Modulated Structures of an Ising Spin System on a Triangular Lattice. I. Triangular Domain Structure

Mean field calculations are performed to study an Ising spin model on a triangular (actually hexagonal) lattice in which the couplings up to the next nearest neighbor and the magnetic field are taken into account. Special attention is focused on possible long-period modulated structures at finite temperatures. It is shown that for antiferromagnetic couplings higher order commensurate structures with a triangular domain structure are stable in a wide temperature range. The mechanism stabilizing those structures is discussed explicitly by using domain boundaries as a key concept and the Ginzburg-Landau type free energy. Finally the theory is applied to the order-disorder transition of β-eucryptite (β-LiAlSiO 4 ) and compared with experiment.