To search for a signature of an intracluster magnetic field, we compare measurements of Faraday rotation of polarised extragalactic radio sources in the line of sight of galaxy clusters with those outside. We correlated a catalogue of 1383 rotation measures (RM) of extragalactic polarised radio sources with X-ray luminous galaxy clusters from the CLASSIX survey (combining REFLEX II and NORAS II). We compared the RM in the line of sight of clusters within their projected radii of r_500 with those outside and found a significant excess of the dispersion of the RM in the cluster regions. Since the observed RM is the result of Faraday rotation in several presumably uncorrelated magnetised cells of the intracluster medium, the observations correspond to quantities averaged over several magnetic field directions and strengths. Therefore the interesting quantity is the standard deviation of the RM for an ensemble of clusters. We found a standard deviation of the RM inside r_500 of about 120 +- 21 rad m^-2. This compares to about 56 +- 8 rad m^-2 outside. We show that the most X-ray luminous and thus most massive clusters contribute most to the observed excess RM. Modelling the electron density distribution in the intracluster medium with a self-similar model, we found that the dispersion of the RM increases with the column density, and we deduce a magnetic field value of about 2 - 6 (l/10kpc)^-1/2 microG assuming a constant magnetic field strength, where l is the size of the coherently magnetised intracluster medium cells. This magnetic field energy density amounts to a few percent of the average thermal energy density in clusters. When we assumed the magnetic energy density to be a constant fraction of the thermal energy density, we deduced a slightly lower value for this fraction of 3 - 10 (l/10kpc)^-1/2 per mille.
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