  A possibility to control magnetic properties by using electric fields is one
of the most desirable characteristics for spintronics applications. Finding a
suitable material remains an elusive goal, with only a few candidates found so
far. Graphene is one of them and offers a hope due to its weak spin-orbit
interaction, the ability to control electronic properties by the electric field
effect and the possibility to introduce paramagnetic centres such as vacancies
and adatoms. Here we show that adatoms magnetism in graphene is itinerant and
can be controlled by doping, so that magnetic moments can be switched on and
off. The much-discussed vacancy magnetism is found to have a dual origin, with
two approximately equal contributions: one coming from the same itinerant
magnetism and the other due to broken bonds. Our work suggests that magnetic
response of graphene can be controlled by the field effect, similar to its
transport and optical properties, and that spin diffusion length can be
significantly enhanced above a certain carrier density.

Mesoscale and Nanoscale Physics