Analytic expressions of the general magneto-optical Kerr effects for a nanometer-thick magnetic layer with a capping layer

We have formulated analytic expressions for magneto-optical Kerr effect (MOKE) of a magnetic layer covered by a capping layer, when two layers are optically thin enough. Within the first order of the thickness of the magnetic and capping layers, the polar and longitudinal magneto-optical Kerr effects of p and s polarized waves can be approximated with simple closed forms for the general cases of an arbitrary oblique incident angle. It is found that the capping layer thickness dependent part can be separated from the first-order term of the magnetic layer thickness, and it turns out to be the simple form for the normal incident case. The validity of the approximated expressions was examined by comparison with the exact numerical solutions, and it is confirmed that the estimated error was small enough for optically thin enough magnetic and capping layers.