  Although it is assumed that magnetic fields in accretion disks are dragged
from the interstellar medium, the idea is likely not applicable to primordial
black holes (PBHs) formed in the early universe. Here we show that magnetic
fields can be generated in initially unmagnetized accretion disks around PBHs
through the Biermann battery mechanism, and therefore provide the small scale
seeds of magnetic field in the universe. The radial temperature and vertical
density profiles of these disks provide the necessary conditions for the
battery to operate naturally. The generated seed fields have a toroidal
structure with opposite sign in the upper and lower half of the disk. In the
case of a thin accretion disk around a rotating PBH, the field generation rate
increases with increasing PBH spin. At a fixed $r/r_{\rm isco}$, where $r$ is
the radial distance from the PBH and $r_{\rm isco}$ is the radius of the
innermost stable circular orbit, the battery scales as $M^{-9/4}$, where $M$ is
the PBH's mass. The very weak dependency of the battery on accretion rate,
makes this mechanism a viable candidate to provide seed fields in an initially
unmagnetized accretion disk, following which the magnetorotational instability
could take over.
