Regular magnetic orders in triangular and kagome lattices

We investigate the possibleregular magnetic order(RMO) for the spin models with globalO(3) spin rotation, based on a group theoretical approach for triangular and kagome lattices. The main reason to study these RMOs is that they are good variational candidates for the ground states of many specific models. In this work, we follow the prescription introduced by Messioet al(2011Phys. Rev.B83184401) for thep6mgroup and extended their work for different subgroups ofp6m, i.e.,p6,p3,p3m1, andp31m. We list all the possible regular magnetic orders for triangular and kagome lattices, which fall into the category of these groups. We calculate the energies and the spin structure factors for each of these states.