Manual The Effects Of A Magnetic Field On Radiation -Memoirs By Faraday Kerr And Zeeman

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In addition, our device could be switched from polarization-insensitive to polarization-sensitive by applying a magnetic field. To the best of our knowledge, this study, combining the electrical, magnetic, and optical effects of hot electrons and Si-based devices, is the first to modulate the efficiency of Si-based photodetectors working at optical telecommunication wavelengths. This strategy would, presumably, also be potentially very useful when applied to other hot electron-based systems and devices.

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    This article has been cited by other articles in PMC. Open in a separate window. Figure 1. THz spectroscopy The transmittance experiments at THz frequencies 0. Figure 2. Charge carriers in strained HgTe. Band structure analysis To understand the origin of the experimentally observed resonances, we analyse the band structure of tensile strained Cd 0.

    Quantized THz Hall effect Experimentally, simultaneous fit of the real and imaginary parts of t p and t c allows the extraction of all transport characteristics, that is, conductivity, charge carrier density, scattering time and CR frequency Figure 3. THz QHE of the surface states. Figure 4. Quantized THz Faraday rotation of Dirac fermions. Theoretical analysis of magnetooptical spectra To analyse the experimental transmission spectra, we follow the formalism described by Berreman 24 , Data availability The data that support the findings of this study are available from the corresponding authors upon reasonable request.

    Additional information How to cite this article: Dziom, V. Peer Review File: Click here to view. Footnotes The authors declare no competing financial interests. References Kane C. Quantum spin Hall effect in graphene. Quantum spin Hall effect and topological phase transition in hgte quantum wells.

    Science , — Topological insulators with inversion symmetry. B 76 , Quantum spin Hall insulator state in HgTe quantum wells. A topological dirac insulator in a quantum spin Hall phase. Nature , — Topological field theory of time-reversal invariant insulators.

    B 78 , Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators. Inducing a magnetic monopole with topological surface states. Surface state charge dynamics of a high-mobility three-dimensional topological insulator. Terahertz response and colossal Kerr rotation from the surface states of the topological insulator bi 2 se 3. Terahertz quantum hall effect of Dirac fermions in a topological insulator. B 87 , Magneto-optical and magnetoelectric effects of topological insulators in quantizing magnetic fields. B 82 , Topological quantization in units of the fine structure constant.

    Anomalous galvanomagnetism, cyclotron resonance, and microwave spectroscopy of topological insulators. B 84 , Optical Hall effect in the integer quantum hall regime. Quantum Faraday and Kerr rotations in graphene. Quantum Hall effect from the topological surface states of strained bulk HgTe. Dirac-screening stabilized surface-state transport in a topological insulator.

    X 4 , Cyclotron-resonance-assisted photocurrents in surface states of a three-dimensional topological insulator based on a strained high-mobility HgTe film. B 92 , Giant magneto-optical Faraday effect in HgTe thin films in the terahertz spectral range. Room temperature electrically tunable terahertz Faraday effect.

    Dielectric measurements in the submillimeter wavelength region. Infrared Phys. Terahertz magneto-optical spectroscopy in HgTe thin films. Optics in stratified and anisotropic media: 4x4-matrix formulation. Infrared and microwave magnetoplasma effects in semiconductors. B 72 , B 89 , Heavy-light hole mixing at zinc-blende interfaces under normal incidence.

    B 54 , — Tunable spin helical Dirac quasiparticles on the surface of three-dimensional hgte. Ab initio study of topological surface states of strained HgTe. EPL , Single valley Dirac fermions in zero-gap HgTe quantum wells. Spin-helical transport in normal and superconducting topological insulators. Status Solidi b , — Spatially resolved photocarrier energy relaxation in low-doped bulk GaAs. B 86 , Discovery of a Weyl fermion semimetal and topological Fermi arcs. For the camera resolution the effective cell size of the camera is the figure of merit.

    The eventual resolution of the imaging sensor is determined by the dimensions of the individual photo-sensitive elements relative to the image projected onto the imaging array in the microscope system. In order to match or exceed the optical resolution of the objective lens and to preserve the spatial resolution of the objective lens in the resulting MO image, the sampling interval of the camera sensor array has to be at least twice the maximum spatial frequency of the sample.

    This relation is given by the Nyquist criterion [ , ]. The camera sensor must be able to sample at intervals equal or less than half the resolution of the microscope. A comparison of the change of resolution for a captured image depending on the camera's cell size is given in figure Corresponding data on the achievable spatial resolution from typical objective lenses is given. Curves for different level of binning are included.

