a branch of physics that studies changes in the optical properties of media upon exposure to a magnetic field and the peculiarities of the interaction of optical radiation (light) with matter placed in the field that are responsible for the changes.
A magnetic field, like any vector field, singles out a specific direction in space; a field in a medium imparts to the medium additional anisotropy, particularly optical anisotropy. (The distinctive feature of the symmetry of a magnetic field is that its intensity H and magnetic induction B are not simply vectors but rather axial vectors.) The energy of an atom, molecule, or ion of the medium begins to depend on the relative direction of the field and the magnetic moment of the atom; as a result, the energy levels of the atom are split (in other words, the field removes the degeneracy of the levels). Correspondingly, the spectral lines of the optical transitions between levels are split. One of the effects of magneto-optics—the Zeeman effect—consists in this. The polarization of Zeeman components (“split” lines) differs; therefore, in a substance placed in a magnetic field the absorption of the same components of transient light (the inverse Zeeman effect) differs as a function of the state of their polarization. For example, upon propagation of monochromatic light along a field (the longitudinal Zeeman effect), its right and left circularly polarized components are absorbed differently (magnetic circular dichroism), whereas in the case of propagation of light across a field (the transverse Zeeman effect) magnetic linear dichroism —that is, different absorption of the components that are linearly polarized parallel and perpendicular to the magnetic field—takes place. These polarization effects display a complex dependence on the wavelength of the radiation (a complex spectral progression), knowledge of which makes possible determination of the extent and character of Zeeman splitting in cases when it is much smaller than the width of the spectral lines. (Analogous effects are observed in luminescence.)
The splitting of spectral lines entails additional splitting of the curves that characterize the dependence of the index of refraction of the medium on the wavelength of the radiation. As a result, upon longitudinal propagation (along the field), the indexes of refraction for light having right and left circular polarization become different (magnetic circular double refraction), whereas linearly polarized monochromatic light experiences rotation of the plane of polarization upon passing through the medium. The latter phenomenon is called the Faraday effect. Near the absorption line (the “jump” on the dispersion curve), Faraday rotation displays a characteristic nonmonotonic dependence on wavelength, the Macaluso-Corbino effect. Upon propagation of light transversely with respect to the magnetic field, the difference in the indexes of refraction for linear polarizations leads to linear magnetic double refraction, which is known as the Cotton-Mouton effect (or the Voigt effect).
The study and use of these effects falls within the range of problems of contemporary magneto-optics.
The optical anisotropy of a medium in a magnetic field is also manifested during reflection of light from its surface. In the case of such reflection a change takes place in the polarization of the reflected light, a change whose character and extent depend on the relative position of the surface, the plane of polarization of the incident light, and the magnetization vector. This effect is observed mainly in ferromagnets and is called the magneto-optical Kerr effect.
The magneto-optics of solids developed intensively in the 1960’s and 1970’s. This is especially true of the magneto-optics of semiconductors and such magnetically ordered crystals as ferrites and antiferromagnets.
A fundamental magneto-optical phenomenon in semiconductors placed in a magnetic field is the appearance of a discrete absorption spectrum for optical radiation beyond the limit of continuous absorption that corresponds to the optical transition between the conduction band and the valence band. These oscillations of the absorption coefficient, or magnetoabsorption oscillations, are due to the specific “splitting” of these bands in the magnetic field into systems of subbands (Landau subbands). The optical transitions between subbands are responsible for discrete absorption lines. The occurrence of Landau subbands results from the fact that the conduction electrons and holes in the magnetic field begin to perform orbital motions in a plane perpendicular to the field. The energy of this motion can change only by steps (discretely); hence the discreteness of optical transitions. The effect of magnetoabsorption oscillations is widely used to determine the parameters of the band structure of semiconductors. The Faraday and Voigt interband effects in semiconductors are connected with this effect.
In turn, Landau subbands split in a magnetic field, because the electron has intrinsic angular momentum—spin. Induced scattering of light by electrons in a semiconductor, with spin reversal relative to the magnetic field, is observed under certain conditions. In this process the energy of the scattered photon changes by the amount of spin splitting of the subband, which is extremely great for some semiconductors. This effect is the basis for the smooth change in the radiation frequency of powerful lasers and for the design of a high-transmission, high-resolution infrared spectrometer.
The study of the Zeeman splitting of the energy levels of small hydrogen-like impurities and excitons is a major branch of semiconductor magneto-optics. The observation of magnetoabsorption and the reflection of infrared radiation in narrow-band semiconductors makes possible the study of the collective oscillations of electron plasma and its interaction with phonons.
In transparent ferrites and antiferromagnets, magneto-optical methods are used to study the spectrum of spin waves, excitons, and impurity energy levels. In the interaction of light with magnetically ordered media, in contrast to diamagnets and paramag-nets, a major role is played by the internal fields of the media (their intensities reach 105-106 oersteds)—which determine spontaneous magnetization (of the sublattices or of the crystal as a whole) and its orientation in the crystal—rather than by the external magnetic field. The magneto-optical properties of transparent ferrites and antiferromagnets can be used in laser-beam control systems (for example, to create light modulators) and for the optical recording and readout of information, especially in electronic computers.
The development of lasers has led to the detection of new magneto-optical effects that are manifested at high light flux intensities. In particular, it has been shown that circularly polarized light, upon passing through a transparent medium, acts as an effective magnetic field and induces magnetization of the medium (called the inverse Faraday effect).
Such effects as the optical orientation of atoms and of the spins of electrons and nuclei in crystals, cyclotron resonance, and electron paramagnetic resonance are closely related to magneto-optical effects. Magneto-optical methods are used in the study of the quantum states responsible for optical transitions, the physicochemical structure of matter, interactions between atoms, molecules, and ions in the ground and excited states, the electron structure of metals and semiconductors, and phase transitions.
REFERENCESBorn, M. Optika. Kharkov, 1937. (Translated from German.)
Vonsovskii, S. V. Magnetizm. Moscow, 1971.
Starostin, N. V., and P. P. Feofilov. “Magnitnaia tsirkuliarnaia anizotropiia v kristallakh.” Uspekhi fizicheskikh nauk, 1969, vol. 97, fasc. 4.
Smith, S. D. “Magneto-Optics in Crystals.” In Encyclopedia of Physics (Handbuch der Physik ), vol. 25, part 2a. Berlin, 1967.
V. S. ZAPASSKII and B. P. ZAKHARCHENIA