Non-Equilibrium Multiplet Excitations probed by the $M_{5,4}$ Branching Ratio in $3d \rightarrow 4f$ X-ray Absorption Spectroscopy

We show that ultrafast electronic $4f$ multiplet transitions in terbium metal are manifested by changes in the relative spectral weight of the $M_5$ and $M_4$ X-ray absorption resonances. Our experimental results are supported by a simulation of excited multiplet spectra with atomistic calculations; they prove that the so-called third rule of Thole and van der Laan, which relates the branching ratio of the spin-orbit split resonances to the total angular momentum $J$ of the excited ion, is also valid in non-equilibrium. The presented detection scheme allows to detect $J$-changing excitation, \textit{i.e}, alterations of spin and orbital states, even in samples without net magnetization. This makes branching-ratio spectroscopy a powerful tool for the quantitative investigation of ultrafast changes in angular momentum $J$.