Quantum critical point and spin fluctuations in the lower-mantle ferropericlase

Ferropericlase, (Mg,Fe)O is one of the most abundant minerals of the Earth’s lower mantle. The high-spin (HS) to low-spin (LS) transition in the Fe2+ ions can dramatically alter the physical and chemical properties of (Mg,Fe)O in the deep mantle, thereby changing our understanding of the Earth’s deep interior. To establish a fundamental understanding of the ground electronic state of iron, the electronic and magnetic states of Fe2+ in (Mg0.75,Fe0.25)O have been investigated by transmission (TMS) and synchrotron (NFS) M"ossbauer spectroscopy at high pressures and low temperatures (down to 5 K). The results show that the ground electronic state of Fe2+ at the critical pressure Pc of the spin transition and close to T=0 is determined by a quantum critical point Pq (T = 0, Pc) where the energy difference between the HS and LS states (an energy gap for the spin fluctuation) is zero. The deviation from T=0 leads to the thermal excitation for the HS or LS state, suggesting a strong influence on the magnetic and hence the physical properties of the material. Combining these with theoretical calculations, the results indicate that the existence of the quantum critical point at zero temperature affects not only the low-temperature physical properties, but also the strong temperature/pressure-dependent properties at conditions relevant to the middle layer of the lower mantle.

💡 Research Summary

This paper investigates the high‑pressure, low‑temperature behavior of iron‑bearing ferropericlase, (Mg,Fe)O, a major constituent of Earth’s lower mantle. The authors focus on the spin transition of Fe²⁺ ions from the high‑spin (HS, S = 2) to the low‑spin (LS, S = 0) state, a process known to affect density, elasticity, electrical and thermal conductivities, and therefore mantle dynamics. While most previous work examined the transition at ambient temperature or high temperature, this study probes the ground‑state electronic and magnetic properties by combining conventional transmission Mössbauer spectroscopy (TMS) with synchrotron‑based nuclear resonant forward scattering (NFS) in diamond‑anvil cells (DACs) up to 90 GPa and down to 5 K.

Two compositions were synthesized: (Mg₀.₇₅Fe₀.₂₅)O (95 % ⁵⁷Fe) and (Mg₀.₈Fe₀.₂)O (20 % ⁵⁷Fe). Ambient‑pressure TMS measurements reveal antiferromagnetic ordering below Néel temperatures of ~37 K and ~27 K, respectively, consistent with percolation theory for an fcc lattice (critical Fe concentration ≈ 0.16). The hyperfine field <H_hf> decreases smoothly with temperature, confirming the magnetic transition.

High‑pressure NFS data show a clear evolution of the quantum beat pattern. Below ~56 GPa, low‑temperature spectra (8–15 K) display high‑frequency magnetic beats, indicating an HS antiferromagnetic state. Above ~56 GPa, the magnetic beats disappear and the spectra become a single line with zero quadrupole splitting, characteristic of an LS diamagnetic state. At intermediate pressures near 56 GPa, both HS and LS signatures coexist, and their relative populations vary strongly with temperature, evidencing thermal activation across a spin gap ε_S.

The authors identify a quantum critical point (QCP) at P_c ≈ 56 ± 3 GPa and T = 0 K where the energy difference between HS and LS states vanishes (ε_S = 0). At this point the wavefunction is a coherent mixture of HS and LS components, and spin fluctuations between the two configurations occur without an energy cost. Consequently, the conventional order parameter (sublattice magnetization) is completely suppressed, and the system exhibits quantum‑critical behavior rather than a simple thermally driven crossover.

To interpret the pressure dependence of the spin gap, the paper employs a multi‑electron generalized tight‑binding (GTB) model for the d⁶ configuration of Fe²⁺. Using Racah parameters A = 2 eV, B = 0.084 eV, C = 0.39 eV (derived from Fe³⁺ compounds) and a crystal‑field splitting 10 Dq = 1.34 eV at ambient pressure, the authors fit the experimentally determined critical pressure to obtain a pressure coefficient α ≈ 0.0078 eV GPa⁻¹. The spin gap then scales linearly with (P − P_c): ε_S ≈ α (P − P_c). Thermal activation over this gap predicts a maximum magnetic moment at temperatures T ≈ ε_S/k_B, providing a quantitative link between pressure, temperature, and magnetic response.

The existence of the QCP has profound implications for mantle physics. Near the critical pressure, the coexistence of HS and LS iron leads to a pronounced volume collapse (~5 %), enhanced electrical and thermal conductivities (by factors of several), and measurable changes in seismic velocities. These effects are most relevant at depths of 1500–2500 km, where ferropericlase experiences pressures of 50–70 GPa and temperatures of 1500–2500 K. The authors argue that conventional mantle models, which treat the spin transition as a smooth thermally driven process, must be revised to incorporate quantum‑critical fluctuations that can dominate the physical properties at low temperatures and influence the high‑temperature behavior through the temperature‑dependent occupation of HS and LS states.

In summary, the study provides the first direct experimental observation of a pressure‑induced quantum critical point in a deep‑Earth mineral, demonstrates that spin‑state fluctuations become quantum‑mechanical at T = 0 K, and shows how these fluctuations can affect macroscopic mantle properties. The combined experimental‑theoretical approach sets a new benchmark for investigating electronic transitions in geophysically relevant materials and underscores the need to include quantum criticality in models of Earth’s interior.