Superionic effect and anisotropic texture in Earth's inner core driven by geomagnetic field

Seismology reveals a complex, heterogeneous, and anisotropic inner core with faster seismic velocities in the polar direction than in equatorial directions, depth-varying anisotropy, and hemispherical dichotomy. Explaining these features is central to understanding inner core evolution and coupling with the outer core. Prior proposals invoke lattice-preferred orientation (LPO) of Fe (hcp or bcc) with fast axes aligned to Earth's rotation, combinations of phases/orientations to account for hemispherical variations, solidification texturing (which may anneal out), flow-driven LPO requiring high viscosity, and Maxwell-stress-driven texturing. However, mechanisms originating at the inner core boundary struggle to explain an isotropic uppermost inner core (UIC) and the formation of a highly anisotropic innermost inner core (IMIC). Here, the study proposes a new mechanism: anisotropic H-ion diffusion in superionic Fe–H alloys under inner-core conditions, coupled with external electric fields associated with the geomagnetic field, aligns Fe–H crystals and generates the observed seismic anisotropy and its depth dependence.

The paper reviews explanations for inner core anisotropy and heterogeneity: (1) LPO of Fe crystals where anisotropic velocities of hcp and bcc Fe can explain polar-equatorial Vp differences, though complex mixtures and orientations are needed for hemispherical variations. (2) Solidification texturing at the ICB, with subsequent annealing potentially erasing anisotropy over time. (3) Flow-induced LPO driven by differential growth, requiring high viscosities (>10^18 Pa s). (4) Maxwell stresses as a driver of texturing. These mechanisms face challenges explaining an isotropic UIC and the emergence of a strongly anisotropic IMIC, as well as hemispherical dichotomy and depth-dependent changes. The study builds on prior work indicating superionic behavior of light elements (H, O, C) in hcp-Fe at inner-core conditions, which softens elasticity and matches seismic velocities, extending this to investigate anisotropy in superionic Fe–H and its response to electric fields.

• Ab initio molecular dynamics (AIMD) simulations were used to compute elastic properties and seismic velocities of superionic hcp-FeH_x (notably FeH0.25) under inner-core pressures and temperatures (up to 360 GPa and 6000 K). Directional compressional wave velocities and anisotropies were calculated, including temperature and composition (H content) dependencies.
• Hydrogen migration pathways in hcp-FeH0.25 were identified, and migration barrier energies along these paths were computed using the climbing-image nudged elastic band (CINEB) method at 2000–6000 K. Paths included O-site to O-site along a-axis (O–O), O–T–O along a-axis, and O–O along c-axis. Lattice parameters at each temperature were obtained from hydrostatic AIMD.
• Diffusion coefficients and activation enthalpies along crystallographic directions (a, b, c, basal plane) were obtained from AIMD via mean-square displacement analysis across 2000–6000 K.
• A neural network potential (NNP), trained on AIMD data (DeepMD framework), enabled large-scale molecular dynamics. Nonequilibrium MD (NEMD) simulations with 640-atom FeH0.25 supercells at 360 GPa and 6000 K were performed under applied external electric fields to probe orientational diffusion and internal energy dependence on crystal orientation relative to the field.
• Elastic constants for hexagonal symmetry (C11, C12, C13, C33, C44) were obtained via stress–strain calculations using small distortions. Bulk and shear moduli were computed using Voigt averaging. Directional seismic velocities (Vp, Vs) and their anisotropies were solved using the Christoffel equation.
• Geophysical context of core fields: Using insights from geodynamo simulations, the study considers poloidal (Bp) and toroidal (Br) magnetic fields at the ICB. The poloidal component is assumed to diffuse into the inner core, generating azimuthal electrical currents (via Ampère’s law), which produce electric fields that interact with anisotropic H-ion diffusion. Conceptual depth-dependent textures (UIC vs deeper IC vs IMIC) were compared against observed PKIKP travel-time residuals and reference Earth models.

