Covariant approach to magnetic anisotropy

In view of recent experiments, the determination of magnetic anisotropy (MA) is revisited, thus leading to unexpected relations between the pertinent tensors. The sudden perturbation of the preferential magnetic direction triggers magnetization dynamics, which can be traced on the femtosecond timescale. Modeling this process provides indirect information on magnetic anisotropy. In magnetic molecular systems, the interplay between the zero-field splitting given by the $D$ tensor and the Zeeman interaction given by the $G$ tensor can be measured spectroscopically, likewise indirectly providing information on MA, but never fully uncovering these tensors. Here, a theory that bridges the gap between the physical experiments, the microscopic mechanisms, and the effective models is established. Expressions for the magnetic anisotropy in terms of the $D$ and $G$ tensors are derived in a covariant form. A minimal experiment where these parameters can be determined is proposed. In particular, by means of the Hellmann-Feynman theorem, we are able to account for the mutual orientation of the principal axes of the $G$ and $D$ tensors, which is an important effect for molecular magnets.