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We present our first results on a new sample containing all single G,K and Mgiants down to V = 4 mag in the Solar vicinity, suitable forspectropolarimetric (Stokes V) observations with Narval at TBL, France. Fordetection and measurement of the magnetic field (MF), the Least SquaresDeconvolution (LSD) method was applied (Donati et al. 1997) that in the presentcase enables detection of large-scale MFs even weaker than the solar one (thetypical precision of our longitudinal MF measurements is 0.1-0.2 G). Theevolutionary status of the stars is determined on the basis of the evolutionarymodels with rotation (Lagarde et al. 2012; Charbonnel et al., in prep.) andfundamental parameters given by Massarotti et al. (1998). The stars appear tobe in the mass range 1-4 M_sun, situated at different evolutionary stages afterthe Main Sequence (MS), up to the Asymptotic Giant Branch (AGB). The samplecontains 45 stars. Up to now, 29 stars are observed (that is about 64 % of thesample), each observed at least twice. For 2 stars in the Hertzsprung gap, oneis definitely Zeeman detected. Only 5 G and K giants, situated mainly at thebase of the Red Giant Branch (RGB) and in the He-burning phase are detected.Surprisingly, a lot of stars ascending towards the RGB tip and in early AGBphase are detected (8 of 13 observed stars). For all Zeeman detected stars vsin i is redetermined and appears in the interval 2-3 km/s, but few giants withMF possess larger v sin i.

Magnetic fields in single late-type giants in the Solar vicinity: How common is magnetic activity on the giant branches?