  Both magnetic fields and photospheric/atmospheric dynamics can be involved in
triggering the important mass loss observed in evolved cool stars. Previous
works have revealed that these objects exhibit a magnetic field extending
beyond their surface. The origin of this magnetic field is still under debate
with mechanisms involving a turbulent dynamo, convection, stellar pulsation,
and cool spots. Our goal is to estimate the magnetic field strength in the
inner circumstellar envelope of six evolved cool stars (five Miras and one Red
Supergiant). Combining this work with previous studies, we tentatively
constrain the global magnetic field type observed and shed light on the
mechanisms at its origin. Using the XPOL polarimeter installed at the IRAM-30 m
telescope, we observed the 28 SiO v = 1, J = 2-1 maser line emission and
obtained simultaneous spectroscopic measurements of the four Stokes parameters.
Applying a careful calibration method for Stokes Q, U, and V, we derive
estimates of the magnetic field strength from the circular and linear
polarization fractions considering the saturated and unsaturated maser cases
under the Zeeman hypothesis. Magnetic field strengths from several Gauss up to
several tens of Gauss are derived. These new and more accurate measurements
constraining the field strength in the 2-5 stellar radii region better than
previous studies and seem to exclude a global poloidal magnetic field type. A
combination of a toroidal and a poloidal field is nevertheless not excluded. A
variation of the magnetic field strength over a two-months timescale is
observed in one Mira star which suggests a possible link to the stellar phase,
i.e. with pulsation/photospheric activity.