    For values of NA of the different objectives see table 2. A sensor cell size of 6. For low magnification images and for the chosen properties of camera and objective lens, the best achievable resolution is limited by the camera, and not the NA of the objective lens. Without binning and below a threshold of about 50 times in magnification, the actual image resolution is determined by the camera property and not by the objective lens.

    Adapting the microscope setups for temperature dependent imaging is straightforward. Cryostats, for low temperature imaging, and heating stages, for the imaging at higher temperatures, can be integrated into the setups. Low temperature applications include the imaging of flux penetration into type-II superconductors with ferrimagnetic MO indicator films [ — ] see also section 8 , the imaging of domains in magnetic semiconductors [ — ], and exchange coupling phenomena in magnetic multilayers [ — ].

    Also magnetic phase transitions at low temperature [ — ] and around room temperature [ ] are of relevance. High temperature observations deal with crystallization processes in soft magnetic nanocrystalline materials [ , ], again with exchange bias phenomena [ ], and the change of magnetic properties with temperature in hard-magnets [ ]. Other applications include for instance rock magnetism [ ] for elevated temperatures, and the investigations of structural phase transitions [ , ] for low temperatures. One obstacle for the use of heating stages and cryostats is related to the use of viewports to optically access the samples.

    Two in principle different approaches are used. In one case, the imaging is performed through an optical window between the magnetic object and the objective lens. With that approach figure 13 a , the use of long-distance objective lenses with an optical correction for the viewing window thickness is required at least for high NA objectives. By this, highest spatial resolution is not possible to achieve. In another approach figure 13 b , the objective lens is integrated into the cryostat or heater and the viewing window is between the objective lens and the microscope.

    Regular high NA objective lenses can be used. Yet, the application of oil immersion lenses is excluded. For both principle variants the viewing window must be stress-free in order to not alter the polarization state of light. A complete integration of electromagnet and focusable objective lens inside a vacuum chamber for temperature dependent measurements has been used in [ ].

    Central aspects of imaging systems for temperature dependent imaging. The sample is mounted on a cold or heating finger. The lens is integrated into the cryostat, respectively heating chamber [ , ]. Vibrational influences need to be reduced by mechanically decoupling or damping of the connected vacuum systems. Internal vibration isolation and a low thermal-expansion support structure help to reduce vibrations and drifts of the sample position. For the applications of external magnetic fields heaters and cryostats are equipped with an extended sample mount, permitting for the high magnetic field applications by allowing a close integration of magnetic pole-tips at the magnetic sample.

    One of the utmost advantages of MO imaging over the majority of other imaging methods is the ability to visualize fast dynamic magnetization processes. However, different definitions of magnetization dynamics exist, ranging from femtosecond processes for ultrafast spin-dynamics, Landau—Lifschitz dynamics on the nanosecond time-scale to eddy-current dominated magnetization dynamics in the micro- to millisecond range for thick samples. Yet, creeping phenomena on the time-scales of seconds or more can be part of it. The whole range of time-scales can be covered by MO microscopy.

    Depending on the requirements of the experiment, different methods are applied to obtain the needed temporal resolution. A discrimination has to be made between single shot imaging and stroboscopic imaging techniques, the latter used for imaging of fast dynamic magnetization processes. Dynamics on time-scales of several seconds or even longer can be imaged directly and in real-time by MO microscopy. Of particular interest for long-term dynamic studies are magnetization relaxation processes as they occur in ultrathin magnetic films. An overview on certain aspects of magnetization reversal studies by MO methods, including MO imaging of thermally activated processes, is given in [ ] and [ ].

    Examples of snapshot domain images from the reversal of magnetic single and multi-layers with perpendicular and in-plane magnetic anisotropy that display thermally activated effects [ — ] are depicted in figure Reprinted with permission from [ ]. Copyright by the American Physical Society. Magnetization dynamics at the kHz range can be imaged by means of stroboscopic imaging using gated image intensifiers as demonstrated firstly for the observation of garnet domains using the Faraday effect [ ]. This method has been revived for the imaging of eddy-current limited magnetization dynamics in magnetic core materials [ — ].

