Abnormal Elasticity of Single-Crystal Magnesiosiderite across the Spin Transition in Earth’s Lower Mantle

Brillouin light scattering and impulsive stimulated light scattering have been used to determine the full elastic constants of magnesiosiderite [$({\mathrm{Mg}}_{0.35}{\mathrm{Fe}}_{0.65}){\mathrm{CO}}_3$] up to 70 GPa at room temperature in a diamond-anvil cell. Drastic softening in $C_{11}$, $C_{33}$, $C_{12}$, and $C_{13}$ elastic moduli associated with the compressive stress component and stiffening in $C_{44}$ and $C_{14}$ moduli associated with the shear stress component are observed to occur within the spin transition between $\sim 42.4$ and $\sim 46.5\mathrm{GPa}$. Negative values of $C_{12}$ and $C_{13}$ are also observed within the spin transition region. The Born criteria constants for the crystal remain positive within the spin transition, indicating that the mixed-spin state remains mechanically stable. Significant auxeticity can be related to the electronic spin transition-induced elastic anomalies based on the analysis of Poisson’s ratio. These elastic anomalies are explained using a thermoelastic model for the rhombohedral system. Finally, we conclude that mixed-spin state ferromagnesite, which is potentially a major deep-carbon carrier, is expected to exhibit abnormal elasticity, including a negative Poisson’s ratio of $-0.6$ and drastically reduced $V_P$ by 10%, in Earth’s midlower mantle.

Figure 1

Velocity measurements of the single-crystal magnesiosiderite [$({\mathrm{Mg}}_{0.35}{\mathrm{Fe}}_{0.65}){\mathrm{CO}}_3$] at high pressures and room temperature. In the Brillouin spectra (a)–(c), black open circles are experimental data and red lines are the best fit to the spectra. The inset images show the crystal color in the transmitted light at corresponding pressures. Using Fourier transformation, the time-dependent impulsive spectra (d)–(f) were modeled to derive the power spectra (g)–(i) in the frequency domain and the $V_P$ of the sample at certain orientations (shown as the Chi angle) at high pressures. Neon pressure medium was also detected in the BLS and ISS spectra at high pressures.

Figure 2

Compressional ($V_P$) and shear ($V_S$) wave velocities of the single-crystal magnesiosiderite [$({\mathrm{Mg}}_{0.35}{\mathrm{Fe}}_{0.65}){\mathrm{CO}}_3$] as a function of the azimuthal angle at high pressures and room temperature. (a) shows the high-spin (HS) state; (b) shows the mixed-spin (MS) state; (c) shows the low-spin (LS) state. Open circles represent experimental results, while solid lines represent the best fits to the experimental data using Christoffel’s equation.

Figure 3

Single-crystal elastic constants of magnesiosiderite [$({\mathrm{Mg}}_{0.35}{\mathrm{Fe}}_{0.65}){\mathrm{CO}}_3$] at high pressures and room temperature. Open circles, experimental results; solid lines, modeled results using the finite-strain fitting for the HS and LS states, respectively. Modeling for the MS state shown by the gray vertical line is based on the elasticity and thermodynamics theory. Dashed lines represent the extrapolated constants of the HS state.

Figure 4

Elastic parameters of magnesiosiderite [$({\mathrm{Mg}}_{0.35}{\mathrm{Fe}}_{0.65}){\mathrm{CO}}_3$] at high pressures. (a) Adiabatic bulk ($K_S$) and shear modulus ($G$); (b) aggregate compressional ($V_P$) and shear ($V_S$) wave velocities; (c) $V_P$ and $V_S$ seismic anisotropy factors (${\mathrm{AV}}_P$, ${\mathrm{AV}}_S$); (d) Poisson’s ratio. Open circles, experimental results; solid lines, best modeled fits to experimental data. Solid lines in (c) are plotted to guide the eyes. Gray areas represent the mixed-spin state region.