  We show that the spin-density wave state on the partially filled honeycomb
and triangular lattices is preempted by a paramagnetic phase that breaks an
emergent Z_4 symmetry of the system, associated with the four inequivalent
arrangements of spins in the quadrupled unit cell. Unlike other emergent
paramagnetic phases in itinerant and localized-spin systems, this state
preserves the rotational symmetry of the lattice but breaks its translational
symmetry, giving rise to a super-lattice structure that can be detected by
scanning tunneling microscopy. This emergent phase also has distinctive
signatures in the magnetic spectrum that can be probed experimentally.
