Analytical expressions for polar magnetoptics in magnetic multilayers

This paper is a comprehensive study of different formalisms used to simulate polar magneto-optical (MO) effects in multilayers. A development of the 4 × 4 matrix calculation to first order in off-diagonal elements of the permittivity tensor gives original analytical expressions. They allow to express the MO effects in multilayers as a sum of contributions from individual layers. Each contribution consists of two components assigned to the interface and propagation effects. The explicit expressions for multilayers containing up to seven layers, together with those obtained in the frame of an ultrathin layer approximation, are shown to be useful both in a qualitative comprehension and in quantitative simulations of the experimental MO Kerr spectra 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 analytical expression is provided for a system consisting of two ultrathin films separated by a non-magnetic spacer and deposited on a non-magnetic substrate. The capabilities of the analytical expressions are demonstrated on MO spectroscopy in a broad spectral range of some well characterized ultrathin magnetic structures. This work has been partially supported by HCM programme “Magnetic properties of novel ultrathin films” (project number ERBCIPDCT940622), NATO Grant “High Technology” (LG931415) and Grant Agency of Czech Republic (# 202/97/1180 and # 202/00/0761).