Magneto-optic Kerr effect

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In physics the magneto-optic Kerr effect (MOKE) or the surface magneto-optic Kerr effect (SMOKE) is one of the magneto-optic effects. It describes the changes to light reflected from a magnetized surface. It is used in materials science research in devices such as the Kerr microscope, to investigate the magnetization structure of materials.

Contents

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

Definition

The magneto-optic Kerr effect manifests when light 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, 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 permittivity, 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. [1]

Geometries

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

MOKE-en.svg

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 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, [2] 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 [3] [4]

Applications

Optical experiment for observing the Magneto-optic Kerr effect Setup Magneto-Optic-Kerr-Effect A.png
Optical experiment for observing the Magneto-optic Kerr effect

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 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. [5] [6]

See also

Related Research Articles

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<span class="mw-page-title-main">Total internal reflection</span> Reflection of a wave from a boundary between two media (rather than refraction)

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<span class="mw-page-title-main">Optical rotation</span> Rotation of the plane of linearly polarized light as it travels through a chiral material

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<span class="mw-page-title-main">Brewster's angle</span> Angle of incidence for which all reflected light will be polarized

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<span class="mw-page-title-main">Circular polarization</span> Polarization state

In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to the direction of the wave.

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<span class="mw-page-title-main">Polarization (waves)</span> Property of waves that can oscillate with more than one orientation

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<span class="mw-page-title-main">Waveplate</span> Optical polarization device

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<span class="mw-page-title-main">Birefringence</span> Property of materials whose refractive index depends on light polarization and direction

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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 magnetic field along the direction of the light propagation. Formally, it is a special case of gyroelectromagnetism obtained when the dielectric permittivity tensor is diagonal. This effect occurs in most optically transparent dielectric materials under the influence of magnetic fields.

<span class="mw-page-title-main">Faraday rotator</span>

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The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index change is directly proportional to the square of the electric field instead of varying linearly with it. All materials show a Kerr effect, but certain liquids display it more strongly than others. The Kerr effect was discovered in 1875 by Scottish physicist John Kerr.

<span class="mw-page-title-main">Specular reflection</span> Mirror-like wave reflection

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<span class="mw-page-title-main">Ellipsometry</span> Optical technique for characterizing thin films

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<span class="mw-page-title-main">Polarizer</span> Optical filter device

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<span class="mw-page-title-main">Voigt effect</span>

The Voigt effect is a magneto-optical phenomenon which rotates and elliptizes linearly polarised light sent into an optically active medium. The effect is named after the German scientist Woldemar Voigt who discovered it in vapors. Unlike many other magneto-optical effects such as the Kerr or Faraday effect which are linearly proportional to the magnetization, the Voigt effect is proportional to the square of the magnetization and can be seen experimentally at normal incidence. There are also other denominations for this effect, used interchangeably in the modern scientific literature: the Cotton–Mouton effect and magnetic-linear birefringence, with the latter reflecting the physical meaning of the effect.

<span class="mw-page-title-main">Fresnel rhomb</span> Optical prism

A Fresnel rhomb is an optical prism that introduces a 90° phase difference between two perpendicular components of polarization, by means of two total internal reflections. If the incident beam is linearly polarized at 45° to the plane of incidence and reflection, the emerging beam is circularly polarized, and vice versa. If the incident beam is linearly polarized at some other inclination, the emerging beam is elliptically polarized with one principal axis in the plane of reflection, and vice versa.

An optical modulator is an optical device which is used to modulate a beam of light with a perturbation device. It is a kind of transmitter to convert information to optical binary signal through optical fiber or transmission medium of optical frequency in fiber optic communication. There are several methods to manipulate this device depending on the parameter of a light beam like amplitude modulator (majority), phase modulator, polarization modulator etc. The easiest way to obtain modulation is modulation of intensity of a light by the current driving the light source. This sort of modulation is called direct modulation, as opposed to the external modulation performed by a light modulator. For this reason, light modulators are called external light modulators. According to manipulation of the properties of material modulators are divided into two groups, absorptive modulators and refractive modulators. Absorption coefficient can be manipulated by Franz-Keldysh effect, Quantum-Confined Stark Effect, excitonic absorption, or changes of free carrier concentration. Usually, if several such effects appear together, the modulator is called electro-absorptive modulator. Refractive modulators most often make use of electro-optic effect, other modulators are made with acousto-optic effect, magneto-optic effect such as Faraday and Cotton-Mouton effects. The other case of modulators is spatial light modulator (SLM) which is modified two dimensional distribution of amplitude & phase of an optical wave.

References

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  2. García-Merino, J. A.; et al. (2018). "Magneto-conductivity and magnetically-controlled nonlinear optical transmittance in multi-wall carbon nanotubes". Optics Express. 24 (17): 19552–19557. doi: 10.1364/OE.24.019552 . PMID   27557232.
  3. 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 (6): 1563. arXiv: cond-mat/0609688 . Bibcode:2007JPhD...40.1563H. doi:10.1088/0022-3727/40/6/S09. S2CID   6079803.
  4. Muduli, Pranaba; et al. (2009). "Study of magnetic anisotropy and magnetization reversal using the quadratic magnetooptical effect in epitaxial CoxMnyGez(111) films". J. Phys.: Condens. Matter. 21 (29): 296005. Bibcode:2009JPCM...21C6005M. doi:10.1088/0953-8984/21/29/296005. PMID   21828544. S2CID   3552070.
  5. Kerr, John (1877). "On Rotation of the Plane of the Polarization by Reflection from the Pole of a Magnet". Philosophical Magazine. 3: 321. doi:10.1080/14786447708639245.
  6. Weinberger, P. (2008). "John Kerr and his Effects Found in 1877 and 1878" (PDF). Philosophical Magazine Letters. 88 (12): 897–907. Bibcode:2008PMagL..88..897W. doi:10.1080/09500830802526604. S2CID   119771088. Archived from the original (PDF) on 2011-07-18.

Further reading