We present a mechanism for generating cosmological magnetic fields during the Epoch of Reionization, based on the photoionization of intergalactic hydrogen. A general formula is presented, together with an example numerical application which yields magnetic field strengths between 10-~(23) to 10~(-19) G on intersource scales. This mechanism, which operates all along Reionization around any ionizing source, participates to the premagnetization of the whole intergalactic medium. Also, the spatial configuration of these fields may help discriminate them from those produced by other mechanisms in future observations.
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