Magnetic phase diagram of the S=1 axial next-nearest-neighbour Ising (ANNNI) model with higher-order spin interaction

Abstract

The three-dimensional S=1 axial next-nearest-neighbour Ising (ANNNI) model is discussed. In addition to the ferromagnetic intra- and interlayer interactions J0 and J1 two types of competing antiferromagnetic interactions are considered between next-nearest layers, i.e. ordinary two-site two-spin J2SiSi+2 ((2-2) model) or three-site four-spin J3SiSi+12Si+2 ((3-4) model) interactions. For both models, the magnetic phase diagrams are obtained by means of the site-dependent molecular field approximation. The phase boundaries among paramagnetic, ferromagnetic and various modulated phases are determined by analysing frequency-dependent susceptibility chi (q), or by solving coupled equations of (Si) and (S12) for spins up to 17, iteratively. The constructed 'devil's flower' of the (3-4) model is characteristically different from that of the (2-2) model, since three-site four-spin interaction is effectively temperature dependent. For the (3-4) model, a new behaviour of re-entrant transition is found for the interaction ratio -0.50>J3/J1>-0.53. The role of the entropy term for this re-entrant transition is discussed in detail by analysing the free energies around the multiphase point (T=0, J3/J1=-0.5).