Magnetic circular dichroism versus orbital magnetization

Abstract

The magnetic circular dichroism sum rule yields an extremely useful ground-state observable, which provides a quantitative measure of spontaneous time-reversal symmetry breaking (T-breaking) in a given material. Here I derive its explicit expression within band structure theory, in the general case: Trivial insulators, topological insulators, and metals. Orbital magnetization provides a different measure of T-breaking in the electronic ground state. The two observables belong to the class of "geometrical" observables; both are local and admit a "density" in coordinate space. In both of them, one could include or exclude selected groups of bands in order to acquire element-specific information about the T-breaking material. Only in the case of an isolated flat band do the contributions to the two observables coincide. Finally, I provide the corresponding geometrical formula-in a different Hilbert space-for a many-body interacting system.