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Large-scale coherent magnetic fields in the intergalactic medium are presumedto play a key role in the formation and evolution of the cosmic web, and inlarge scale feedback mechanisms. However, they are theorized to be extremelyweak, in the nano-Gauss regime. To search for a statistical signature of theseweak magnetic fields we perform a cross-correlation between the Faradayrotation measures of 1742 radio galaxies at $z > 0.5$ and large-scale structureat $0.1 < z< 0.5$, as traced by 18 million optical and infrared foregroundgalaxies. No significant correlation signal was detected within the uncertaintylimits. We are able to determine model-dependent $3 \sigma$ upper limits on theparallel component of the mean magnetic field strength of filaments in theintergalactic medium of $\sim 30 \ \mathrm{nG}$ for coherence scales between$1$ and $2.5 \ \mathrm{Mpc}$, corresponding to a mean upper bound RMenhancement of $\sim 3.8 \ \mathrm{rad/m^{2}}$ due to filaments along allprobed sight-lines. These upper bounds are consistent with upper bounds foundpreviously using other techniques. Our method can be used to further constrainintergalactic magnetic fields with upcoming future radio polarization surveys.

Constraints on Large-Scale Magnetic Fields in the Intergalactic Medium Using Cross-Correlation Methods