Phase Transitions in a Coupled Electron and Spin Model on the Shastry-Sutherland Lattice

The thermodynamics of a simple electron-spin model proposed recently for a description of magnetization processes in rare-earth tetraborides is studied numerically by the canonical Monte Carlo method in two-dimensions. The model is based on the coexistence of two subsystems, and namely, the spin subsystem described by the Ising model and the electronic subsystem described by the free-electron model on the Shastry-Sutherland lattice (SSL). Moreover, both subsystems are coupled by the anisotropic spin-dependent interaction of the Ising type. At T=0 the system exhibits the magnetization plateau (MP) at m/$m_s$=1/2, 1/3, 1/5, 1/7, 1/9 and 1/11 of the saturated spin magnetization $m_s$. For the largest phases corresponding to m/$m_s$=0, 1/3 and 1/2 we have examined the nature of the phase transitions from the low-temperature ordered phase (LTOP) to the high-temperature disordered phase (HTDP). It is shown that all phases persist also at finite temperatures (up to the critical temperature $T_c$) and that the phase transition at the critical point is of the second order for the m/$m_s$=0 phase and of the first order for the m/$m_s$=1/3 and 1/2 phases.