  M dwarfs are the most numerous stars in our Galaxy with masses between
approximately 0.5 and 0.1 solar mass. Many of them show surface activity
qualitatively similar to our Sun and generate flares, high X-ray fluxes, and
large-scale magnetic fields. Such activity is driven by a dynamo powered by the
convective motions in their interiors. Understanding properties of stellar
magnetic fields in these stars finds a broad application in astrophysics,
including, e.g., theory of stellar dynamos and environment conditions around
planets that may be orbiting these stars. Most stars with convective envelopes
follow a rotation-activity relationship where various activity indicators
saturate in stars with rotation periods shorter than a few days. The activity
gradually declines with rotation rate in stars rotating more slowly. It is
thought that due to a tight empirical correlation between X-ray and magnetic
flux, the stellar magnetic fields will also saturate, to values around ~4kG.
Here we report the detection of magnetic fields above the presumed saturation
limit in four fully convective M-dwarfs. By combining results from
spectroscopic and polarimetric studies we explain our findings in terms of
bistable dynamo models: stars with the strongest magnetic fields are those in a
dipole dynamo state, while stars in a multipole state cannot generate fields
stronger than about four kilogauss. Our study provides observational evidence
that dynamo in fully convective M dwarfs generates magnetic fields that can
differ not only in the geometry of their large scale component, but also in the
total magnetic energy.
