  We show that axion domain walls gain spontaneous magnetization in early
universe by trapping either electrons or positrons with their spins polarized.
The reason is that the walls produces an attractive potential for these
particles. We argue that the wall bounded by an axionic superconducting string
leaves a magnetic field after its decay. We obtain a field $\sim 10^{-23}$
Gauss on the scale of horizon at the recombination.
