  We show that a primeval seed magnetic field arises due to spin-degeneracy
breaking of fermions caused by the dragging of inertial frames in the curved
spacetime of rotating astrophysical bodies. This seed magnetic field would
arise even due to electrically neutral fermions such as neutrons. As an
example, we show that an ideal neutron star rotating at $500$ revolutions per
second, having mass $0.83$ M$_{\odot}$ and described by an ensemble of
degenerate neutrons, would have $0.12$ Gauss seed magnetic field at its center
arising through the breaking of spin-degeneracy.
