Random transverse single-ion anisotropies in the mixed spin-1 and spin-1/2 Blume–Capel quantum model: Mean-field theory calculations

Abstract

We have used mean-field theory based on the Bogoliubov inequality for the free energy to study the effects of random transverse single-ion anisotropies and magnetic field on the mixed spin-1 and spin-1/2 Blume– Capel quantum model with the coordination number z = 3. The interactions of the transverse crystal fields D x and D y act only on the spin-1 sites and are randomly active with probability p and q and inactive with probability 1−p and 1−q respectively. The thermal behaviours of the order parameters are studied to determine the nature of phase transitions and to calculate the phase diagrams on the (ϕ x = D x /J z, k B T /J ), ( p, k B T /J ) and (q, k B T /J ) planes. It is found that the model exhibits only second-order phase transitions. The compensation temperatures are also observed and their lines, T comp -lines, are depicted on the (ϕ x , k B T /J ) planes. The hysteresis loops are obtained by introducing an external magnetic field on the system which reveals that the coercive field decreases with temperature and with positive values of ϕ x and ϕ y . It is also found that remanent magnetisation increases with negative values of ϕ x and ϕ y .