Impact of charge stripes on magnetization processes in rare-earth tetraborides

We examine the impact of charge stripes on magnetization processes in rare-earth tetraborides within a complex model which takes into account the electron and spin subsystem as well as the coupling (of the Ising type) between both subsystems. The charge stripes in this model are induced by adding the phenomenological, spatially varying local potential $V_i$. Our assumption is based on a comparison of structural and electronic similarities between the rare-earth tetraborides and rare-earth hexaborides/dodecaborides, where such charge stripes (as a consequence of the Jahn–Teller effect) were experimentally observed. It is shown that the form and intensity of local potential $V_i$ (the type of charge stripes) have dramatic impact on the stability of individual plateaus on magnetization curves. The largest effects have been observed for the periodic potential forming the full charge stripes alternating with chessboard charge stripes. This type of charge ordering leads to magnetization curves with extremely simple structure consisting of only two main magnetization plateaus with fractional magnetization m=1/2 and m=1/3, the stability regions of which depend strongly on the model parameters. It is shown that with increasing intensity of local potential $V_i$ the 1/2 plateau (1/3 plateau) is generally stabilized (suppressed) and this effect is further enhanced by increasing spin-electron coupling leading to total disappearance of the 1/3 plateau, exactly as is observed in TmB${}_4$ and ErB${}_4$. It should be noted that although charge stripes are introduced here ad hoc, the fact that our picture of magnetization processes is fully consistent with experimental measurements in TmB${}_4$ and ErB${}_4$ indicates that this assumption is reasonable and could serve as motivation for experimental physicists to find such a type of charge ordering in these materials.