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 $Bsim 10^{-14}-10^{-11}~{rm G}$, 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.
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