Generalized Landau-Peierls formula for orbital magnetism of many-body systems: Effects of spin fluctuations

A simple and general formula for the orbital magnetism has been obtained for a many-body system in which the one-particle self-energy function depends on both energy and momentum variables. The result is an extension of the Landau-Peierls formula, which is valid only in the case of an energy-independent self-energy. Using this formula the effects of spin fluctuations on the orbital susceptibility of ininerant electrons in a nondegenerate band are examined near the Curie temperature $T_C$. If the spin-orbit interaction is neglected, the orbital susceptibility is modified only to order ${\left(\frac{T_C}{{\epsilon }_F}\right)}^2$, where ${\epsilon }_F$ is the Fermi energy. In the presence of the spin-orbit interaction, there is a contribution proportional to the static spin susceptibility which is divergent at $T=T_C$. However this contribution is generally small since the proportionality constant is of order ${\alpha }^2$, where $\alpha ={\mathrm{}\left(137\right)\mathrm{}}^{-1\mathrm{}}$ is the fine-structure constant.