Theory of Magnetization in Bloch Electron Systems

Abstract

The exact formulas for magnetization and magnetic susceptibility are derived for Bloch electrons in terms of Bloch wave functions. They are extensions of the previous work to general cases where the spin–orbit interaction as well as the Zeeman term is included, the potential is noncentrosymmetric, and the time-reversal symmetry is broken. The obtained magnetization for Bloch electrons is a natural generalization of the free-electron magnetic moment including the effect of the spin–orbit interaction. The obtained susceptibility has six contributions and the physical meaning of each term is clarified. The new formula contains the Landau–Peierls, Pauli, and Van Vleck susceptibilities, the atomic diamagnetism, and contributions from the “Berry curvature”. In the atomic limit, the obtained formula reduces to two contributions: the atomic diamagnetism and a generalized form of the Van Vleck susceptibility modified by the spin–orbit interaction. It is also found that, in general cases, the Pauli, Van Vleck (inte...