    From stroboscopic MO Kerr effect microscopy observations, the dynamic magnetization process on nanocrystalline tape wound cores is clarified. Of particular interest in these studies were magnetic excess losses, the related eddy-current driven magnetic domain wall refinement, and the repeatability of the magnetization processes. An exemplary image of such a measurement, displaying patch-like domain behavior, is displayed in figure 15 a. High and variable repetition rates and continuously adjustable time resolutions are possible with such imaging systems.

    The coarse hexagonal capillary structure of the microchannel plate MCP image intensifier results in an effective reduction of spatial resolution. The use of a two-stage or three-stage MCP image intensifier can partly reduce that circumstance. Images with microsecond time resolution obtained by means of different techniques. At least partial repeatability of the magnetization processes is required for stroboscopic imaging. Single shot imaging of magnetization relaxation in exchange-biased perpendicular anisotropy thin films was realized by imaging with an arc flash lamp [ ].

    Yet, the typical dependence of light intensity with time for the imaging with such schemes is strongly influenced by the long exponential decay of intensity of the illuminating light pulse.

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    An exemplary single shot image from an asymmetric magnetization reversal in an exchange-biased thin film with out-of-plane anisotropy is displayed in figure 15 b. A similar illumination scheme was used for the imaging of magnetic field induced transformations in magnetic shape memory alloys [ , ]. Single shot imaging of the magnetization reversal in a grain oriented electrical steel sheet, however, is also possible with a large field MO microscope see section 3.

    Some microsecond resolution is achievable by direct imaging at low exposure times with regular CCD-based cameras without the need of image intensifiers figure 15 c. Wide-field imaging on the nanosecond time-scale [ ] has been realized by similar ways as discussed in the previous section. Also here, time resolution is achieved by imaging with a gated image intensifier. The principal use of such a camera system for the imaging of magnetization dynamics in recording head writers in the nanosecond time range was demonstrated [ ].

    In an alternative pioneering approach [ — ], using pulsed Q-switched ruby and gas lasers and in combination with gated illumination, a temporal resolution down to some nanoseconds is achieved. Stroboscopic wide-field imaging with mode-locked picosecond lasers has been used for investigations of magnetization dynamics of thin film elements on the micrometer length scale. Different techniques were applied, all relying on pulsed magnetic field applications with sub-nanosecond rise-times [ — ].

    In the laser-based stroboscopic imaging schemes, time resolution is defined from the laser pulses. A continuous dc recording of the camera signal is applied. Nearly jitter-free time-resolved wide-field MO Kerr effect microscopy with picosecond time resolution and with phase-locked harmonic excitation is demonstrated in [ ]. Such a system allows for the direct imaging under a continuous microwave field excitation. By this the direct imaging of fundamental dynamic modes of magnetic domain and domain wall states in soft magnetic thick film elements becomes possible.

    Domain wall oscillations can be imaged directly and domain wall velocities can be extracted. The basic imaging setup is displayed in figure Stroboscopic time-resolved imaging setup consisting of a mode-locked laser as an illumination source, a standard MO microscope, and a GHz magnetic field excitation source. The mode-locked Nd:YVO 4 laser runs from the same clock as the rf signal generator, providing low jitter imaging conditions [ ]. The shown amplifier and the oscilloscope are optional.

    A magnetic rf-field is applied through a coplanar wave-guide. A phase-locked loop is used to synchronize the repetition rate of the passively mode-locked laser system to the reference clock signal, by constantly adjusting the laser cavity length, controlling its frequency and phase. With the clock synchronizer feedback system, a timing jitter of less than 0. The direct observation of magnetization processes up to several GHz excitation frequencies is possible with such a microscope system.

    In general, picosecond time-resolved MO imaging is performed in a stroboscopic differential imaging mode with varying the phase between the rf field excitation and the imaging laser pulse. Two individual differential images are formed from the difference of two magnetization states at different time delays. By imaging in this manner, only alterations of magnetization become visible in the domain response images.

    Exemplary data demonstrating the imaging of precessional magnetization response, the direct observations of nanosecond domain wall displacements and spin-wave generation from magnetic thin films samples are displayed in figure Despite the application of in-plane microwave field excitations, out-of-plane contributions of magnetization precession including dynamic magneto-static coupling between individual magnetic domains are imaged figures 17 a and b.

