Origin and Uses of the Faraday Rotation in Magnetic Crystals

Abstract

Light transmitted by a magnetic crystal interacts with the magnetization. In particular, the axis of linear polarization undergoes a rotation proportional to the fractional projection of M on the direction of propagation. This magneto-optical rotation, the Faraday rotation in magnetic materials, has been studied for many years. The advent of insulating magnetic materials has led to renewed interest of two sorts: (1) The rotational dispersion coupled with that of the absorption coefficient in some cases makes possible the spectroscopic assignment of optical transitions which show magnetic effects. Thus we may use the rotation to extract information on the magnetic behavior of energy levels well above the ground state. (2) Any experimental or technological use of the rotation makes it necessary to take into account the attendant absorption of light. Some insulating magnetic materials have very high values of the rotation per unit attenuation. The magneto-optical rotation may then be used to ``see'' both dc (domain structure) and rf (magnetostatic spin waves) magnetization distributions within the crystal. Furthermore, the low rotation attenuation is crucial in a number of magneto-optical devices: rotators, wide-band modulators, phase shifters, memories, the YIG laser, etc.

Second-Order Optical Nonlinearities in Coordination Chemistry: The Case of Bis(salicylaldiminato)metal Schiff Base Complexes

“…This is commonly called the Faraday rotation. [46] This effect, which modifies the angle between E (the electric field component of the light) and β, should therefore modulate the NLO behavior of the solid. Nevertheless, the β value of the chromophores would not be affected by such a magnetic transition.…”

Magnetooptics in Cylindrical Structures

“…Please note that their product obeys p z q z = 1, which is another way to represent the eigenvalue equation, Equation (21). In Equation (20), the arguments of the Bessel functions for the core become…”

“…In the microwave region, the effect of M is deduced from the tensor nature of magnetic permeability with the scalar electric permittivity [17] while in the near infrared and visible regions, the analysis assumes the tensor nature of electric permittivity with magnetic permeability reduced to its vacuum value [18,19]. In both cases, the diagonal and off-diagonal tensor elements are even and odd functions of M, respectively [18][19][20][21][22][23]. In the infrared and visible spectral regions, a more rigorous treatment would account for the tensorial nature of both material parameters [24][25][26][27][28][29].…”

Dual-Workfunction Gate Engineering in a Corner Parasitics-Free Shallow-Trench-Isolation Complementary-Metal-Oxide-Semiconductor Technology

“…As in FeF3 and FeB03 it is probably associated with the charge-transfer absorption in the near ultraviolet. For magneto-optic applications the figure of merit is the rotation per unit attenuation (Dillon 1968), which is plotted in figure 2 with literature data on FeF3 (Kurtzig and Guggenheim 1970), FeB03 (Kurtzig et al 1969), Y3Fe501~ (Dillon 1968) and LuFeO3 (Wolfe et aZl970) for comparison. The latter, of course, are spontaneously magnetised at room temperature but because FeF3 and FeB03 are birefringent, the Faraday rotations quoted for them are the limiting values which would have been measured in the absence of birefringence.…”