Collinear Neel-type ordering in partially frustrated lattices

We consider two partially frustrated S = 1/2 antiferromagnetic spin systems on the triangular and pentagonal lattices. In an elementary plaquette of the two lattices, one bond has exchange interaction strength alpha (alpha less than or equal to 1) whereas all other bonds have exchange interaction strength unity. We show that for alpha less than a critical value cu,, collinear Neel-type ordering is possible in the ground state. The ground-state energy and the excitation spectrum have been determined using linear spin-wave theory based on the Holstein-Primakoff transformation. [S0163-1829(98)04625-6].