Lattice Parameter Governs Magnetic Ground State Selection in Tsai-Type Intermetallic Compounds

Identifying the key parameters that govern magnetic ground states in complex intermetallics remains a central challenge in materials chemistry. Although the valence-electron concentration (e/a) has frequently been used to classify magnetism in Tsai-type approximant crystals, its predictive power is limited across different alloy families and constituent elements. Here, we demonstrate that the lattice parameter serves as a unified structural parameter governing magnetic ground state selection in Tsai-type icosahedral compounds. Within the framework presented in this work, magnetic ground states collapse onto a single phase diagram that is independent of alloy family and rare-earth species: antiferromagnetic order emerges above a critical lattice parameter of ∼14.72 Å, whereas ferromagnetic order is stabilized within the intermediate range 14.62 Å ≲ a ≲ 14.72 Å. These results indicate that the lattice parameter serves as an experimentally accessible structural parameter that encodes the electronic information traditionally represented by e/a and thereby provides a unified description of magnetic ground state selection. The trends revealed in the present work provide a useful guideline for identifying compositions that may stabilize previously unexplored magnetic phases, including antiferromagnetic quasicrystals and hedgehog-like magnetic textures.