  We study the effects of galaxy formation physics on the magnetization of the
intergalactic medium (IGM) using the IllustrisTNG simulations. We demonstrate
that large-scale regions affected by the outflows from galaxies and clusters
contain magnetic fields that are several orders of magnitude stronger than in
unaffected regions with the same electron density. Moreover, like magnetic
fields amplified inside galaxies, these magnetic fields do not depend on the
primordial seed, i.e. the adopted initial conditions for magnetic field
strength. We study the volume filling fraction of these strong field regions
and their occurrence in random lines of sight. As a first application, we use
these results to put bounds on the photon-axion conversion from spectral
distortion of the CMB. As photon-axion coupling grows with energy, stronger
constraints could potentially be obtained using data on the propagation of
gamma-ray photons through the IGM. Finally, we also briefly discuss potential
applications of our results to the Faraday Rotation measurements.
