  In the standard model there are charges with abelian anomaly only (e.g.
right-handed electron number) which are effectively conserved in the early
universe until some time shortly before the electroweak scale. A state at
finite chemical potential of such a charge, possibly arising due to asymmetries
produced at the GUT scale, is unstable to the generation of hypercharge
magnetic field. Quite large magnetic fields ($\sim 10^{22}$ gauss at $T\sim
100$ GeV with typical inhomogeneity scale $ \sim \frac{ 10^6}{T}$) can be
generated. These fields may be of cosmological interest, potentially acting as
seeds for amplification to larger scale magnetic fields through non-linear
mechanisms. Previously derived bounds on exotic $B-L$ violating operators may
also be evaded.
