Spherically symmetric Earth models yield no net electron spin

Abstract

Terrestrial experiments that use electrons in Earth as a spin-polarized source have been demonstrated to provide strong bounds on exotic long-range spin-spin and spin-velocity interactions. These bounds constrain the coupling strength of many proposed ultralight bosonic dark-matter candidates. Recently, it was pointed out that a monopole-dipole coupling between the Sun and the spin-polarized electrons of Earth would result in a modification of the precession of the perihelion of Earth. Using an estimate for the net spin polarization of Earth and experimental bounds on Earth’s perihelion precession, interesting constraints were placed on the magnitude of this monopole-dipole coupling. Here we investigate the spin associated with Earth’s electrons. We find that there are about 6×1041 spin-polarized electrons in the mantle and crust of Earth oriented antiparallel to their local magnetic field. However, when integrated over any spherically symmetric Earth model, we find that the vector sum of these spins is zero. In order to establish a lower bound on the magnitude of the net spin along Earth’s rotation axis we have investigated three of the largest breakdowns of Earth’s spherical symmetry: the large low shear-velocity provinces of the mantle, the crustal composition, and the oblate spheroid of Earth. From these investigations we conclude that there are at least 5×1038 spin-polarized electrons aligned antiparallel to Earth’s rotation axis. This analysis suggests that the bounds on the monopole-dipole coupling that were extracted from Earth’s perihelion precession need to be relaxed by a factor of about 2000. Published by the American Physical Society 2025