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Unformatted text preview: Chapter 12: Solid state physics 65 12.4 Magnetic feld in the solid state The following graph shows the magnetization versus Feldstrength for different types of magnetism: diamagnetism ferro paramagnetism χ m = ∂ M ∂ H M M sat H 12.4.1 Dielectrics The quantum mechanical origin of diamagnetism is the Larmorprecession of the spin of the electron. Starting with a circular electron orbit in an atom with two electrons, there is a Coulomb force F c and a magnetic force on each electron. If the magnetic part of the force is not strong enough to signiFcantly deform the orbit holds: ω 2 = F c ( r ) mr ± eB m ω = ω 2 ± eB m ( ω + δ ) ⇒ ω = ω ± eB 2 m 2 + · · · ≈ ω ± eB 2 m = ω ± ω L Here, ω L is the Larmor frequency . One electron is accelerated, the other decelerated. Hence there is a net circular current which results in a magnetic moment μ . The circular current is given by I =- Ze ω L / 2 π , and μ = IA = I π ρ 2 = 2 3 I π r 2 . If N is the number of atoms in the crystal it follows for the susceptibility,...
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