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Recent experimental advances in ultrafast science put different processesoccurring on the electronic timescale below a few femtoseconds in focus. In thepresent theoretical work, we demonstrate how the transformation and propagationof the density matrix in the basis of irreducible spherical tensors can beconveniently used to study sub-few fs spin-flip dynamics in the core-excitedtransition metal compounds. With the help of the Wigner-Eckart theorem, such atransformation separates the essential dynamical information from the geometricfactors governed by the angular momentum algebra. We show that an additionalreduction can be performed by the physically motivated truncation of thespherical tensor basis. In particular, depending on the degree of coherence,the ultrafast dynamics can be considered semi-quantitative in the notablyreduced spherical basis when only total populations of the basis states of thegiven spin are of interest. Such truncation should be especially beneficialwhen the number of the high-spin basis states is vast, as it substantiallyreduces computational costs.

Spin-flip dynamics in core-excited states in the basis of irreducible spherical tensor operators