  We theoretically argue that, in doped AB bilayer graphene, the
electron-electron coupling can give rise to the spontaneous formation of
fractional metal phases. These states, being generalizations of a more common
half-metal, have a Fermi surface that is perfectly polarized not only in terms
of a spin-related quantum number, but also in terms of the valley index. The
proposed mechanism assumes that the ground state of undoped bilayer graphene is
a spin density wave insulator, with a finite gap in the single-electron
spectrum. Upon doping, the insulator is destroyed, and replaced by a fractional
metal phase. As doping increases, transitions between various types of
fractional metal (half-metal, quarter-metal, etc.) are triggered. Our findings
are consistent with recent experiments on doped AB bilayer graphene, in which a
cascade of phase transitions between different isospin states was observed.
