Three-sublattice order in triangular- and Kagomé-lattice spin-half antiferromagnets

We study the possibility of {}3 ×{} {}3 antiferromagnetic order in the S=1/2 triangular- and Kagom\'e-lattice Heisenberg models. An Ising-like anisotropy is introduced into the Hamiltonian, which picks a pair of ground states out of the manifold of the classically ordered states. To study properties of the Heisenberg model, we develop series expansions around one ordered state. We find that the Kagom\'e-lattice model is disordered, whereas the triangular-lattice model is very close to the critical point for antiferromagnetism; if ordered, the latter has an order parameter much smaller than that predicted by spin-wave theory.