Ground state and thermodynamic properties of the coupled double-Ising model: application to rare-earth tetraborides

Abstract

A combination of the standard Metropolis algorithm and the parallel tempering method is used to study ground-state and thermodynamic properties of the coupled double Ising (CDI) model on the Shastry-Sutherland lattice (SSL). This model is derived from the complex spin-electron model, in which electrons described by the Hubbard model and spins described by the Ising model interact via the anisotropic spin-dependent interaction of the Ising type, under the following three conditions: (i) the Hubbard interaction between electrons in the conduction band is sufficiently large; (ii) the number of conduction electrons is equal to the number of the lattice points; (iii) there is the easy axis spin anisotropy in the system. The model is solved numerically for the selected combinations of spins from the electron ($s=1/2$) and spin ($S=1,3/2,2$) Ising branch which represent very realistically the situation in TmB$_4$, ErB$_4$ and HoB$_4$ compounds, where in addition all three conditions are simultaneously satisfied. It is shown that the interlpay between the electron and spin branch of the CDI model leads to the suppression of the 1/3 magnetization plateau (the main magnetization plateau found in the ordinary Ising model on the SSL) and the stabilization of magnetization plateaus with $m\sim 1/2$, which is in perfect agreement with the experimental measurements in TmB$_4$ and ErB$_4$ compounds. A nice correspondence between theoretical and experimental results is also obtained for the temperature dependence of the specific heat capacity, where the low-temperature peak corresponding to the electron branch of the CDI model is followed by high-temperature peak of the spin branch. This opens a new route for exploring the physics of other complex spin-electron systems in which the above-mentioned conditions (i)-(iii) are fulfilled.