Monte Carlo study of finite-temperature transition in R₂(R = Yb and Er)M₂(M = Ti and Sn)O₇ anisotropic pyrochlore

The Monte Carlo simulations based on the Metropolis algorithm was used to investigate the magnetic behavior of Yb₂Ti₂O₇, Er₂Ti₂O₇ and Er₂Sn₂O₇ systems using classical Heisenberg spin model. The thermodynamic observables are averaged over Monte Carlo simulations. The order parameter was computed as a function of temperature for two different configurations. The results show that the thermal phase transition is probably continuous and at most very weakly first order. The variation of the spin components with temperature for the two configurations exhibits different magnetic phases, and the spin configurations are deduced and presented.