  Atmospheric magnetic fields in stars with convective envelopes heat stellar
chromospheres. Starting with the historical Mount Wilson monitoring program,
CaH&K lines have been widely used to trace stellar magnetic activity, and as a
proxy for rotation period and consequently for stellar age. Monitoring stellar
activity has also become essential in filtering out false-positives due to
magnetic activity in extra-solar planet surveys. The Ca H&Kemission is
traditionally quantified through the R'HK-index, which compares the
chromospheric flux in the doublet to the overall bolometric flux of the star.
Much work has been done to characterize this index for FGK-dwarfs, but M-dwarfs
were left out of these analyses and no calibration of their Ca ii H&K emission
to an R'HK exists to date. We set out to characterize the magnetic activity of
the low and very low-mass stars by providing a calibration of the R'HK-index
that extends to the realm of M-dwarfs, and by evaluating the relation between
R'HK and the rotation period. We calibrated the bolometric and photospheric
factors for M-dwarfs to properly transform the S-index into the R'HK. We
monitored magnetic activity through the Ca ii H&K emission lines in the HARPS
M-dwarf sample. The R'HK index, like the fractional X-ray luminosity L_X/Lbol,
shows a saturated correlation with rotation, with saturation setting in around
a ten days rotation period. Above that period, slower rotators show weaker Ca
ii activity, as expected. Under that period, the R'HK index saturates to
~10^-4. Stellar mass modulates the Ca ii activity, with R'HK showing a constant
basal activity above 0.6Msun and then decreasing with mass between 0.6Msun and
the fully-convective limit of 0.35Msun. Short-term variability of the activity
correlates with its mean level, stars with higher R'HK index show larger R'HK
variability, as previously observed for earlier spectral types.