    Precessional domain wall motion with out-of-plane magnetization components is seen in figure 17 c [ ]. The domain wall precession acts as a source for spin-waves within the central magnetic domains as seen in figure 17 d. The spin-waves propagate with 0. Moreover, the direct imaging of standing spin-waves at field excitations up to several GHz is possible by the technique, an example of which is displayed in figure 17 e. Stroboscopic Faraday imaging of sub-picosecond processes using femtosecond lasers is demonstrated in [ ]. No saturated background image see also section 4.

    A pump-and-probe all-optical switching experiment is applied to a ferrimagnetic GdFeCo thin film sample. Exemplary data of the evolution of magnetization during the all-optical switching event is displayed in figure The images represent a map of individually determined MO Kerr angles of polarization.

    A general challenge of MO Kerr or Faraday imaging is the obtained low magnetic domain contrast as a result of the weak nature of the MO effects. In practice, the realizable magnetic domain image quality is determined by the achievable signal-to-noise ratio. For a given plane of incidence and a given magnetic material, the SNR is mainly influenced by two additional experimental parameters. Firstly, for the set MO sensitivity the overall MO contrast needs to be optimized by proper setting of the polarization optics.

    This is in first approximation done by correct setting of the analyzer angle in order to obtain the optimum SNR. Secondly, the MO or domain contrast is amplified and image noise is reduced by digital image processing, by which clear and low-noise domain images are produced. For a given setting of illumination, the MO contrast is mostly determined by the analyzer settings, meaning the angle of analyzer rotation from maximum extinction in the optical microscope path. For digital imaging applications, the figure of merit is the SNR of the captured domain image with a variation of magnetization along the sensitivity direction.

    It represents the ratio of the measured light signal to the combined noise of different origin. Unwanted image signal components originate from the used electronics and from variations of the incident photon flux. Common sources of noise in a digital imaging system are therefore photon noise, dark noise, and read noise [ ].

    Dark noise and read noise are directly determined by the digital camera system. The overall SNR for a digital imaging system can be approximated by. D is the dark current value and N r denotes the read noise [ , ]. B is the number of binned camera pixels. Subsequently, we will focus on the regime, where photon noise is dominating and other noise sources are not relevant, thereby neglecting very short exposure and integration times. In most cases will be valid. The first term in the equation is defined by the used illumination and camera settings.

    The SNR can be increased by integrating or averaging over time, using a high quantum efficiency digital camera and binning. The variation of the overall photon energy has a small contribution. The second term is determined by the analyzer setting and the strength of the MO effect. By optimization of the analyzer's uncrossing angle, maximum SNR is obtained. The points of best SNR are indicated. Two main conclusions become obvious from the shown modelling results. However, the reduction of SNR is relatively low. The relevance of such calculations for applied MO microscopy should be treated with care.

    Yet, the shown general dependencies are in agreement with results from experiments. Fast image processing provides the basis of state-of-the-art MO imaging. By digital image processing techniques such as digital Fourier filtering [ , ], real-time background subtraction, and averaging of MO signals improved quality magnetic domain images became practical.

    Digital image processing in real-time was firstly applied for low-contrast imaging in medical [ ] and biological [ — ] imaging applications and was later adapted for the use in magnetic domain imaging. Many different schemes for the improvement of MO signals are conceivable. The main objective is obtaining a high contrast magnetic signal, in which non-magnetic contrast contributions are eliminated. Most of the applied routines for contrast enhancement are based on differential imaging of magnetic states. With alterations of optical polarization or of the magnetic settings purely magnetic high contrast response images are acquired.

    SNR is improved by averaging multiple image frames. Naturally, gain and offset to the digital camera sensor can be applied in order to achieve a maximum camera contrast [ ]. Imaging by alteration of the optical polarization conditions relies on a modulation of polarization [ — ] or on differential imaging of the same magnetic state imaged with two different analyzer or polarizer settings in the microscope. Practically, better imaging quality is obtained by changing the state of polarization of the illumination settings, as compared to the analyzer settings.

    For this kind of differential imaging, no alteration of the magnetization state is needed. This makes it most applicable, where an alteration of magnetization is not feasible. For instance, it is applied for domain observations of permanent magnet materials [ — ] or where a modification of the magnetic state of interest is unwanted [ 22 ]. An alternative method relies on the fitting of the local sensitivity function from multiple MO images [ ] see figure An exemplary set of two raw magnetic images taken from an extended soft magnetic metal film using two different polarization conditions is displayed in figures 20 a and b.

    Obtaining both images under different conditions of polarization, an inversion of the MO contrast is achieved. After subtracting the images, the weak magnetic domain contrast can be amplified and a clear high contrast magnetization domain map is achieved figure 20 c. All images are obtained by averaging over 32 image frames.

