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Giant radio galaxies (GRGs) are physically large radio sources that extendwell beyond their host galaxy environment. Their polarization properties areaffected by the poorly constrained magnetic field that permeates theintergalactic medium on Mpc scales. A low frequency ($<$ 200 MHz) polarizationstudy of this class of radio sources is now possible with LOFAR. Here weinvestigate the polarization properties and Faraday rotation measure (RM) of acatalog of GRGs detected in the LoTSS. This is the first low-frequencypolarization study of a large sample of radio galaxies selected on theirphysical size. We explore the magneto-ionic properties of their under-denseenvironment and probe intergalactic magnetic fields using the Faraday rotationproperties of their radio lobes. We use RM synthesis in the 120-168 MHz band tosearch for polarized emission and to derive the RM and fractional polarizationof each detected source component. We study the depolarization between 1.4 GHzand 144 MHz using images from the NVSS. From a sample of 240 GRGs, we detected37 sources in polarization, all with a total flux density above 56 mJy. Thefractional polarization of the detected GRGs at 1.4 GHz and 144 MHz isconsistent with a small amount of Faraday depolarization (a Faraday dispersion$<$ 0.3 rad m$^{-2}$). Our analysis shows that the lobes are expanding into alow-density ($<10^{-5}$ cm$^{-3}$) local environment permeated by weak magneticfields ($<$0.1 $\mu$G) with fluctuations on scales of 3 to 25 kpc. The presenceof foreground galaxy clusters appears to influence the polarization detectionrate up to 2R$_{500}$. In general, this work demonstrates the ability of LOFARto quantify the rarefied environments in which these GRGs exist and highlightsthem as an excellent statistical sample to use as high precision probes ofmagnetic fields in the intergalactic medium and the Milky Way.

The LOFAR view of intergalactic magnetic fields with giant radio galaxies