Context : Analysis of high-resolution spectropolarimetric time-series 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 .

Aims : In this study we analyse a new set of high-quality four Stokes parameter observations of the magnetic Ap star HD 119419 – 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 .

Methods : We made use of the circular and linear polarisation data collected for HD 119419 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 .

Results : We present a new set of high-precision mean longitudinal magnetic field measurements and derive a revised stellar rotational period by comparing our measurements with the literature data .
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 HD 119419 .
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 .

Conclusions : This full Stokes vector analysis of HD 119419 extends the modern hot-star magnetic mapping investigations to an open cluster Ap star with a well-determined age .
Further Magnetic Doppler imaging studies of cluster members will allow us to study the field topologies and chemical abundance spots as a function of stellar age .