• Superionic Fe–H exhibits strong directional dependence of H-ion diffusion: the lowest migration barriers occur along the c-axis. CINEB barriers decrease with temperature, and anisotropy arises from the non-ideal c/a ratio.
• AIMD-derived diffusion activation enthalpies (at 360 GPa) are anisotropic: a-axis 2.23±0.12 eV, b-axis 1.78±0.12 eV, c-axis 1.55±0.16 eV, basal plane 1.91±0.08 eV. Despite higher a-axis barriers, equivalent a-axis paths yield diffusion comparable to c-axis at 6000 K.
• Seismic velocity anisotropy in FeH0.25 changes with temperature: as T rises from 0 to 4000 K, Vp along c decreases and compressional anisotropy reaches a minimum of about 3.9%. From 4000 to 6000 K, the a-axis becomes the fastest direction and anisotropy increases, reaching about 5.3% at 6000 K. Increasing hydrogen content can reverse the fastest direction; FeH0.0625 retains fastest Vp along c akin to pure hcp-Fe, whereas higher H contents reverse it.
• Under external electric fields (NNP-NEMD at 360 GPa, 6000 K), H diffusion is promoted along the field direction, and the internal energy is lower when the crystal c-axis is parallel to the field. The energy difference grows with time, implying that even weak inner-core fields can produce significant cumulative energetic preference for alignment.
• External-field-driven orientational ionic flux in superionic Fe–H induces diffusion-induced stress (DIS). At inner-core temperatures (above recrystallization for Fe alloys), DIS promotes recrystallization and grain growth, aligning grains with c-axes toward the electric field direction.
• Geomagnetic implications: The poloidal magnetic field component can penetrate the inner core, with associated azimuthal electrical currents. Near the ICB (shallow IC), combined effects of poloidal and toroidal fields and other mass fluxes lead to isotropic H diffusion, consistent with the isotropic UIC. Deeper, the field-driven alignment yields textures that produce seismic anisotropy matching observations, including faster polar Vp than equatorial, depth-dependent changes, and features of the IMIC (e.g., slowest directions at angles around −45° to −50° from the rotation axis). The model explains hemispherical and depth-dependent anisotropy patterns and links inner-core texture to the geomagnetic field.

The results identify anisotropic superionic diffusion of hydrogen in hcp Fe–H as a mechanism that, under external electric fields, produces energetically favored crystal orientations. Because the inner core is permeated by poloidal geomagnetic fields and associated electric currents, this mechanism naturally drives lattice-preferred orientation with c-axes aligned relative to the field. The ensuing elastic anisotropy reproduces key seismological signatures: faster polar than equatorial compressional velocities, depth variation in anisotropy, and distinct behavior in the UIC versus the IMIC. The model also rationalizes why the UIC can be isotropic (mixed influences of poloidal/toroidal fields and other fluxes near the ICB) while the deeper core becomes strongly anisotropic as the poloidal field dominates diffusion alignment. Thus, the work provides a unifying framework that couples inner-core structure to geomagnetic field dynamics via superionic transport, without requiring extremely high viscosities or persistent solidification textures.

This study proposes and quantifies a geomagnetic-field-driven alignment mechanism in superionic Fe–H, rooted in anisotropic hydrogen diffusion with the lowest barriers along the c-axis. Molecular dynamics (ab initio and neural-network) and elastic calculations show that external electric fields lower internal energy when the c-axis aligns with the field and generate diffusion-induced stress that promotes recrystallization into aligned textures. Considering poloidal field penetration into the inner core, the mechanism explains isotropy of the UIC, depth-dependent anisotropy, and IMIC features, as well as faster polar seismic velocities. The findings suggest a strong coupling between the inner-core anisotropic texture and the geomagnetic field.

• The structure and intensity of the core magnetic field are poorly constrained; downward extrapolations from the surface and model-based inferences introduce uncertainty in field geometry and strength at depth.
• The analysis does not consider potential tilting of the poloidal field component, which could affect alignment geometry.
• Near the ICB, additional processes (toroidal fields, thermal/viscous convection, concentration gradients) may influence diffusion and texture, complicating simple alignment predictions.
• Computational models focus on FeH0.25 (with some composition variations) and rely on AIMD-trained NNPs; real inner-core compositions and multicomponent effects may introduce additional complexities not explicitly modeled.