  The aim of this work is to investigate the average properties of the
intra-cluster medium (ICM) magnetic fields, and to search for possible
correlations with the ICM thermal properties and cluster radio emission. We
have selected a sample of 39 massive galaxy clusters from the HIghest X-ray
FLUx Galaxy Cluster Sample, and used Northern VLA Sky Survey data to analyze
the fractional polarization of radio sources out to 10 core radii from the
cluster centers. Following Murgia et al (2004), we have investigated how
different magnetic field strengths affect the observed polarized emission of
sources lying at different projected distances from the cluster center. In
addition, statistical tests are performed to investigate the fractional
polarization trends in clusters with different thermal and non-thermal
properties. We find a trend of the fractional polarization with the cluster
impact parameter, with fractional polarization increasing at the cluster
periphery and decreasing toward the cluster center. Such trend can be
reproduced by a magnetic field model with central value of few $\mu$G. The
logrank statistical test indicates that there are no differences in the
depolarization trend observed in cluster with and without radio halo, while the
same test indicates significant differences when the depolarization trend of
sources in clusters with and without cool core are compared. The comparison
between clusters with high and low temperatures does not yields significant
differences. Although therole of the gas density should be better accounted
for, these results give important indications for models that require a role of
the ICM magnetic field to explain the presence of cool core and radio halos in
galaxy clusters.
