The magneto-optical Kerr effect (MOKE) is observed as a net rotation and elliptical polarization of incident vertically linearly polarized light as it is reflected from a magnetized sample. [1] This change in the polarization state (or the intensity) of an incident electromagnetic wave arises due to the interaction of the electric and magnetic fields of the waves with the spin of the electrons in the material that occurs through the spin-orbit interaction. The magnitude of this change in polarization is proportional to the magnetization of the sample. Amount of rotation (in radians) and of ellipticity (ratio between the minor and major axis of the ellipse) induced in the reflected beam is of the order of 1/1000, i.e. relatively small. However, MOKE technique derives its surface sensitivity from the limited thickness of the deposited magnetic film, which can be as thin as one atomic layer [2,3]. MOKE magnetometry has emerged as a very popular tool for magnetic characterization of thin films due to its simplicity, low cost and high sensitivity. The simplest MOKE setups require a stabilized laser source, one polarizer, one light detector and an electromagnet to generate the magnetic field. In reflection mode, one distinguishes between three Kerr effects, depending on the relative orientation of the magnetization M with respect to the plane of incidence of the light: the polar, the longitudinal and transverse Kerr effect as defined schematically in Fig. 1.

Microscopic origin: According to Maxwell the Kerr effect /Faraday effect is a consequence of the two circular modes (which composes the linear polarized light) having different velocities of propagation. This leads to a difference in the dielectric constants of left- and right-circularly polarized light and can accounts for the Faraday rotation. It is now established that the spin-dependent dielectric constant is a consequence of the spin-orbit interaction which couples the electron spin to its motion [2,3]. The change of the wave-functions due to the spin-orbit interaction is now believed to gives rise to a correct order-of-magnitude of the difference of the two refractive indices. A full derivation of the magneto-optic effect in a ferromagnet using perturbation theory can be found from Argyres [4]

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Macroscopic Formalism: Macroscopic descriptions of the magneto-optic effect are based on an analysis of the dielectric properties of a medium. Maxwell expressed linearly polarized light as being a superposition of two circularly polarized components, and realized that the Faraday effect is a result of the different propagating velocities of the two circular modes. The dielectric property of a medium is characterized by a 3x3 tensor e_ij with i, j= 1, 2, 3. In general, this dielectric tensor can be decomposed into symmetric and antisymmetric parts. The symmetric part can be diagonalized by an appropriate rotation of coordinates. If the three eigenvalues are the same, the medium is isotropic, and the dielectric tensor is reduced to a dielectric constant. Otherwise, the medium is anisotropic. Nevertheless, the normal modes of the symmetric tensor, e_xx  are linearly polarized light. Therefore, the symmetric part of the dielectric tensor does not give rise to the Faraday effect and hence will be assumed to be isotropic. When a beam of light is incident from a nonmagnetic medium 0 to a magnetic medium 1, having an arbitrary direction of the magnetization as shown in Fig. 1, the dielectric tensor e_ij  can be written as follows: [5]

........(1)

where e_zz  = e_xx  for simplicity. The magnetooptical constant Q is defined as Q =ie_xy /e_xx  and a_x ,a_yand a_z are the direction cosines for the magnetization vector, M_s. The next step is to determine the elements of the Fresnel reflection matrix by solving Maxwell equations for the above dielectric tensor. The Fresnel reflection matrix is written in the following way.

........................(2)

The subscript and superscript notation signify, for example, that r_sp is the coeffcient for relating the reflected s-wave to the incident p-wave [6]. Notice then that the diagonal elements,  r_pp and  r_ss, are the coe�cients signifying how much of the original polarization-state is simply reflected, while the off-diagonal elements,  r_ps and  r_sp, give rise to the net rotation and elliptical polarization that is the magneto-optical Kerr effect. By solving the Maxwell equations the Fresnel reflection coefficients can be evaluated for an arbitrary magnetization direction [5]. These are expressed in the following way: