Detailed and practical expressions are given for the magneto-optical Kerr effect (MOKE) for various configurations of two media. One is a magneto-optic (MO) one, and the other is a nonmagnetic (NM) medium. For a system of two thick media with a single interface, with a first-order approximation in MOKE term Q, the Kerr function is determined by the product of a MOKE term Q and an optical term η. A second type of system includes a thin MO (or NM) layer deposited on a thick NM (or MO) substrate. For a MO/(NM-substrate) configuration, the Kerr function is related to the Kerr effects from the air/MO and MO/NM interfaces, and to the Faraday effects of the MO layer, as well as to interference effects. The enhancement factor can be expected to be large by proper choice of materials. For a NM/(MO-substrate) configuration, the total Kerr function is related to the Kerr effect from the NM/MO interface and can be enhanced by interference. The enhancement factor is expected to be less than one if the NM layer is strongly absorbing. Calculations of Kerr effects for examples of the PtMnSb/AuAl2 and Fe/Cu configurations are given. These indicate that the peaks shown in the onset region of the interband transitions of Cu can be attributed to a dramatic change of the refractive index in that region. The merits of a MO/(NM-metallic) structure have been evaluated, and indicate that a better Kerr enhancement effect can be achieved if the refractive index of the MO layer is larger than one and is much larger than that of the metallic material. A drawback to this configuration comes from the fact that a MO material with a large refractive index value usually is not expected to have a large intrinsic Kerr effect.
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