Phase transitions in a spin-1 system with the three-atom interaction

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Abstract
The Hamiltonian describing spins localised on lattice sites contains the bilinear and biquadratic pair interactions, as well as the three-atom interactions of the type (Si.Sj)*(Sj.Sk). The molecular field approximation is applied to study the ground state properties and the interrelations between the three collinear phases taken into account: ferromagnetic (or antiferromagnetic), paramagnetic and quadrupolar. The following properties of the system are due to the three-atom interaction: (i) a nonsaturated ferromagnetic ground state; (ii) contraction or expansion (depending on the sign of the interaction) of the quadrupolar region on the phase diagram; (iii) up to three consecutive transitions (first or second order) on cooling; (iv) heat magnetisation and 'sluggish' magnetisation against temperature curves. In some respects the three-atom interaction acts like the single-ion anisotropy of the type (Szf)2.