The J1-J2 model on the face-centered-cubic lattices

The antiferromagnetic systems on the face-centered-cubic lattices are studied in detail by the Heisenberg J1-J2 model by the Green's function method. The studied configurations contain the well-known three ones, called type-I, II and III, respectively, and an intermediate one suggested from experiment of MnSe2. Our results show that the intermediate configuration cannot be described by the present model. For the well-known three configurations, at the parameter boundaries J2/J1 = 0 and 0.5, nonzero Néel temperatures can be calculated. At the boundary J2/J1 = 0, both the type-I and type-III can exist, and the former is more stable than the latter at T = 0+ K. At the boundary J2/J1 = 0.5, only the type-II is stable at T = 0+K, but above some very low temperature, the type-III will be more stable. When the J2 value is less and very close to 0.5, there may be other magnetically disordered configurations at T = 0+K. We find that under appropriate J2/J1 ratios, the sublattice magnetizations versus temperature of the type-I and II can be almost identical, which explains the neutron scattering experiment in NiS2 that showed the coexistence of the two states.