Numerical study of magnetization processes in rare-earth tetraborides

Abstract

We present a simple model for a description of magnetization processes in rare-earth tetraborides. 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 Falicov-Kimball model on the Shastry-Sutherland lattice (SSL). Moreover, both subsystems are coupled by the anisotropic spin-dependent interaction of the Ising type. We have found, that the switching on the spin-dependent interaction ($J_z$) between the electron and spin subsystems and taking into account the electron hopping on the nearest ($t$) and next-nearest ($t'$) lattice sites of the SSL leads to a stabilization of new magnetization plateaus. In addition, to the Ising magnetization plateau at $m^{sp}/m_s^{sp}=1/3$ we have found three new magnetization plateaus located at $m^{sp}/m_s^{sp}=1/2$, 1/5 and 1/7 of the saturated spin magnetization $m_s^{sp}$. The ground-states corresponding to magnetization plateaus have the same spin structure consisting of parallel antiferromagnetic bands separated by ferromagnetic stripes.Comment: 5 pages, 6 figure

Magnetization plateaus and phase diagrams of the Ising model on the Shastry–Sutherland lattice

“…(12) and the specific heat from Eq. (14). Then we can carry out numerical integration and calculate the entropy and free energy of the system.…”

“…(7-10) and Eqs. (12)(13)(14)(15)(16) numerically in order to verify the stability of the phase transition temperatures, and the obtained results are presented in Figs. 3 and 4.…”

“…Besides the long range interactions, when dipole-dipole interaction is used, a tiny plateau at m/m S ¼2/3 is predicted [13]. Moreover, a model that is combination of electron and spin subsystems was examined to understand the magnetization process in RB4, and beside the magnetization plateau at m/m S ¼1/3, three new magnetization plateaus at m/m S ¼1/2, 1/5 and 1/7 of the saturated magnetization were indicated [14]. It is also mentioning that different magnetization plateaus have been observed, e.g., at 1/8, 1/4, 1/3, in agreement with experimental observations in a related compound and other stable plateaus are obtained at 1/9, 1/6, 2/9 by using the nonperturbative ContractorRenormalization method for strong enough magnetic fields [15] and additional magnetization plateaus for more exotic values like 1/9, 1/7, 1/6, 1/5 and 2/9 have been suggested by using torque measurements [16].…”

Exact ground states of a spin-12Ising-Heisenberg model on the Shastry-Sutherland lattice in a magnetic field

“…However, the magnetic behavior of the rare-earth tetraborides RB 4 is basically affected by the Ising (easy-axis) anisotropy due to strong crystalfield effects acting on rare-earth ions in contrast to the almost isotropic magnetic behavior of the transition-metal copper ions in SrCu 2 (BO 3 ) 2 . The metallic character along with the substantial Ising anisotropy make a comprehensive description of magnetic properties of the rare-earth tetraborides much more complex, because one has to take into account the coupling between spin and electronic subsystems described in terms of Ising (or XXZ Heisenberg) and FalicovKimball models on the Shastry-Sutherland lattice, respectively [33,34]. ( In the present work, two independent rigorous analytical methods will be employed for investigating the ground state of the spin-1/2 Ising-Heisenberg model on the ShastrySutherland lattice in a magnetic field, which accounts for the XXZ Heisenberg intradimer and Ising interdimer couplings.…”

Magnetic Phase Diagram of TmB_{4} under High Pressure

“…Another model is based on the coexistence of two subsystems, namely the spin subsystem, described by the Ising model, and the electronic subsystem described by the Falicov-Kimball model on the SSL. Moreover, both subsystems are coupled by an anisotropic spin-dependent interaction of the Ising type [8]. A complete and exact solution of the ground-state problem for the Ising model on the SSL in an applied eld was found recently in [9].…”