Evidence repeatedly suggests that cosmological sheets, filaments and voids may be substantially magnetised today. The origin of magnetic fields in the intergalactic medium is however currently uncertain. We discuss a magnetogenesis mechanism based on the exchange of momentum between hard photons and electrons in an inhomogeneous intergalactic medium. Operating near ionising sources during the epoch of reionisation, it is capable of generating magnetic seeds of relevant strengths over scales comparable to the distance between ionising sources. Furthermore, when the contributions of all ionising sources and the distribution of gas inhomogeneities are taken into account, it leads, by the end of reionisation, to a level of magnetisation that may account for the current magnetic fields strengths in the cosmic web.
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