  Non-abelian gauge theories may have a ferromagnet-like vacuum with a non-zero
magnetic field, which also exists at finite temperature. We argue that the
formation of the ferromagnet-like vacuum at GUT scales gives rise to a Maxwell
magnetic field imprinted on the comoving plasma, and that it is energetically
favourable to align the field in different correlation volumes. This results in
a coherent magnetic field pertaining the whole universe, with a magnitude
$B_{now}\simeq 10^{-14}\G$, which is of the correct size to serve as the seed
field for the galactic dynamo.
