  Analysis of high-resolution spectropolarimetric observations of early-type
magnetic stars is currently the most advanced method of obtaining detailed
information on their surface magnetic field topologies and horizontal spot
distributions. In this study we analyse a new set of high-quality four Stokes
parameter observations of the magnetic Ap star HD119419 - a member of the 14
Myr old Lower Cen-Cru association - for the purpose of studying the surface
field topology and mapping the chemical abundance spots. We made use of the
circular and linear polarisation data collected for HD119419 with the HARPSpol
instrument at the ESO 3.6-m telescope. These observations were analysed with a
multi-line magnetic diagnostic technique and modelled in detail with a Magnetic
Doppler imaging code. We present a new set of mean longitudinal magnetic field
measurements and derive a revised stellar rotational period. We also
redetermine the basic stellar atmospheric parameters. Our four Stokes parameter
magnetic inversions reveal a moderately complex surface field topology with a
mean field strength of 18 kG and a maximum local strength of 24 kG. A poloidal
dipolar component dominates the magnetic energy spectrum of the surface field
in HD119419. However, significant contributions of the higher-order spherical
harmonic components are also present. We show that the dipole plus quadrupole
part of the reconstructed field geometry is incapable of reproducing the
observed amplitudes and shapes of the Stokes Q and U profiles. The chemical
abundance distributions of Fe, Cr, Ti, and Nd, derived self-consistently with
the magnetic field geometry, are characterised by large abundance gradients and
a lack of clear correlation with the magnetic field structure. This full Stokes
vector analysis of HD119419 extends the modern hot-star magnetic mapping
investigations to an open cluster Ap star with a well-determined age.
