Application of permittivity tensor for accurate interpretation of magneto-optical spectra

The inaccuracies of widely used approximations to the theory of the off-diagonal elements ε1= ε′1 + iε″1 of the permittivity tensor are examined. Errors occurring in the ‘‘diamagnetic’’ case can become important when curve fitting is employed to extract parameter values from Bi-substituted magnetic garnets. A discrepancy between the exact and approximate forms of the ε′1 relation (which is responsible for Faraday rotation and Kerr ellipticity at lower energies) as a function of transition energy is found in the low-energy (wavelength λ∼1 μm) tails of the lines and originates from the dropping of a nonresonant term from the complete theory. Errors also occur in the line shapes near resonance where the ratio of the excited-state splitting to the Lorentzian linewidth approaches unity (Δ/Γ→1). A family of curves with Δ/Γ as a parameter is presented, and an exact expression relating Δ/Γ to the resonance value of ε′1/ε″0 (where ε″0 is the imaginary part of the diagonal element ε0) is derived.