Long sequences of order–order transitions with a temperature-dependent rotation of the magnetization in anisotropic quartic spin Hamiltonians

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Abstract
The anisotropic spin Hamiltonian of the form H= 1/2 (axs2x +ays2y+azs2z) + 1/4 (bxs4x+bys4y +bzs4z) + 1/2 (cxs2ys2z +cys2zs2x +czs2xs2y) can give rise to eight different phases (isotropic; Ising-type in any one of the directions x, y, z; or xy-like in any one of the planes xy, yz, or zx; xyz phase). A comprehensive mean-field study of the possible sequences of phases and types of phase transitions, exhibited upon variation of the temperature for different choices of the Hamiltonian parameters, is presented. While the resultant magnetization is always a decreasing function of the temperature, each one of the components can have a different temperature dependence, giving rise to various orientations of the resultant magnetization.