Based on an effective parameter method in the mean-field approximation, the temperature dependence of the single-ion anisotropy constants in the uniaxial one-sublattice system has been exhaustively studied within the three-constant approximation to the anisotropy free energy. Another important basis of our investigation is the connection between the experimentally measured anisotropy constants and the theoretically more fundamental anisotropy coefficients. A significant concept of anisotropy flow is introduced to detect all the possible types of spin-reorientation transitions driven by temperature evolution in the system. Seven types of temperature dependence of the first anisotropy constant and 14 types of spin-reorientation transitions are discovered in this one-sublattice system. Phase diagrams for these temperature behaviors and the spin-reorientation transitions are given by means of analytical and numerical calculations. [S0163-1829(99)05141-3].
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