We introduce a new mechanism for generating magnetic fields in the recombination era. This Harrison-like mechanism utilizes vorticity in baryons that is sourced through the Bose-Einstein condensate of axions via gravitational interactions. The magnetic fields generated are on the galactic scales $sim 10,{rm kpc}$ and have a magnitude of the order of $Bsim10^{-23},{rm G}$ today. The field has a greater magnitude than those generated from other mechanisms relying on second order perturbation theory, and is sufficient to provide a seed for battery mechanisms.
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