Magneto-optic Kerr effect
(MOKE) is one of the magneto-optic effects
. It describes the changes of light reflected from magnetized
that is reflected from a magnetized surface can change in both polarization
. 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
MOKE can be further categorized by the direction of the magnetization
vector with respect to the reflecting surface and the plane of incidence.
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.
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
vectors, namely the standard Fresnel amplitude
coefficient of reflection
and the Kerr coefficient
. The Kerr coefficient is typically much smaller than the coefficient of reflection.
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
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
. 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
In addition to the polar
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
magnetization components. Those effects
are referred to as Voigt effect
or quadratic Kerr effect.
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.
The magneto-optic Kerr effect was discovered in 1877 by John Kerr
- J. Kerr, Phil. Mag. 3, 321 (1877).
- Kerr Calculation Applet – Java applet, computes the Kerr angle of multilayered thin films
- yeh-moke – Free software computes the Magneto-optic Kerr effect of multilayered thin films