Modulated Structure of an Ising Spin System on a Triangular Lattice. II. Complete Devil's Staircase

Abstract

A study is made on an Ising spin system on a triangular (actually hexagonal) lattice which contains the couplings of the nearest neighbor ( J 1 ) and the next-nearest neighbor ( J 2 <0: antiferromagnetic). A mean field approximation is employed. Infinite numbers of higher-order commensurate structures with one-dimensional modulation are shown to be stabilized at finite temperatures. Analytic calculations are performed at low temperatures to find that the model exhibits a complete devil's staircase at \(J_{1}{\gtrsim}0\) and ordinary staircases with infinite steps at \(J_{1}{\lesssim}0\) and \(J_{1}{\lesssim}2|J_{2}|\). It is shown that most of the phases stabilized around J 1 =0 are partially disordered states. Numerical calculations are also made to construct a global phase diagram. The structure of the phase diagram is discussed in terms of domain boundary. In this context the order-disorder transition of (Nb 1- x Ta x ) 2 C is compared with the theory.