Villari effect modulation of the Seebeck response in amorphous ferromagnetic ribbons modeled with the modified Langevin function and Mott's formula

Stress-tunable thermopower in positively magnetostrictive amorphous ribbons offers a route to low-power magnetoelastic sensing that draws no excitation current through the ribbon, but no compact analytical law links uniaxial tensile stress to the relative Seebeck change. We present the first such law, a closed-form four-parameter response equation. It converts stress into an effective anisotropy field through the Villari effect. The resulting magnetization is described by a two-component modified Langevin function, and the thermoelectric response is obtained from Mott's formula with spin-disorder and magnon channels. Validation against measurements on METGLAS 2605SA1, 2605CO, and the newly reported 2605S3A yields coefficients of determination R2 ≥ 0.992 (adjusted R2 ≥ 0.990) with RMSE≤0.029% for stresses up to ∼217 MPa. At the mean temperature of ∼350 K, spin-disorder scattering dominates the stress-dependent Seebeck coefficient for all three alloys, consistent with spin-caloritronic transport in structurally disordered ferromagnets, while the magnon contribution is statistically negligible. The model provides a quantitative basis for comparing compositions and calibrating thermoelectric stress-sensitive elements.