Magneto-optical Faraday effect

Turning next to more local techniques, the magneto-optical Faraday effect will be discussed first (Alers 1957, Kirchner 1968, Huebener et al. 1972, KobUschka and... 

Keller, N. Mistrik, J. Visnovsky, S. Schmool, D. S. Dumont, Y. Renaudin, P. Guyot, M. Krishnan, R., Magneto-optical Faraday and Kerr effect of orthoferrite thin films at high temperatures, Eur. Phys. J. B 2001, 21(1), 67-73... 

The magneto-optic Kerr effect (MOKE), discovered by John Kerr in 1877, is similar to the Faraday effect, except it rotates the plane of polarization of light reflected from a solid that contains a magnetic field. As such it is a valuable tool for visualizing magnetic domains. 

The inverse Faraday effect depends on the third Stokes parameter empirically in the received view [36], and is the archetypical magneto-optical effect in conventional Maxwell-Heaviside theory. This type of phenomenology directly contradicts U(l) gauge theory in the same way as argued already for the third Stokes parameter. In 0(3) electrodynamics, the paradox is circumvented by using the field equations (31) and (32). A self-consistent description [11-20] of the inverse Faraday effect is achieved by expanding Eq. (32) ... 

Faraday was thus able to enunciate his two laws of electrolysis. His second law implied that both matter and electricity were atomic in nature. Faraday was deeply opposed to atomism, especially the theory proposed by John Dalton, and indeed held a very antimaterialist view. It was clear to Faraday, however, that the law of definite proportions also required some sort of atomic theory. What Faraday proposed in the 1840s was that matter was perceived where fines of force met at a particular point in space. A direct experimental outcome of this radical theory was Faraday s discovery in 1845 of the magneto-optical effect and diamagnetism. The field theory that Faraday developed from this was able to solve a number of problems in physics that were not amenable to conventional approaches. This was one reason why field theory was taken up quite quickly by elite natural philosophers such as William Thomson (later Lord Kelvin) and James Clerk Maxwell. 

Natural optical activity is based on the structure of the molecules (optically active centres). Artificial optical rotation is found in magnetic fields the Faraday-Verdet effect or Magneto-Optic Effect, discovered by Michael Faraday in 1845. The theoretical basis for this effect was developed by James Clerk Maxwell in the 1860s and 1870s. From investigations on small molecules we know that the study of magneto-optical rotation offers interesting correlations with the chemical structure and that additive properties of the Verdet constant have been found. 

In the next section we summarize the theoretical background for coupled cluster response theory and discuss certain issues related to their actual implementation. In Sections 3 and 4 we describe the application of quadratic and cubic response in calculations of first and second hyperpolarizabilities. The use of response theory to calculate magneto-optical properties as e.g. the Faraday effect, magnetic circular dichroism, Buckingham effect, Cotton-Mouton effect or Jones birefringence is discussed in Section 5. Finally we give some conclusions and an outlook in Section 6. 

The use of Faraday rotation spectroscopy to study high Rydberg members and to measure their / values is a recent development. Little early work was done on magneto-optical effects in the vacuum ultraviolet, which can only be explained in terms of technical difficulties, since the subject is not intrinsically new. 

Magneto-optical rotation (MOR) has a long history, stretching back as early as the work of Faraday [152] and Macaluso and Corbino [153], who related MOR to the Zeeman effect [154] well before the advent of quantum mechanics. The Zeeman effect is much used in classical spectroscopy for the determination of J values and g factors, and this is discussed in many standard texts. 

A good introduction to electro- and magneto-optical effects can be found in the book by Harvey on Coherent Light [158]. The main effects and the relationship between them are indicated in table 4.1. Many atoms are readily produced as vapour columns, using standard laboratory methods [159]. The natural mode in which to conduct experiments on unperturbed free atoms is therefore in transmission. As table 4.1 emphasises (the reason is given below), the Faraday effect contains equivalent information to the Zeeman effect in transmission. Actually, what Harvey calls the Zeeman effect in transmission is usually referred to as the inverse Zeeman effect [160], to distinguish it from the Zeeman effect observed in emission.5... 

Fig. 4.8. Basic geometry for the observation of the dispersed Faraday effect the polariser P is crossed with an analyser A, and propagation along an axis Oz is parallel to the field lines B in the region of the atomic absorption cell. Rotation of the plane of polarisation through an angle (p occurs as a result of magneto-optical birefringence (after J.-P. Connerade [161]).

The magneto-optical effects can be studied either in transmission (Faraday effect) or in reflection (Kerr effect). For metallic systems magneto-optical studies made by... 

The temperature dependence of the Faraday and Kerr rotation in a number of amorphous Gd1 xFex alloys was studied by Hartmann (1982). Results obtained for the latter alloys are reproduced in fig. 53. These results have to be compared with the temperature dependence of the magnetization shown for Gd0 2Fe0 8 in fig. 52. It follows from the results of Hartmann that all the Gdt xFex alloys shown in fig. 53 have a compensation temperature, which decreases with increasing Fe concentration. However, no such features are seen in the magneto-optical effect in the sample is merely due to one of the two sublattice magnetizations. In accordance with this feature is the observation by means of hysteresis loops at temperatures above Tcomp but inverted types of hysteresis loops at temperatures... 

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