Theory of the Diamagnetic Interactions among the Conduction Electrons in Metals

The thermodynamic potential of a metal in the presence of a weakly nonuniform magnetic field of induction $B\left(r\right)\mathrm{}$ is evaluated. The calculation is a mean-field theory for the interaction between the magnetization at different points in the metal, and is restricted to magnetic field strengths for which the Fermi energy is large compared to the separation between Landau levels. An integral equation for the spatially varying part of the magnetic induction is obtained by minimizing the appropriate thermodynamic potential of the system. The solution of this integral equation is studied. Both domain-type and magnetization-density-wave solutions can be obtained for appropriate Fermi surfaces. The nature of each of these solutions as discussed.