Itinerant versus localized magnetism in spin-gapped metallic half-Heusler compounds: Stoner criterion and magnetic interactions

Spin-gapped metals have recently emerged as promising candidates for spintronic and nanoelectronic applications, enabling functionalities such as sub-60 mV/dec switching, negative differential resistance, and nonlocal spin-valve effects in field-effect transistors. Realizing these functionalities, however, requires a deeper understanding of their magnetic behavior, which is governed by a subtle interplay between localized and itinerant magnetism. This interplay is particularly complex in spin-gapped metallic half-Heusler compounds, whose magnetic properties remain largely unexplored despite previous studies of their electronic structure. In this work, we systematically investigate the magnetic behavior of spin-gapped metallic half-Heusler compounds $XYZ$ ($X$ = Fe, Co, Ni, Rh, Ir, Pd, Pt; $Y$ = Ti, V, Zr, Hf, Nb, Ta; $Z$ = In, Sn, Sb), revealing clear trends. Co- and Ni-based compounds predominantly exhibit itinerant magnetism, whereas Ti-, V-, and Fe-based systems may host localized moments, itinerant moments, or a coexistence of both. To uncover the origin of magnetism, we apply the Stoner model, with the Stoner parameter $I$ estimated from Coulomb interaction parameters (Hubbard $U$ and Hund's exchange $J$) computed using the constrained random phase approximation (cRPA). Our analysis shows that compounds not satisfying the Stoner criterion tend to remain nonmagnetic. On the contrary, compounds that satisfy the Stoner criterion, generally exhibit magnetic ordering. highlighting the crucial role of electronic correlations and band structure effects in the emergence of magnetism. For compounds with magnetic ground states, we compute Heisenberg exchange parameters, estimate Curie temperatures (${T}_{\mathrm{C}}$), and analyze spin-wave properties, including magnon dispersions and stiffness constants. These results provide microscopic insight into the magnetism of spin-gapped metallic half-Heuslers and establish a predictive framework for designing spintronic materials with tailored magnetic properties.