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Hieronder een aantal links over het magneto-optische Kerr effect bij elkaar geplakt.

1.

from: http://www-pcs.phy.cam.ac.uk/TFMWWW/Members/Cyrus_Daboo/MOKE/MOKE.html

Magneto-optic Kerr Effect (MOKE)

Contents

Introduction

The Magneto-optic Kerr effect (MOKE) and the Faraday effect correspond to a change in the intensity or polarisation state of light either reflected from (Kerr) or transmitted through (Faraday) a magnetic material. This is shown very simply in the diagram below.

 Since the amount of change in the polaristaion state or intensity is proportional to the magnetisation in the material it is possible to use these two effects to examine magnetic properties.

Theory

The Kerr and Faraday effects occur because the magnetisation in the material produces a change to the dielectric tensor of that material. In an isotropic material one can write:

 Where D is the electric displacement and E is the electric field and these are related to each other through the dielectric tensor as shown. The eigenmodes of the electomagnetic wave propogation in this case correspond to plane-polarised waves with the same velocities

 In a magnetic material, the dielectric tensor has additional off-diagonal terms. These change the nature of the eigenmodes and their corresponding velocities, resulting in a change in the polarisation state on transmission or reflection.

 Ignoring second order effects (which are small) the off-diagonal terms in the dielectric tensor are directly proportional to the components of the magnetisation. The dielectric tensor can now be written as:

 where Qx, Qy and Qz are proportional to the three components of the magnetisation vector in the material. The reflection and transmission coefficients thus depend on these terms as well. For example, for a non-magnetic/magnetic layer system the Fresnel coefficients for reflection in the presence of a magnetisation perpendicular to the interface for light at normal incidence are:

 The suffixes on the reflection coefficients above signify the incident and refelected polarisation states. Thus the cross-term rps signifies a rotation of the plane of polarisation which is proportional to the magnetisation.

Experimental setup

There are three principal modes of operation for MOKE:
 
 
Longitudinal MOKE
This geometry provides a signal proportional to the component of magnetisation that is parallel to the film plane and the plane of incidence of the light. The magnetic field is applied parallel to the plane of the film and the plane of incidence of the light. A polaristaion rotation is detected using crossed polarisers.

 

 


 
 

Transverse MOKE
This geometry provides a signal proportional to the component of magnetisation that is parallel to the film plane but perpendicular to the plane of incidence of the light. The magnetic field is applied perpendicular to the plane of incidence of the light. A change in the intensity of p-polarised incident light is detected.

 

 


 
 

Polar MOKE
This geometry provides a signal proportional to the component of magnetisation that is perpendicular to the film plane. The magnetic field is applied perpendicular to the plane of the film. A polaristaion rotation is detected using crossed polarisers.

 

 

cd102@phy.cam.ac.uk

 

 

2.
from: http://physg.uni-bielefeld.de/helium/carsi1.htm

The Kerr Effect


If a beam of plane polarized light illuminates a metallic surface the reflected light will in general be elliptically polarized. If, however, the plane of polarization of the incident light (here defined as the plane containing the electric vector) is either parallel or perpendicular to the plane of incidence then the reflected light is also plane polarized. That this is so is in no way due to any peculiarities of metallic reflection but follows straightaway from the fact that the plane of incidence is a plane of symmetry for the system. Incident light polarized parallelly or perpendicularly to this plane is therefore always reflected as plane polarized light. This symmetry is destroyed by the presence of a magnetic field, for although a uniform magnetic field possesses a plane of symmetry perpendicular to the direction of the field its sign is associated with an unsymmetrical rotation about this direction. Consequently, if the reflecting surface is magnetized the reflected light will in general be elliptically polarized even if the incident light is polarized parallel or perpendicular to the plane of incidence. This phenomenon is known as the Kerr effect. The degree of ellipticity imparted to the reflected beam is small and the effect can be regarded as a rotation of the plane of polarization of the light on reflection. The effect is greatest in the ferromagnetic metals, is smaller in ferrites and barely observable in paramagnetic metals. There are three different dispositions of the magnetic field with respect to pane of incidence and these give rise to three different effects each governed by slightly different laws. These are:

 (a) Polar effekt (figure 1 (a)), i.e. magnetization normal to the reflecting surface. The effect is largest in this case and it is the only situation in which an effect exists light incident normally on the surface

(b) Longitudinal effect (figure 1 (b)), i e magnetization in the plane of the reflecting surface parallel to the plane of incidence. This is often referred to as the meridional effect. The rotation is smaller than for the polar effect usually by a factor of 3 or 4.

