Effects of electron correlations on transport properties of iron at Earth’s core conditions

Based on first-principles resistivity calculations, it was recently concluded that the thermal conductivity of iron in Earth’s core was too high to sustain thermal convection, thus invalidating such geodynamo models; new calculations including electron correlations find that electron–electron scattering is comparable to the electron–phonon scattering at high temperatures in iron, doubling the expected resistivity, and reviving conventional geodynamo models. Conductivity of the core Numerical calculations based on density functional theory and electron–phonon scattering have recently been used to predict that the conductivity of iron at the pressure and temperature conditions of the Earth's core is substantially higher than previously thought, to the point that it would be difficult to sustain the geodynamo with thermal convection. But now Peng Zhang et al . have combined a self-consistent density functional theory with dynamical mean-field theory, and find that electron–electron scattering is comparable to electron–phonon scattering at such high temperatures. They predict a lower conductivity for iron at core conditions compared to the earlier calculations, which is once again consistent with thermal convection driving the geodynamo. Earth’s magnetic field has been thought to arise from thermal convection of molten iron alloy in the outer core, but recent density functional theory calculations have suggested that the conductivity of iron is too high to support thermal convection 1 , 2 , 3 , 4 , resulting in the investigation of chemically driven convection 5 , 6 . These calculations for resistivity were based on electron–phonon scattering. Here we apply self-consistent density functional theory plus dynamical mean-field theory (DFT + DMFT) 7 to iron and find that at high temperatures electron–electron scattering is comparable to the electron–phonon scattering, bringing theory into agreement with experiments and solving the transport problem in Earth’s core. The conventional thermal dynamo picture is safe. We find that electron–electron scattering of d electrons is important at high temperatures in transition metals, in contrast to textbook analyses since Mott 8 , 9 , and that 4 s electron contributions to transport are negligible, in contrast to numerous models used for over fifty years. The DFT+DMFT method should be applicable to other high-temperature systems where electron correlations are important.