Magneto-optic Kerr effect

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

Several grains of NdFeB with magnetic domains made visible via contrast with a Kerr-microscope.

Definition

The light that is reflected from a magnetized surface can change in both polarization and reflected intensity. 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 $\epsilon$ .

Geometries

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

Polar MOKE

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 MOKE

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 MOKE

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 $|r-k|^{2}$ .

Quadratic MOKE

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.

Applications

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.

Discovery

The magneto-optic Kerr effect was discovered in 1877 by John Kerr.^[1]^[2]

References

^ Kerr, John (1877). "On Rotation of the Plane of the Polarization by Reflection from the Pole of a Magnet". Philosophical Magazine. 3: 321.
^ Weinberger, P. (2008). "John Kerr and his Effects Found in 1877 and 1878" (PDF). Philosophical Magazine Letters. 88 (12): 897–907. doi:10.1080/09500830802526604.

External links

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
MOKE Microscope – Magneto-Optical Kerr Effect Microscope [PDF: 3.2MB]

[1] Kerr, John (1877). "On Rotation of the Plane of the Polarization by Reflection from the Pole of a Magnet". Philosophical Magazine. 3: 321.

[2] Weinberger, P. (2008). "John Kerr and his Effects Found in 1877 and 1878" (PDF). Philosophical Magazine Letters. 88 (12): 897–907. doi:10.1080/09500830802526604.

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