First-order approximations of the general magneto-optical Kerr effects for an optically thin capping layer

We formulate analytic expressions for the magneto-optical Kerr effect (MOKE) of a magnetic layer covered by an optically thin capping layer, which is common in ex situ experimental situations. Within the first order of a capping layer thickness, polar and longitudinal magneto-optical Kerr effects of p and s polarized waves can be approximated with simple closed forms. They cover all cases of an oblique incident angle with various polarizations and magnetization directions. Especially, it is found that it becomes an extremely simple form for the normal incident case. The dependence of magneto-optical Kerr effects on the thickness and the optical properties of the capping layer is found with these analytic expressions. The validity of the approximated expressions is confirmed via exact numerical solutions for various materials, and it is found that the estimated error is less than 5% for the capping layer thickness 2⁢πd1|n2|λ∼0.1. We present a guideline for a choice of capping layers for MOKE signal enhancement.