The influence of double-exchange and Heisenberg interaction on magnetization processes in rare-earth tetraborides

Abstract

We present a comprehensive model for a description of magnetization processes in rare-earth tetraborides (RET). The model is based on the coexistence of two subsystems, and namely, the spin subsystem described by the XXZ Heisenberg model and the electronic subsystem described by the generalized Hubbard model on the Shastry–Sutherland lattice. Moreover, both subsystems are coupled locally by the anisotropic double-exchange interaction, which besides the usual Jz term of the Ising type takes into account also the Jxy term representing the spin-flip processes. The model is solved numerically using the exact Lanczos method on the cluster of L=12 sites and the truncated Lanczos method on the cluster of L=36 sites. The special attention is paid on a description of individual and combined effects of the double-exchange interaction Jxy and the Heisenberg Jxy′ interaction on the stabilization of magnetization plateaus with fractional magnetization. We have found that the Jxy and Jxy′ interaction terms exhibit fully opposite effects on the stability of the main 1/2 and 1/3 plateau phases. While the Jxy interaction destroys the 1/2 plateau and stabilizes the 1/3 plateau, the Jxy′ interaction stabilizes the 1/2 plateau and destroys the 1/3 plateau. For Jxy>0 and Jxy′>0 only small combined effects of Jxy and Jxy′ on the stability of the 1/3 and 1/2 plateaus are found in the weak coupling limit (Jxy/Jz≤0.5 and Jxy′/Jz′≤0.5), but in the opposite limit the significant effects of these terms on the suppression of the 1/3 plateau and the stabilization of 1/2 plateau are observed.