Kramers-Kronig consistent IR-Vis magneto-optical coupling constants of doped garnet

Abstract We report a quantitative determination of wavelength-dependent, Kramers--Kronig (KK) consistent magneto-optical (MO) coupling constants in doped iron garnet thin films using vector magneto-optical generalized ellipsometry (VMOGE) combined with a full 4×4 Müller-matrix optical model for back-scattered light. Two few micrometer thick, liquid-phase-epitaxy grown garnet films, (Dy 1.97 Lu 0.64 Bi 0.39 ) 3 (Fe 3.80 Ga 1.20 ) 5 O 12 (sample S1) and (Dy 2.47 Lu 0.47 Bi 0.06 ) 3 (Fe 3.98 Ga 1.02 ) 5 O 12 (sample S2), were investigated over the 400-1000 nm spectral range. The complex MO coupling constant Q (λ) was extracted from differential Müller-matrix elements under magnetic saturation, yielding both real and imaginary components that satisfy KK relations. The analysis demonstrates that diagonal dielectric functions and off-diagonal MO response can be treated within a unified, physically consistent framework, even in the presence of thickness-fringe interference in transparent films. Comparative analysis of the two compositions reveals pronounced differences in magnetic and MO response arising from variations in effective Fe sublattice occupancy, rare-earth substitution, and Bi incorporation, without implying general materials tunability. The presented methodology provides a robust and general approach for the KK-consistent characterization of magneto-optical materials and multilayer systems relevant to sensing and photonic applications.