Magnetization processes in metallic Shastry−Sutherland systems: A comprehensive review

Rare-earth tetraborides RB4 are unique frustrated magnets in which strongly anisotropic localized 4f moments coexist with itinerant 5d electrons on the geometrically frustrated Shastry−Sutherland lattice. Their magnetization curves display remarkably rich sequences of fractional plateaus, ranging from the robust 1/2 state in ErB4 and TmB4 to intricate cascades in HoB4 and TbB4, whose microscopic origins cannot be captured by localized-spin models alone. This review provides a comprehensive and unified theoretical picture of the mechanisms that stabilize these commensurate magnetic textures. We begin with long-range oscillatory RKKY interactions that naturally emerge from the metallic character of the RB4 compounds and show how accurate numerical treatment reveals a dense hierarchy of competing plateau phases. We then move to explicit spin-electron models, where electron itinerancy, Coulomb repulsion, transverse exchange terms, and realistic mixed-spin configurations jointly reconstruct the plateau stability diagram and reproduce the dominant experimental features. Further extensions, such as the coupled double-Ising (CDI) mapping and charge-stripe potentials, reveal how subtle electronic textures selectively suppress or enhance magnetization plateaus, enabling microscopic control over the competition between the 1/3 and 1/2 plateaus and linking magnetization processes to the magnetocaloric response. The theoretical frameworks reviewed here establish that the interplay of geometrical frustration, itinerant electrons, electronic correlations, and exchange anisotropy is essential for understanding the magnetic and thermodynamic behavior of metallic Shastry−Sutherland materials. The resulting picture not only explains the material-dependent plateau sequences observed in rare-earth tetraborides but also provides a versatile platform for designing new frustrated magnets with tunable fractional states and enhanced magnetocaloric performance.