Analytical expressions for polar magnetoptics in magnetic multilayers

This paper is a comprehensive study of different formalisms used to simulat e polar magneto-optical (MO) effects in multilayers. A development of the 4 x 4 matrix calculation to first order in off-diagonal elements of the perm ittivity tensor gives original analytical expressions. They allow to expres s the MO effects in multilayers as a sum of contributions from individual l ayers. Each contribution consists of two components assigned to the interfa ce and propagation effects. The explicit expressions for multilayers contai ning up to seven layers, together with those obtained in the frame of an ul trathin layer approximation, are shown to be useful both in a qualitative c omprehension and in quantitative simulations of the experimental MO Kerr sp ectra of a wide variety of ultrathin magnetic structures. They can be used to separate the different contributions arising from the interfaces due to intermixing or spin polarization (including interface roughness) as well as to simulate magnetically coupled multilayers. As an example, the analytica l expression is provided for a system consisting of two ultrathin films sep arated by a non-magnetic spacer and deposited on a non-magnetic substrate. The capabilities of the analytical expressions are demonstrated on MO spect roscopy in a broad spectral range of some well characterized ultrathin magn etic structures.