Journal of Magnetism and Magnetic Materials 89 (1990) 107-123 North-Holland 107 UNIVERSAL APPROACH TO MAGNETO-OPTICS * J. ZAK 1, E.R. MOOG, C. LIU and S.D. BADER Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA Received 5 March 1990 Magneto-optics is described in a unique framework. Reflection and transmission of a general multilayer system is expressed by means of medium boundary and propagation matrices which are universal and apply to any configuration of films and media. The results for the magneto-optic coefficients are cast in the form of sets of four linear, inhomogeneous equations. It is shown that in the thin-film limit, the Kerr effect obeys an additivity law for a system consisting of any number of magnetic films. Computer simulations were performed on different film-configurations, including an overlayer, a sandwich and a superlattice. 1. introduction The surface magneto-optic Kerr effect (SMOKE) has recently become an important tool in probing magnetism in ultrathin magnetic films [1-10]. The effect i~' ,If ,_'s more than a century old [11] and a theory for it was developed by Voigt [12]. The Kerr effect manifezts itself in the change of polarization (polar and longitudinal effect) or intensity (transverse effect) of polarized light when reflected from the surface of a magnetized medium. On a microscopic level the Kerr effect is a consequence of the interaction between the radiation field and the electrons which under exchange lead to magnetization of the solid [13]. Phenomeno- logically, magneto-optic effects at optical frequencies are treated by means of a dielectric tensor [14]. A detailed description of the Kerr effect in bulk materials is given in a number of references [15-18]. It turns out that obtaining explicit results for the Kerr coefficients involves rather complicated algebra [19]. A comprehensive theory exists also for multilayer structures [20-25]. In view of the broad recent interest in the Kerr effect as a tool for the investigation of magnetism, it seems worthwhile to have a framework that is applicable equally well to both bulk and multifilm systems. In this paper a universal approach is developed for the determination of the magneto-optic coefficients in which magnetic and non-magnetic films are treated on the same footing. The approach is based on the definition of two kinds of matrices: The medium boundary, and the medium propagation matrix. These two kinds of matrices have the same physical meaning in both magnetic and non-magnetic media. A full description of the magneto-optic coefficients is given by means of these two matrices. By using these m~triceS nne i~ shl e tn snnlv th,= hnnndsry onnrlltlnnc cllr,=r'tlv tn th,~ maonptt~-~ntlc" c,n~ffh'-i~nt= Zh~ httor then satisfy sets of linear equations. Thus, for each polarization (s or p) the magneto-optic coefficients satisfy four linear inhomogeneous equations. For the treatment of two media with one boundary, only the medium boundary matrix is used, and one rederives the magneto-optic coefficients in a very simple way. In our approach the two media can both be non-magnetic, one of them magnetic or both magnetic! The same type of a medium boundary matrix is applicable to all three situations. * Work supported by US Department of Energy, BES-Materials Sciences, contract #W-31-109-ENG-38. i Permanent address: Physics Department, Technion, Haifa, Israel. 0304-8853/90,/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)