Develop a microscopic account of the coupled structural and CEF evolution

Develop a quantitative microscopic account of how transition-metal d bands, Ge p states, and the local Sm environment jointly determine the element-dependent crystal-electric-field anisotropy and ground-state evolution in SmTr2Ge2.

Background

The paper identifies an empirical correlation between changes in the Ge internal coordinate, Sm–Ge and Ge–Ge distances, the c-axis lattice-parameter trend, and the evolution from easy-plane to easy-axis anisotropy across SmTr2Ge2. However, the authors treat this relationship only qualitatively and do not calculate the local electrostatic or hybridization-derived potential acting on the Sm 4f electrons.

A quantitative microscopic treatment would require evaluating how the transition-metal d bands and Ge p states modify the local crystal field around Sm, for example through first-principles calculations. Establishing this relationship would explain the mechanism behind the change from a Γ6 to a Γ71 CEF ground state near the Ni–Cu boundary.

References

A quantitative discussion of the element-dependent CEF anisotropy would require a more microscopic evaluation of how the local potential acting on Sm evolves, for example, by first-principles calculations, and is left for future work.

— Systematic Evolution of Magnetic Anisotropy and Crystal-electric-field Ground States in SmTr2Ge2  (2609.30871 - Higashinaka et al., 25 Sep 2026) in Section 3, final paragraph of the discussion of the crystal structure and CEF evolution