Protonic thermoelectric effect of Superionic H$_2$O and magnetic field generation in Uranus and Neptune
The origin of the anomalous magnetic fields of Uranus and Neptune, with significant tilts and multi-dipole configurations, is central to understanding the internal structure and evolution of the ice giants. Recent investigations confirmed that superionic H$_2$O ice is thermodynamically stable and constitutes the dominant H$_2$O phase within their icy mantles. Here, we use deep learning and ab initio molecular dynamics to investigate the thermal and protonic transport properties of superionic H$_2$O ice. We demonstrate that superionic H$_2$O ice exhibits a pronounced protonic thermoelectric effect, with a maximum Seebeck coefficient that can reach $\sim 620$ $μ$V K$^{-1}$ within the interior of Uranus, whereas Neptune's is lower, within the range of 570-585 $μ$V K$^{-1}$. Consequently, the temperature gradients in the icy mantles can induce proton migration, thereby driving magnetic field generation. Based on this mechanism, and within a dipolar approximation that captures the mean field, the disparities in mean dipolar magnetic field strength between Uranus and Neptune can be explained exclusively by their differing internal temperature gradients, and the predicted mean field strengths are comparable to those observed by Voyager 2.