(c) Transverse effect (figure 1 (c)), i e. magnetization in the plane of the reflecting surface and perpendicular to the plane of incidence This is sometimes referred to as the equatorial effect. Any other situation can easily be seen to be a combination of two or more of these.
MOKE,  He* Group,  Research Group D1, Faculty of Physics, University of Bielefeld



This page was updated on 15-April-1996 by
Carsten Graf
 

3.

from: http://emtech.boulder.nist.gov/div814/magtech/kerrscop.htm

The Kerr Optical Analysis Platform at NIST/EEEL

Kerr optical microscopy is a method by which magnetic domains may be imaged using conventional polarizing microscope optics. This method employs the magneto-optic Kerr effect (MOKE) as a contrast mechanism. This method is convenient in that it requires minimal sample preparation and does not require vacuum or sophisticated scanning mechanisms. Resolution, however, is constrained by optical diffraction effects to approximately the wavelength of light (0.4-0.7 micrometers).

MOKE describes the property of ferromagnetic material to alter the polarization state of light upon reflection. The simplist and strongest of the effects is the rotation of polarization of reflected light when normally incident on a body which is magnetized perpendicularly to the reflection surface. This is called the polar MOKE. The magnitude of polar MOKE ranges from 0.1-1 degree, depending on the composition of a sample and the wavelength of the light. If the body is magnetized parallel to the reflection surface, the polarization of incident light may still be affected if the incidence is oblique and the plane of incidence is parallel to the sample magnetization. In this case of longitudinal MOKE, both the polarization angle and degree of ellipticity are affected. This form of MOKE is most frequently employed in the imaging of domains structures since most ferromagnetic samples do not exhibit magnetization perpendicular to the surface. It is, however, an order of magnitude smaller than for polar MOKE and therefore requires sophisticated detection electronics.

The Kerr optical analysis platform at NIST/EEEL has both microscopic imaging (qualitative) and hysteresis looping (quantitative) capabilities. Both imaging and looping use the same microscope optics. To image domains, the light reflected from the sample passes through a polarization analyzer and is then detected with a high performance CCD camera capable of 16 bit dynamic range. The digitized image of the sample surface may be processed by a computer to enhance the visibility of magnetic domains. To measure the hysteretic properties of the sample, the reflected light from a small spot on the sample surface is diverted to a modulating polarization analyzer. The polarization signal is converted to a 50 kHz ac electric signal which is measured using a lock-in amplifier. By plotting the measured Kerr signal against the field applied to the sample during a sweep, the hysteresis loop for a given material may be obtained. This provides such important material parameters such as the coercivity, saturation field, ratio of remanent to saturation magetization, and permeability at the coercive point. 

Kerr microscope image of magnetic domains in an 8 micrometer wide stripe of NiFe thin film. The magnetic element is the sensor in a magnetoresistive device. The current leads are used to measure the field-dependent resistivity of the MR stripe. MR sensors are rapidly becoming the predominant readback element in commercial disk drives due to their superior signal-to-noise characteristics. For optimum performance, the magnetic element should remain in a single domain state. This picture shows a device which was intentionally prepared in a three-domain state by application of an external magnetic field. Correlation of the transport properties of the device with the details of the domain pattern provide insight into possible modes of device failure.

Kerr microscope image of YIG

This is a conventional Kerr microscope image of magnetic "stripe" domains in a film of yttrium iron garnet (YIG). The domains are made visible by the magneto-optic Kerr (MOKE) effect, by which the polarization of reflected light is slightly rotated in a magnitude proportional to the magnetization of the film. The magnetization of the film is oriented perpendicular to the film plane. To lower its magnetostatic energy, the film breaks up into this stripe domain pattern. Each stripe is approximately five micrometers in width. Kerr microscopy is a powerful means of readily imaging domain patterns in films at the relatively low resolution of ~1 micrometer. Higher resolution imaging methods available at NIST/EEEL include magnetic force microscopy (MFM) and (in the near future) scanning near-field magneto-optic microscopy (MOKE-SNOM).
Return to Home Page 
silva@boulder.nist.gov

 

 
 
 

4.
from http://www.ifw-dresden.de/IFF/12/magnetik12/detail/moke_e.html
 

Magnetic hysteresis loops by Magnetooptical Kerr Effect

A MOKE equipment can be used to quickly characterise the prepared magnetic films. Our MOKE setup permits the measurement of hysteresis loops up to an external magnetic field of about 0.4T at room temperature.
Experimental Setup

Linear polarised light of a very bright red LED propagates under 45° onto the reflecting sample surface. Another linear polariser is placed into the reflected beam to analyse the polarisation. Its crossed positioning vanishes the light intensity. But, a sample magnetisation leads to an additional polarisation tuning. Thus, a photo current flows out of the detector with

Iphoto ~ cos²(½ pi + phi) --> phi², for small angles phi.

Experimentally, the polarisation tuning is compensated by a Faraday rotator in a feedback loop which minimises the photo current. If the samples magnetisation changes under a variable external magnetic field B one can observe the hysteresis loop in the output of the regulator signal.

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Author: Michael Stehle <stehle@ifw-dresden.de>

Constructed: Nov. 25th, 1996
Updated: Feb. 27th, 1997