Optical and Magneto-Optical Spectroscopy of Magnetic Nanostructures.

Abstract

We present the method of separating the magnetic contributions to the measured (MO) effect from several magnetic materials (or several magnetic layers) contained in nanostructure. The method is based on singular value decomposition. We use the method to separate hysteresis loops of hard magnetic Fe particles and soft magnetic FeNbB alloy on wheel side of as-quenched FeNbB ribbons and to determine the volume fraction of Fe particles in the surface layer of the ribbon. Then we use the method to separate the hysteresis loops of four ferromagnetic layers from a (TbFe/Si3N4)4 multilayer stack structure using the spectroscopy measurements of polar magneto-optical effect. In order to extend this method to separate the measured MO effect quadratic in magnetization, we have determined the four principal spectra (the permittivity ε(0) unperturbed by magnetization, the element K describing linear magneto-optical tensor and the elements G44 and G11−G12 describing quadratic magneto-optical tensor) from ab-initio calculations of the permittivity tensor of cubic bcc Fe, fcc Co, and fcc Ni, which fully describe the magneto-optical effects up to second order in magnetization for arbitrary sample’s orientation and arbitrary magnetization direction.