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Magneto-optic Kerr effect (MOKE) is one of the magneto-optic effects. It describes the changes of light reflected from magnetized media.

## DefinitionEdit

The light that is reflected from a magnetized surface can change in both polarization and reflectivity. The effect is identical to the Faraday effect except that the magneto-optical Kerr effect is a measurement of the reflected light, while the Faraday effect is a measurement of the transmitted light. Both effects result from the off-diagonal components of the dielectric tensor $\epsilon$.

## GeometriesEdit

MOKE can be further categorized by the direction of the magnetization vector with respect to the reflecting surface and the plane of incidence.

### Polar MOKEEdit

When the magnetization vector is perpendicular to the reflection surface and parallel to the plane of incidence, the effect is called the polar Kerr effect. To simplify the analysis, near normal incidence is usually employed when doing experiments in the polar geometry.

### Longitudinal MOKEEdit

In the longitudinal effect, the magnetization vector is parallel to both the reflection surface and the plane of incidence. The longitudinal setup involves light reflected at an angle from the reflection surface and not normal to it, as above in the polar MOKE case. In the same manner, linearly polarized light incident on the surface becomes elliptically polarized, with the change in polarization directly proportional to the component of magnetization that is parallel to the reflection surface and parallel to the plane of incidence. This elliptically polarized light to first-order has two perpendicular $E$ vectors, namely the standard Fresnel amplitude coefficient of reflection $r$ and the Kerr coefficient $k$. The Kerr coefficient is typically much smaller than the coefficient of reflection.

### Transversal MOKEEdit

When the magnetization is perpendicular to the plane of incidence and parallel to the surface it is said to be in the transverse configuration. In this case, the incident light is also not normal to the reflection surface but instead of measuring the polarity of the light after reflection, the reflectivity $r$ is measured. This change in reflectivity is proportional to the component of magnetization that is perpendicular to the plane of incidence and parallel to the surface, as above. If the magnetization component points to the right of the incident plane, as viewed from the source, then the Kerr vector adds to the Fresnel amplitude vector and the intensity of the reflected light is $|r+k|^2$. On the other hand, if the component of magnetization component points to the left of the incident plane as viewed from the source, the Kerr vector subtracts from the Fresnel amplitude and the reflected intensity is given by $|r-k|^2$.

In addition to the polar, longitudinal and transverse Kerr effect which depend linear on the respective magnetization components, there are also higher order quadratic effects, for which the Kerr angle depends on product terms involving the polar, longitudinal and transverse magnetization components. Those effects are referred to as Voigt effect or quadratic Kerr effect.

## ApplicationsEdit

The MOKE is the key operation principle of magneto-optical drives. It is also used in so-called Kerr microscopes to visualize the magnetic domain structure of a sample. The Kerr microscope is an optical light microscope with an additional polarizer and an analyzer to obtain a different contrast from different magnetic orientation.

## DiscoveryEdit

The magneto-optic Kerr effect was discovered in 1877 by John Kerr.