Title: Probing intergalactic intergalactic magnetic fields with LOFAR LoTSS DR2 data

Abstract: We use Faraday rotation measurements from the latest catalog LoTSS DR2 from LOFAR to probe intergalactic magnetic fields. To identify the extragalactic component of the observed rotation measure (RM) we use two different techniques: residual rotation measure (RRM) and close radio pairs. For the RRM approach, we conclude that, despite smaller measurement errors in the LOFAR data, robust and conservative treatment of the systematic uncertainties in the Galactic contribution to RM results in the constraint on a homogeneous volume-filling magnetic field at the level 2.4 nG, slightly weaker than previous constraints from NVSS data, and does not allow to probe the presence of over-magnetized bubbles predicted by the AGN feedback model of the IllustrisTNG. Analyzing close radio pairs we found that in only 0.5% of our mock realizations of observed data, the expected contribution from the over-magnetized bubbles does not exceed LoTSS DR2 data.