X-ray Magneto-Optical Kerr Effect Based on Circular-Polarization Eigenmode

Abstract

We have derived the magneto-optical Kerr matrix based on the circular-polarization eigenmode instead of the linear-polarization mode by using arbitrary-eigenmode transformation matrices. The Kerr matrix derived here is given simply in terms of the well-known reflection coefficients of the linear-polarization mode. Using the derived Kerr matrix, we have calculated the amplitudes and the phases of the electric fields of individually separated left- and right-handed circular components of waves reflected from a model system of Co (100~\AA)/Si substrate with either orientation of opposite longitudinal magnetizations for $s$-polarized incident X-rays at the Co $L_3$ edge ($h\nu=$ 778.1 eV) and far below it ($h\nu=$ 770.1 eV). From these calculations, we can readily determine the Kerr rotation, the Kerr ellipticity, the Kerr intensity, and the degree of circular polarization of the reflected waves. The Kerr matrix of the circular-polarization mode is found to be very useful in theoretical and experimental investigations of a variety of magnetic thin films because of its ability to decompose individual components of any polarization eigenmodes.