    The principle polarizer settings are indicated. In the standard approach, a background image that displays no or an averaged out magnetic signal or a homogeneous magnetic information figure 20 d is acquired, which is then subtracted from the magnetic domain pattern of interest [ — ] figure 20 e. The resulting MO domain image is displayed in figure 20 f. Most of the images shown in this article are acquired by this technique. Real-time and high contrast domain imaging is achievable by this method. In an alternative approach neither of the MO images is acquired in a homogenous state of magnetization.

    Differential images are obtained from variations of magnetization with a small magnetic stimulus [ 27 , , , ]. The method of differentiating of slightly altered domain states has gained renewed attention for the imaging of small nanostructures, especially for the investigation of magnetic field- and current-induced domain wall motion in magnetic nanowires [ — ].

    Likewise, the same approach is used for time-resolved stroboscopic imaging schemes that rely on repeatable magnetic events [ — , ]. Variations of the imaging scheme, including more complicated imaging sequences are discussed in [ ]. In imaging techniques relying on magneto-optical indicator films, a differential image in the indicator film is acquired by removal of the magnetic sample of investigation, keeping the indicator film in place [ ]. For samples with locally varying reflectivity, however, the total MO intensity difference between images for positive and negative magnetization saturation can be uneven.

    The Effects of A Magnetic Field on Radiation: Momoirs by Faraday, Kerr and Zeeman

    Examples are samples with surface topography, different or locally changing roughness, and optically anisotropic polycrystalline large grain materials. The local effective MO sensitivity variation is then superimposed on the magnetic domain image, by which an interpretation of the magnetization distribution is hampered. Related to quantitative domain imaging, the procedure applies only to MO images obtained for a single sensitivity direction.

    A signature of such an imaging error would be a lateral inhomogeneity in MO intensity, the difference between images for positive and negative magnetic saturation along the sensitivity axis. The thus effective non-uniformity of the MO sensitivity will be superimposed on the magnetic domain image. Various examples together with improved MO images are given in [ ]. Surprisingly, the technique is not used routinely so far.

    The method can also be applied for correction of uneven illumination in not properly set MO microscopes. Instabilities in the optical illumination source and mechanical instabilities reduce the quality of the results. Magnetic sample or microscope movements of only a few nanometers lead to a degradation of the MO image.

    Hence, a very steady intensity illumination source and a mechanically stable microscope are a prerequisite for all differential imaging schemes. Mechanical instabilities can be partly compensated by digital image cross-correlation, by which an improved alignment of the background and the domain state image is achieved. With sub-pixel digital image alignment, image drifts with accuracy below one nanometer can be compensated, an example of which is shown in figure The technique can be applied after imaging, but also in situ and in real-time.

    Klug, Kiel University. Despite its advantages for the understanding of magnetization patterns of complicated magnetic domain structures, quantitative magnetic MO microscopy is a technique that is hardly applied for magnetic materials investigations. It is based on the use of a complicated calibration scheme involving multiple calibration images, by which the angular MO sensitivity function in the MO microscope is determined [ — ] experimentally. Similar vectorial mapping of magnetization can be obtained by other domain imaging techniques like spin-polarized scanning electron microscopy [ — ] and by differential phase contrast imaging DPC with Lorentz microscopy [ , ].

    Restrictions of the MO microscopy approach lie in the presumed sinusoidal MO sensitivity function. Existing errors can partly be eliminated by including a quadratic Voigt term in the fitting of the sensitivity functions [ ].

    What is FARADAY EFFECT? What does FARADAY EFFECT mean? FARADAY EFFECT meaning & explanation

    Examples of applied quantitative MO domain imaging include low magnetic anisotropy ribbons [ ] and mixed anisotropy hybrid magnetic property thin films [ ], where an easy domain interpretation is not feasible. Magnetization maps from thin films with orthogonally laterally distributed magnetic anisotropy axes are displayed in figure 22 see also [ ] and section 7. Real-time imaging with vector information of the magnetic domains is not possible with this imaging technique.

    The corresponding magnetization vector distribution is displayed in b. Multiple wavelength imaging schemes are used routinely in life science microscopy investigations [ — ]. An MO imaging approach for the simultaneous imaging of multiple magnetization components based upon a dual-wavelength approach is demonstrated in [ ]. In this imaging scheme two imaging paths are merged in the microscope. For the demonstrated implementation of the technique two fiber-coupled high power LEDs with different optical wavelengths are applied concurrently for illumination.

