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We consider a system of 2D fermions on a triangular lattice with wellseparated electron and hole pockets of similar sizes, centered at certainhigh-symmetry-points in the Brillouin zone. We first analyze Stoner-typespin-density-wave (SDW) magnetism. We show that SDW order is degenerate at themean-field level. Beyond mean-field, the degeneracy is lifted and is either$120^{\circ}$ "triangular" order (same as for localized spins), or a collinearorder with antiferromagnetic spin arrangement on two-thirds of sites, andnon-magnetic on the rest of sites. We also study a time-reversal symmetricdirectional spin bond order, which emerges when some interactions are repulsiveand some are attractive. We show that this order is also degenerate at amean-field level, but beyond mean-field the degeneracy is again lifted. We nextconsider the evolution of a magnetic order in a magnetic field starting from anSDW state in zero field. We show that a field gives rise to a canting of an SDWspin configuration. In addition, it necessarily triggers the directional bondorder, which, we argue, is linearly coupled to the SDW order in a finite field.We derive the corresponding term in the Free energy. Finally, we consider theinterplay between an SDW order and superconductivity and charge order. Forthis, we analyze the flow of the couplings within parquet renormalization group(pRG) scheme. We show that magnetism wins if all interactions are repulsive andthere is little energy space for pRG to develop. However, if system parametersare such that pRG runs over a wide range of energies, the system may developeither superconductivity or an unconventional charge order, which breakstime-reversal symmetry.

Itinerant fermions on a triangular lattice: unconventional magnetism and other ordered states