A silicate dynamo in the early Earth

Abstract

The Earth's magnetic field has operated for at least 3.4 billion years, yet how the ancient field was produced is still unknown. The core in the early Earth was surrounded by a molten silicate layer, a basal magma ocean that may have survived for more than one billion years. Here we use density functional theory-based molecular dynamics simulations to predict the electrical conductivity of silicate liquid at the conditions of the basal magma ocean: 100-140 GPa, and 4000-6000 K. We find that the electrical conductivity exceeds 10,000 S/m, more than 100 times that measured in silicate liquids at low pressure and temperature. The magnetic Reynolds number computed from our results exceeds the threshold for dynamo activity and the magnetic field strength is similar to that observed in the Archean paleomagnetic record. We therefore conclude that the Archean field was produced by the basal magma ocean.

Fig. 1. Electrical conductivity.

The electronic σ_el (red), ionic σ_ion (blue), and total σ_total =  σ_el +  σ_ion (green) electrical conductivity along the magma ocean isentrope (black) for low-spin (top of range shown) and high-spin (bottom of range) results. Along the magma ocean isentrope, the electrical conductivity increases with depth because the effects of increasing temperature outweigh the effects of increasing pressure. Inset. The electrical conductivity of the bulk silicate Earth liquid from our simulations, including the electronic (large symbols) and ionic (small symbols with 1σ uncertanties) contributions at 6000 K (red) and 4000 K (purple) in spin-polarized (diamonds) and non-spin-polarized (squares) calculations. Lines are best fits to the form $\sigma ={\sigma }_0{T}^{-1}\exp \left[-\left(E^{*}+P{V}^{*}\right)∕RT\right]$ for the electronic non-spin-polarized results (σ₀ = 1.994e9 S/m, E* = 108.6 kJ/mol, V* = 0.0611 cm³/mol, light solid lines) and shifted uniformly downward to account for spin-polarization (σ₀ = 1.754e9 S/m, bold solid lines), and to the ionic contribution (σ₀ = 1.0811e9 S/m, E* = 131.0 kJ/mol, V* = 0.437 cm³/mol, dashed lines).

Fig. 2. Electronic density of states in the silicate liquid.

At 100 GPa and 6000 K in spin-polarized (a) and non-spin-polarized (b) states. Contributions from s- (blue), p- (green) and d-like (red) states are shown separately and the dominant atomic contributions to each are indicated. The vertical black line is the Fermi level.

Fig. 3. Magnetic Reynolds number and magnetic field strength.

a The magnetic Reynolds number (red) and Dynamo number (blue) computed from our electrical conductivity results and thermal evolution model with shading indicating the difference between low-spin (top of range) and high-spin (bottom of range) results compared with the respective critical values of R_m = 40 and D = 100 (thick horizontal lines). b Magnetic field strength computed from our model (red line) compared with paleomagnetic data: diamonds from the PINT database, and circles (Thellier–Coe method) and squares (565C method) from zircons. We note that the evidence of a field prior to the oldest whole-rock PINT data at 3.45 Ga relies on the single-crystal zircon results, which have been questioned as not deriving from a primary magnetic carrier.