Theory of Diamagnetic Susceptibility of Metals

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Abstract
In order to calculate the diamagnetic susceptibility of real metals, we have generalized the pseudopotential method to the case of a metal in a magnetic field. A general equation of motion is obtained, from which we first derive an expression for the core diamagnetism. We then derive an expression for the diamagnetic susceptibility of Bloch electrons in a magnetic field in terms of a pseudopotential. If our pseudopotential is replaced by the actual lattice potential, the result reduces exactly to expressions derived by other authors for the diamagnetic susceptibility of Bloch electrons. However, we believe that our method is the simplest manner in which this result can be derived. By the use of the pseudopotential and degenerate perturbation theory we obtain the result in a form from which computation can be made easily. We have computed the diamagnetic susceptibility of all the alkali metals and of aluminum. From our expression, the diamagnetic susceptibility of any polyvalent metal to which our approximations apply can be easily computed. We have also found a satisfactory explanation of why certain metals have very high diamagnetic susceptibility. We contradict Glasser's conclusion that the diamagnetic susceptibility and the paramagnetic susceptibility are nonadditive, and correct some algebraic errors in the work of Samoilovich and Rabinovich.

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