  Magnetism is a prototypical phenomenon of quantum collective state, and has
found ubiquitous applications in semiconductor technologies such as dynamic
random access memory (DRAM). In conventional materials, it typically arises
from the strong exchange interaction among the magnetic moments of d- or
f-shell electrons. Magnetism, however, can also emerge in perfect lattices from
non-magnetic elements. For instance, flat band systems with high density of
states (DOS) may develop spontaneous magnetic ordering, as exemplified by the
Stoner criterion. Here we report tunable magnetism in rhombohedral-stacked
few-layer graphene (r-FLG). At small but finite doping (n~10^11 cm-2), we
observe prominent conductance hysteresis and giant magnetoconductance that
exceeds 1000% as a function of magnetic fields. Both phenomena are tunable by
density and temperature, and disappears for n>10^12 cm-2 or T>5K. These results
are confirmed by first principles calculations, which indicate the formation of
a half-metallic state in doped r-FLG, in which the magnetization is tunable by
electric field. Our combined experimental and theoretical work demonstrate that
magnetism and spin polarization, arising from the strong electronic
interactions in flat bands, emerge in a system composed entirely of carbon
atoms. The electric field tunability of magnetism provides promise for
spintronics and low energy device engineering.
