  We present a study of the magnetic field properties of NGC 4038/9 (the
`Antennae' galaxies), the closest example of a late stage merger of two spiral
galaxies. Wideband polarimetric observations were performed using the Karl G.
Jansky Very Large Array between 2 and 4 GHz. Rotation measure synthesis and
Faraday depolarization analysis was performed to probe the magnetic field
strength and structure at spatial resolution of $\sim1$ kpc. Highly polarized
emission from the southern tidal tail is detected with intrinsic fractional
polarization close to the theoretical maximum ($0.62\pm0.18$), estimated by
fitting the Faraday depolarization with a volume that is both synchrotron
emitting and Faraday rotating containing random magnetic fields. Magnetic
fields are well aligned along the tidal tail and the Faraday depths shows
large-scale smooth variations preserving its sign. This suggests the field in
the plane of the sky to be regular up to $\sim20$ kpc, which is the largest
detected regular field structure on galactic scales. The equipartition field
strength of $\sim8.5~\mu$G of the regular field in the tidal tail is reached
within a few 100 Myr, likely generated by stretching of the galactic disc field
by a factor of 4--9 during the tidal interaction. The regular field strength is
greater than the turbulent fields in the tidal tail. Our study comprehensively
demonstrates, although the magnetic fields within the merging bodies are
dominated by strong turbulent magnetic fields of $\sim20~\mu$G in strength,
tidal interactions can produce large-scale regular field structure in the
outskirts.
