  We present new generation mechanisms of magnetic fields in supernova remnant
shocks propagating to partially ionized plasmas in the early universe. Upstream
plasmas are dissipated at the collisionless shock, but hydrogen atoms are not
dissipated because they do not interact with electromagnetic fields. After the
hydrogen atoms are ionized in the shock downstream region, they become cold
proton beams that induce the electron return current. The injection of the beam
protons can be interpreted as an external force acting on the downstream proton
plasma. We show that the effective external force and the electron return
current can generate magnetic fields without any seed magnetic fields. The
magnetic field strength is estimated to be $B\sim 10^{-14}-10^{-11}~{\rm G}$,
where the characteristic lengthscale is the mean free path of charge exchange,
$\sim 10^{15}~{\rm cm}$. Since protons are marginally magnetized by the
generated magnetic field in the downstream region, the magnetic field could be
amplified to larger values and stretched to larger scales by turbulent dynamo
and expansion.
