Picogauss magnetic fields in voids from ultra-high energy cosmic rays
  We argue that ultra-high energy cosmic rays emitted by galaxy clusters result
in electric currents in filaments of the large-scale structure that are
sufficient to generate magnetic fields in voids of the magnitude of ~1e-12 G
and the coherence length of up to tens of Mpc. These fields satisfy both the
lower and upper observational bounds on magnetic fields in voids without a need
of any primordial component.
