In
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
the magneto-optic Kerr effect (MOKE) or the surface magneto-optic Kerr effect (SMOKE) is one of the
magneto-optic effect
A magneto-optic effect is any one of a number of phenomena in which an electromagnetic wave propagates through a medium that has been altered by the presence of a quasistatic magnetic field. In such a medium, which is also called gyrotropic or ...
s. It describes the changes to light reflected from a
magnet
A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, ...
ized surface. It is used in
materials science research in devices such as the Kerr microscope, to investigate the
magnetization
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...
structure of materials.
Definition
The magneto-optic Kerr effect relates
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
that is reflected from a magnetized surface and may change both
polarization and
reflected intensity. The magneto-optic Kerr effect is similar to the
Faraday effect
The Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the ...
, which describes changes to light transmission through a magnetic material. In contrast, the magneto-optic Kerr effect describes changes to light reflected from a magnetic surface. Both effects result from the off-diagonal components of the
dielectric tensor . These off-diagonal components give the magneto-optic material an
anisotropic
Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
permittivity
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
, meaning that its permittivity is different in different directions. The permittivity affects the speed of light in a material:
where
is the velocity of light through the material,
is the material permittivity, and
is the magnetic permeability; and thus the speed of light varies depending on its orientation. This causes fluctuations in the phase of polarized incident light.
This effect is often quantified in terms of its Kerr angle and its Kerr ellipticity.
The Kerr angle
is the angle that linearly polarized light will be rotated after hitting the sample.
The Kerr ellipticity
or
(not to be confused with ellipticity from mathematics) is the ratio of the semimajor and semiminor axes of the elliptically polarized light, generated from reflection of linearly polarized light.
Geometries
MOKE can be further categorized by the direction of the
magnetization
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...
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, and because the other two configurations have vanishing Kerr rotation at normal incidence, 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 is used for polar MOKE. 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
Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular the ...
coefficient of reflection
and the Kerr coefficient
. 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
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
.
Quadratic MOKE
In addition to the ''polar'', ''longitudinal'' and ''transverse'' Kerr effect which depend linearly 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 alloy
Heusler compounds are magnetic intermetallics with face-centered cubic crystal structure and a composition of XYZ (half-Heuslers) or X2YZ (full-Heuslers), where X and Y are transition metals and Z is in the p-block. The term derives from the name ...
s such as Co
2FeSi and Co
2MnGe
Applications
Microscopy
A Kerr microscope relies on the MOKE in order to image differences in the magnetization on a surface of magnetic material. In a Kerr microscope, the illuminating light is first passed through a
polarizer filter, then reflects from the sample and passes through an ''analyzer'' polarizing filter, before going through a regular optical microscope. 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 changes in polarization are converted by the analyzer into changes in light intensity, which are visible. A computer system is often used to create an image of the magnetic field on the surface from these changes in polarization.
Magnetic Media
Magneto Optical (MO) Drives were introduced in 1985. MO discs were written using a laser and an electromagnet. The laser would heat the platter above its
Curie temperature
In physics and materials science, the Curie temperature (''T''C), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Cur ...
at 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.
See also
*
Faraday effect
The Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the ...
*
Fresnel equations
The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by Augustin-Jean Fres ...
*
John Kerr
*
Thin-film optics
Thin-film optics is the branch of optics that deals with very thin structured layers of different materials. In order to exhibit thin-film optics, the thickness of the layers of material must be similar to the coherence length; for visible l ...
*
Voigt Effect
*
Zeeman Effect
The Zeeman effect (; ) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel priz ...
References
Further reading
*
* {{cite book , editor=Etienne Du Trémolet de Lacheisserie , editor2=D. Gignoux , editor3=Michel Schlenker , year=2005 , isbn=978-0-387-22967-6 , title=Magnetism Fundamentals I , publisher=Springer Science & Business Media , page=507 , url=https://www.springer.com/gp/book/9780387229676, ref=Magnetism Fundamentals I
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
DF: 3.2MBbr>
MOKE tutorial– A step by step tutorial on the longitudinal, polar and transverse Magneto-Optical Kerr Effect.
Broadband magneto-optical Kerr spectroscopy
Magneto-optic effects