    An individual independent positioning of illumination settings for both light sources, like oblique and orthogonally aligned planes of incidence, is possible by this. Accordingly, illumination conditions for simultaneous s- and p-mode longitudinal MO sensitivity can be obtained. The imaging beams are coupled into the illumination light path through a wavelength sensitive dichroic mirror figure 23 a , compare to figure 9.

    Other arrangements are possible. Most important, in the reported scheme, the reflected light is yet again divided into two separate light paths that are directed onto two synchronized high sensitivity microscope cameras, by which two domain images under different MO conditions are ultimately obtained. In an alternative arrangement an image splitter is used, which enables recording of MO images simultaneously with one camera system figure 23 b.

    Alternatively, by sequentially imaging and synchronizing the individual LEDs with the exposure of a regular camera system, similar results can be obtained, but with only nearly simultaneous imaging. Using an image splitter the primary image gets divided into two separate images.

    For the complete illumination and observation scheme, including the conjugate image planes IP and aperture planes AP , see figure 9. In general, the use of a divided optical illumination and observation path allows for the direct extraction of different complementary magnetic information. The multi-channel image approach permits complicated imaging schemes, like combination images involving multiple applied MO sensitivity conditions, including mixed Kerr and Voigt imaging and quantitative evaluation from one magnetic pattern.

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    So far imaging with only one pair of images was possible [ 2 ]. An illustrative example of an advanced measurement involving four complementary MO images of a single unaltered domain structure from an epitaxial iron film is displayed in figure Concurrently obtained d diagonally aligned Kerr and e Voigt image after change of the fiber output alignment. The corresponding illumination arrangements in the back focal plane of the objective are indicated.

    Imaging: R. Malik, Kiel University; sample: D. From such an analysis, the magnetization distribution of samples with complicated magnetization behavior can be derived and magnetic domain features remaining hidden with standard single sensitivity domain imaging techniques are directly exposed. In particular, the biggest advantage of the multicomponent measuring scheme is the possibility of real-time imaging of multiple components, by which, among other potentialities, the quantitative imaging of magnetic domain in motion becomes realizable.

    The application of real-time magnetic vector imaging to complicated domain processes in stressed magnetostrictive films for magnetoelectric sensor application is first demonstrated and used for the understanding of the noise mechanism in magnetoelectric composite sensors [ ] figure Magnetization reversal in an amorphous magnetostrictive FeCoSiB layer. The orientation of the applied magnetic field is horizontal. Yet, dual beam—dual sensitivity imaging is not limited to quantitative evaluation of magnetization.

    Other embodiments of imaging include the separation of in-plane and out-of-plane magnetic contrast in oblique plane of incidence MO microscopy and layer selective magnetic domain imaging. By local ion irradiation regions with locally varying magnetic properties are obtained similar to [ ]. Shown is a generated square element with oblique plane of anisotropy, displaying a mixed longitudinal and polar MO contrast figures 26 a and b , surrounded by a matrix with pure in-plane anisotropy.

    By addition and subtraction of MO images obtained with opposite oblique incidence, pure polar figure 26 c and pure longitudinal in-plane sensitivity figure 26 d images are obtained. The latter is not possible by other means in MO microscopy see also section 2. In d only in-plane components of magnetization are visible. The settings of illumination are indicated in a and b. Experiments together with P. Mazalski and A. Maziewski, University of Bialystok. Moreover, the dual imaging scheme can be applied to the simultaneous imaging of individual layer magnetization in multilayer stacks.

    Displayed in figure 27 are two domain images from the same structure, which are recorded simultaneously in a dual image arrangement. Only one single digital camera image with two domain images is shown. Clearly, two dissimilar domain patterns corresponding mainly to the top and bottom layer magnetization, respectively, are distinguished. Magnetic domain images obtained simultaneously with different depth sensitivity by double wavelength microscopy using an image splitter.

    The same plane of incidence is used. Malik [ ]. In conclusion, using two imaging paths, domain images with different sensitivities are recorded simultaneously. Quantitative domain imaging, layer selective magnetic domain imaging in multi-layered thin film structures, as well as the separation of in-plane and out-of-plane magnetization components in film structures with out-of-plane and in-plane magnetization components are now possible. An extension to time-resolved imaging techniques is straightforward. Even being a standard method in optical microscopy, dark field imaging is almost never used for MO microscopy applications [ , ].

