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 $6 \times 10^{41}$ spin-polarized electrons in the mantle and crust of Earth oriented anti-parallel 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 $5 \times 10^{38}$ spin-polarized electrons aligned anti-parallel 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.