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 $(\varphi _x=D_{x}/J z, k_{\mathrm {B}}T/J)$, $(p, k_{\mathrm {B}}T/J)$ and $(q, k_{\mathrm {B}}T/J)$ planes. It is found that the model exhibits only second-order phase transitions. The compensation temperatures are also observed and their lines, $T_{\mathrm {comp}}$-lines, are depicted on the $(\varphi _x,k_{\mathrm {B}}T/J)$ 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 $\varphi _x$ and $\varphi _y$. It is also found that remanent magnetisation increases with negative values of $\varphi _x$ and $\varphi _y$.