  Several arguments have been presented that favour a scenario in which the low
detection rate of magnetic fields in Herbig Ae stars can be explained by the
weakness of these fields and rather large measurement uncertainties.
Spectropolarimetric studies involving sharp-lined Herbig Ae stars appear to be
promising for the detection of such weak magnetic fields. These studies offer a
clear spectrum interpretation with respect to the effects of blending, local
velocity fields, and chemical abundances, and allow us to identify a proper
sample of spectral lines appropriate for magnetic field determination.
High-resolution spectropolarimetric observations of the three sharp-lined
Herbig Ae stars HD101412, HD104237, and HD190073 have been obtained in recent
years with the HARPS. We used these archival observations to investigate the
behaviour of their longitudinal magnetic fields. To carry out the magnetic
field measurements, we used the multi-line singular value decomposition method.
We discovered that different line lists for HD101412 yield differences in both
the shape of the Stokes V signatures and their field strengths. They could be
interpreted in the context of the impact of the circumstellar matter and
elemental abundance inhomogeneities on the measurements of the magnetic field.
Due to the small size of the Zeeman features on the first three epochs and the
lack of near-IR observations, circumstellar and photospheric contributions
cannot be estimated unambiguously. In the Stokes V spectrum of HD104237, we
detect that the secondary component, a T Tauri star, possesses a rather strong
magnetic field <B_z>=129G, while no significant field is present in the primary
component. Our measurements of HD190073 confirm the presence of a variable
magnetic field and indicate that the circumstellar environment may have a
significant impact on the observed polarization features.
