Application of the Berreman formalism for modeling magneto-optical Kerr effects in multilayered structures

Objectives. Materials composed of numerous ultrathin layers, each having a thickness on the order of several nanometers, constitute an advanced class of composite structures exhibiting unique physical properties not typically found in conventional materials. These materials are of significant interest in both scientific and industrial sectors due to their adaptability and broad potential for application. Researchers are particularly intrigued by structures incorporating both magnetic and non-magnetic layers. The investigation of magneto-optical phenomena—particularly the Kerr effect—within these structures contributes to a deeper understanding of their physical characteristics, as well as enhancing prospects for their practical implementation. Since, to ensure the accurate interpretation of experimental data, it is imperative to consider potential interference effects, it becomes necessary to develop a mathematical model of the structure for comparing experimental findings with theoretical calculations. The purpose of this study is to analyze one of the modeling methods for multilayer structures in which magneto-optical Kerr effects can manifest themselves in individual or all layers.

Methods. The Berreman method, which is based on the matrix representation of Maxwell’s differential equations, is used to model all three magneto-optical Kerr effects (polar, longitudinal, transverse) in multilayer thin-film structures.

Results. For optically isotropic materials, Berreman matrices have been derived for experimental configurations required to observe the transverse, polar, and longitudinal Kerr effects. A method is additionally proposed to account for the influence of thick layers within the investigated structure.

Conclusions. For the matrices presented in this paper, the Berreman method was used to analyze magneto-optical Kerr effects in an isotropic medium. As well as allowing us to obtain accurate formulas for magneto-optical effects, this provided more accurate modeling of complex multilayer structures, as well as contributing to an in-depth understanding of their physical characteristics, which provides new opportunities for analyzing and searching a wide range of materials.

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