Analytical calculation of dielectric permittivity tensor from magneto-optical ellipsometry measurements

Abstract

Magneto-optical ellipsometry combines ellipsometry and magneto-optical Kerr effect measurements which are two powerful techniques. The main difficulty is usually in data processing as a number of parameters should be extracted from measured ellipsometric (ψ, Δ) and magneto-ellipsometric (δψ, δΔ) parameters. Standard procedure of solving magneto-ellipsometry equations involves numerical calculations. In this paper we show that it is possible to find out all elements of dielectric permittivity tensor without numerical calculation methods. It means that the inverse problem of magneto-optical ellipsometry can be solved analytically in the case of expansion of magneto-ellipsometric parameters δψ and δΔ with respect to two small parameters. We present a full set of mathematical expressions that enable us to calculate complex refraction index and complex magneto-optical parameter of a sample from magneto-optical ellipsometry measurements, thereby obtaining diagonal and off-diagonal complex elements of dielectric permittivity tensor. This analytical approach can be used in case of the contribution from magnetism into reflection coefficients being small.

A versatile method for exploring the magnetooptical properties of polar saturated and unsaturated ferromagnetic metallic thin films

“…M ∥ H. The MO coupling constant Q = Q(λ) defines the MO figure of merit of magnetizable materials in MO sensors or in MO memory devices [17]. Analytical solutions can be used as an initial guess for the complex MO coupling constant Q [28]. We have numerically calculated the off-diagonal dielectric tensor of permalloy (Ni 81 Fe 19 ) using the 4 × 4 Müller matrix and determined the complex MO coupling constants in the standard approach [14].…”