    Yet, dark-field MO imaging based on the Faraday effect is demonstrated for the investigations of Bloch lines and conically shaped bubble domains in transparent epitaxial ferrimagnetic garnet films [ — ]. With an inclined plane of incidence using a high aperture condenser lens together with a low aperture objective lens, diffractive MO contrast images of the magnetic domain boundaries and internal domain wall features are obtained from diffraction.

    While the directly transmitted light is omitted, the MO image is produced purely from the diffracted light. Despite recent advances in diffractive MO magnetometry on periodic magnetic nanostructures [ — ], dark field MO imaging in reflection remains untested.

    In general, imaging of a complete magnetization loop with varying magnetic field H ext by MO microscopy provides a large amount of microscopic information, which is usually viewed as a series of sequentially obtained magnetization maps M x , y , H ext. From this data a regular magnetization loop can be derived, by which the data is reduced to its most essential core. However, valuable information is lost thereby. Only a few attempts have been made to bridge that gap. In [ ] a method of representation of multiple images is introduced that allows for compact representation of magnetization reversal information.

    Analyzing and plotting the information obtained from histograms of individual reversal maps, the information of fractions of different kinds of domains and magnetization components is gained. In another attempt [ ] the reversal of magnetization in single quasi 1D magnetic stripes with H ext is analyzed and the data is presented in a 3D map of the magnetic reversal process See also figure 17 d for a similar approach for time-resolved imaging data of spin-wave propagation from a single domain.

    Exemplary domain images of the magnetic reversal of the magnetostrictive phase of a magnetoelectric composite are displayed in figure 28 a. A map of the complete reversal extracted from line-plots for the individual field steps of the overall reversal process is shown in figure 28 b. Decreasing the magnetic field from saturation, first narrow domains develop which coarsen with decreasing field.

    At a certain threshold field, a reorganization process takes place and wide domains instantaneously nucleate. In the reversed field, narrow domains penetrate from the edges and a continuous domain refinement [ ] takes place. All this can be followed from the presentation displayed in figure 28 b. Plotting the histogram in a similar way as in [ , ] figure 28 c , the development of multiple domains, magnetic domain coarsening, and the continuous domain refinement can be understood in a similar way.

    As the MO sensitivity direction is chosen perpendicular to the applied magnetic field, a hysteresis loop cannot be extracted. However, the evolution of the transverse components of magnetization in the individual domains with field can be tracked. The magnetic field H ext axis is displayed on the right.

    The shown example demonstrates only some of the possibilities of presenting large datasets of domain imaging data. Fourier components or the application to continuous quantitative imaging are other possible ways for data analysis. As set out, MO microscopy offers a great variety of ways for the investigation of magnetic materials. MO microscopy is one of the most versatile techniques to image magnetic domains and magnetization processes. The ability to observe the magnetic domain structure is especially important for the understanding of the origin of magnetic properties.

    Also, the performance of magnetic devices correlates with the spatial distribution and time evolution of the magnetization. Significant results in fundamental science, applied physics, and engineering have been obtained by MO microscopy. An incomplete overview of data obtained from various material systems on different length scales is shown in figure Magnetic domain images from electrical steel with a nearly perfect and b misaligned orientation of grains samples: R.

    Magnetic domain patterning by ion irradiation in g , h extended FeCoSiB layers and i exchange-biased samples [ ]. Shown are examples from grain-oriented electrical steel figures 29 a and b , see also section 7. Stress relaxation, occurring at the edges can lead to an avoidance of closure domain structure [ ], closure domains are repelled from the edges in positive magnetostrictive tensile stressed Ni 45 Fe 55 films figure 29 f.

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    An alternative way of patterning by local ion irradiation leads to domain formation without the need of magneto-static energy contributions figures 29 g — i as will be discussed in section 7. Low magnetic anisotropy leads to complicated domain structures in soft magnetic CoFe-based films [ , ] as seen in figures 29 j and k.

    Soft magnetic thin films with out-of-plane anisotropy display different types of magnetic stripe domains [ , ] figures 29 l and m , the characteristics of which can be studied by MO microscopy see also figure 11 a. Magnetic domain formation due to nucleation and incomplete annihilation strongly influences the magnetization processes in perpendicular anisotropy thin films [ ] figure 29 n.