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.
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