The application of high-resolution spectropolarimetry has led to major progress in understanding the magnetism and activity of late- type stars. During the last decade, magnetic fields have been discovered and mapped for many types of active cool stars using spectropolarimetric data. However, these observations and modeling attempts are fundamentally incomplete since they are based on the interpretation of the circular polarization alone. Taking advantage of the newly built HARPS polarimeter, we have obtained the first systematic observations of several cool active stars in all four Stokes parameters. Here we report the detection of magnetically induced linear polarization for the primary component of the very active RS CVn binary HR 1099 and for the moderately active K dwarf ensuremathın Eri. For both stars the amplitude of linear polarization signatures is measured to be åisebox-0.5ex~10$^-4$ of the unpolarized continuum, which is approximately a factor of 10 lower than for circular polarization. This is the first detection of the linear polarization in line profiles of cool active stars. Our observations of the inactive solar-like star ensuremathα Cen A show neither circular nor linear polarization above the level of i̊sebox-0.5ex~10$^-5$, indicating the absence of a net longitudinal magnetic field stronger than 0.2 G.
Based on observations obtained at the European Southern Observatory (ESO programs 083.D-1000(A) and 084.D-0338(A)).