The XXL Survey: XXXIX. Polarised radio sources in the XXL-South field
  Aims: We investigate the properties of the polarised radio population in the
central 6.5 deg$^{2}$ of the XXL-South field observed at 2.1 GHz using the
Australia Telescope Compact Array (ATCA) in 81 pointings with a synthesised
beam of FWHM 5.2''. We also investigate the ATCA's susceptibility to
polarisation leakage.
  Methods: We performed a survey of a 5.6 deg$^{2}$ subregion and calculated
the number density of polarised sources. We derived the total and polarised
spectral indices, in addition to comparing our source positions with those of
X-ray-detected clusters. We measured the polarisation of sources in multiple
pointings to examine leakage in the ATCA.
  Results: We find 39 polarised sources, involving 50 polarised source
components, above a polarised flux density limit of 0.2 mJy at 1.332 GHz. The
number density of polarised source components is comparable with recent
surveys, although there is an indication of an excess at $\sim1$ mJy. We find
that those sources coincident with X-ray clusters are consistent in their
properties with regard to the general population. In terms of the ATCA leakage
response, we find that ATCA mosaics with beam separation of $\lesssim 2/3$ of
the primary beam FWHM have off-axis linear polarisation leakage $\lesssim 1.4$
% at 1.332 GHz.
