or oxidation state. For eight-fold coordinated Fe$^{2+}$ we
observe a significantly weaker nonlinear volume dependence.