By D. Wagner and D. ter Haar (Auth.)
The current ebook comprises primarily the cloth of a lecture sequence at the thought of magnetism, which was once held for college students of physics at a medium complicated point. The set-up follows the typical subdivision of magnetic ingredients, i.e. diamagnetism used to be handled first, then paramagnetism, and at last ee handled ferromagnetism, antiferromagnetism and ferrimegnetism. obviously a few elements of this box, magnetism, needed to be handled in much less element than different elements, because the quantity of the booklet was once constrained. therefore within the first a part of the e-book we've got positioned emphasis at the de Hassv-van Alpen impact, which iw very instructive as to the habit of electrons in crystals. within the moment half the impact of the crystal box on tha paramagnetism of atoms and attached difficulties (Kramers theorem, adiabatic demagnetization, paramagnetism resonance, ...) were handled extra generally
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E. of the constants of integration, we obtain fik = c -[rAH]. 41). When the electron travels along closed curves in these planes, the curves can be quantised according to the BohrSommerfeld quantisation rule. This rule, however, yields the sought quantum states only for large quantum numbers, that is, near the classical limiting case (see Landau and Lifshitz, 1958). In our case, however, this condition obviously seems to be satisfied as, for example, in the above-mentioned case of rubidium, at a field strength of 10^ oe, about the lowest 1000 Landau levels are involved (2μ^Ηη ^ 0 · In its most general form for periodic orbits the Bohr-Sommerfeld rule reads Sp dq = (η+φ)Η, where ρ is the momentum conjugate to the position coordinate; inte gration is carried out over a closed orbit, φ is an indefinite constant (0 φ 1) which is equal to γ in the case of a linear harmonic oscillator.
Electric resistance (Shubnikow-de Haas eflfect), thermal conductivity. , which will not be con sidered in this book. There are several review articles on these eflfects (see, for example, Ziman, 1962; Kahn and Frederikse, 1959; Pippard, 1960). 6. Cyclotron Resonance Classical free electrons in a magnetic field travel on circular orbits in planes normal to the magnetic field; the orbital frequency is given according to eqn. 4), with ωο = 0, by the double Larmor frequency, which was denoted by (cyclotron frequency) in the previous section and defined by eqn.
7) for the diamagnetism of atoms. The Landau diamagnetism can therefore be considered only a first term of a series expansion for the exact formula (Wilson, 1958; Kjeldaas and Kohn, 1957). 37) as was to be expected, since the electrons in sodium, and also in potassium, may be considered to behave hke free electrons in a relatively good approximation (w* ^ w). Another deviation from Sommerfeld's electron model is obtained when we consider the electron-electron Coulomb interaction. Hitherto this problem is only dealt with (Stephen, 1962) for electron gases of high densities (r^ < 1) so that the methods applied cannot be used in the case of metals.