Calculation of the magnetic susceptibility of a degenerate ideal gas of electrons in the case of anisotropic effective mass
DOI:
https://doi.org/10.17721/1812-5409.2023/1.15Keywords:
ideal electron gas, magnetic susceptibility, effective massAbstract
Dependence of the diamagnetic susceptibility of a degenerate ideal gas of electrons on the orientation of the magnetic field strength vector relative to the crystal axes, which is due to the anisotropy of the effective mass of electrons is considered. The presence of a diamagnetic susceptibility of a degenerate ideal gas of electrons is one of the fundamental results of the application of quantum mechanics and statistical physics to the description of magnetic phenomena. For an ideal gas of electrons in vacuum, the magnetic susceptibility has diamagnetic and paramagnetic components, the origin of which is due to different mechanisms. At low values of the magnetic field strength and high temperatures, their values are proportional to each other. Since the total value of the susceptibility is measured, it is impossible to separate them. Moreover, when measuring the magnetic susceptibility of a crystal, the contribution of conduction electrons cannot be separated from the contributions of the electrons of atoms, unless some features of the behavior of the magnetic susceptibility of conduction electrons are known. In this article, the calculation of the angular dependence of the effective mass of electrons due to the anisotropy is carried out. The angular dependence of the diamagnetic susceptibility is calculated for the practically important case when the distances between the nearest magnetic levels are small compared to the temperature. It is shown that the angular dependence of the diamagnetic susceptibility coincides with the angular dependence of the cyclotron mass squared, which can be determined from independent cyclotron resonance experiments. It is proposed to use the results obtained to separate the diamagnetic susceptibility of conduction electrons from susceptibilities due to other mechanisms.
Pages of the article in the issue: 108 - 111
Language of the article: Ukrainian
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