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 $\epsilon$. These off-diagonal components give the Magneto Optic material an anisotropic permittivity. The permittivity affects the speed of light in a material:

$v_p = \frac{1}{\sqrt{\epsilon \mu}}$

where v_p is the velocity of light through the material, $\epsilon$ is the material permittivity, and μ is the material permeability; and thus the speed of light varies depending on its orientation. This causes fluctuations in the phase of polarized incident light.

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. Quadratic magneto-optic Kerr effect (QMOKE) is found strong in Heusler alloys such as Co₂FeSi and Co₂MnGe^{[1] [2]}

Applications

Microscopy

A Kerr Microscope relies on the MOKE in order to image differences in magnetic orientation. In addition to a regular optical microscope, a polarizer and analyzer are needed as a source and sensor for polarized light. Because the different MOKE geometries require different polarized light, the polarizer should have the option to change the polarization of the incident light (circular, linear, and elliptical). When the polarized light is reflected off the sample material, a change in any combination of the following may occur: Kerr rotation, Kerr Ellipticity, or polarized amplitude. The analyzer then receives the incoming light and passes the data to a computer system which can back out the magnetic field from these changes in polarization.

In conjunction with the Kerr Microscope, Magneto Optical Imaging Films (MOIF) can be used to better image magnetic domains in ferromagnetic materials. These films can be made out of an Yttrium Iron Garnet and are usually substituted with certain rare earth elements. Because the manufacturing process of these films is so specialized, they aren't commercially available.

Magnetic Media

Magneto Optical (MO) Drives were introduced in 1985, and were originally WORM (write once, read many) drives, meaning they could be added to but not erased. Although they are not widely used today, they were reliable both in accurate writing and consistent data retention. Typical sizes ranged from 100 megabytes (MB) up to 9.2 gigabytes (GB). MO drives checked the data as it was being written, and thus took longer than typical CD's or DVD's. However this allowed for increased data integrity.

MO discs were written using laser and an electromagnet. The laser would heat the platter above its Curie Temperature and which point the electromagnet would orient that bit as a 1 or 0. To read, the laser is operated at a lower intensity, and emits polarized light. Reflected light is analyzed showing a noticeable difference between a 0 or 1.

Discovery

The magneto-optic Kerr effect was discovered in 1877 by John Kerr.^[3][4]

See also

• Faraday effect
• Fresnel equations
• John Kerr
• Thin-film optics
• Voigt Effect
• Zeeman Effect

References

1. ^ Hamrle, J et al. (2007). "Huge quadratic magneto-optical Kerr effect and magnetization reversal in the Co₂FeSi Heusler compound". J. Phys. D: Appl. Phys 40: 1563. arXiv:cond-mat/0609688. Bibcode 2007JPhD...40.1563H. doi:10.1088/0022-3727/40/6/S09. 
2. ^ Muduli, Pranaba et al. (2009). "Study of magnetic anisotropy and magnetization reversal using the quadratic magnetooptical effect in epitaxial Co_xMn_yGe_z(111) films". J. Phys.: Condens. Matter 21: 296005. Bibcode 2009JPCM...21C6005M. doi:10.1088/0953-8984/21/29/296005. 
3. ^ Kerr, John (1877). "On Rotation of the Plane of the Polarization by Reflection from the Pole of a Magnet". Philosophical Magazine 3: 321. http://books.google.com/?id=5Ueejs8_9gwC&printsec=frontcover&dq=Kerr+Effects+of+a+Magnetic+Field+on+Radiation. 
4. ^ Weinberger, P. (2008). "John Kerr and his Effects Found in 1877 and 1878". Philosophical Magazine Letters 88 (12): 897–907. Bibcode 2008PMagL..88..897W. doi:10.1080/09500830802526604. http://www.computational-nanoscience.de/Weinberger/Famous-Papers/PML-2008.pdf. 

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]
• MOKE tutorial - A step by step tutorial on the longitudinal, polar and transverse Magneto-Optical Kerr Effect.