Electrical Conductivity of Multi-Component Silicate Melt in the Magma Ocean

The electrical conductivity of silicate melts is well studied at low pressure where it is known to be low and dominated by ionic charge carriers. The observation that oxide melts become reflective on shock compression suggests that electrical conductivity may be much greater in the deep magma ocean and that electrons may be the dominant charge carriers. However, the conductivity has not been measured at the relevant conditions and existing theory has focused on compositionally simple end member systems. Here we compute the electrical conductivity of a six component silicate melt from first principles. We use DFT+U molecular dynamics with and without spin polarization combined with the Kubo-Greenwood formula. The composition is chosen to be representative of the bulk silicate earth and contains SiO2, MgO, FeO, CaO, Al2O3, and Na2O. At 100 GPa, and 5000 K, we find that the electrical conductivity exceeds 1000 S/m. The magma ocean may be capable of producing a magnetic field in the earliest stages of Earth's evolution when the metallic iron-rich core is not able to cool quickly enough to sustain a dynamo. The key requirement is that the electrical conductivity of silicate melt exceed 1000 S/m, a condition that our results satisfy.