Branching ratio in x-ray absorption spectroscopy

TLDR

Second‑order spin‑orbit interactions significantly affect the branching ratios in high‑spin Ni compounds. The study explains the origin of nonstatistical branching ratios in spin‑orbit‑split X‑ray absorption spectra and provides rules to assess spin state and spin‑orbit splitting from experimental branching ratios. Atomic calculations of transition‑metal core‑hole states, accounting for initial‑state spin‑orbit splitting and core‑hole–valence electrostatic interactions, were used to derive general rules applicable to solids. The calculations reveal that the branching ratio peaks for Hund’s‑rule ground states and decreases progressively for higher S, L, and J levels, while crystal‑field‑induced low‑spin ground states further reduce the ratio.

Abstract

The origin of nonstatistical branching ratios in spin-orbit-split x-ray absorption spectra is explained. Atomic calculations for transition metals show a systematic change which is due to initial-state spin-orbit splitting and electrostatic interactions between core hole and valence electrons. We have formulated the results of these atomic calculations in general rules, which are also applicable to solids. In the free atom the branching ratio reaches a maximum for the Hund's-rule ground state and its value decreases gradually for S, L, and J levels of higher energy. The presence of a crystal field results in a lower branching ratio when it produces a low-spin ground state. The rules can be used to assess the spin state and the spin-orbit splitting from the experimental branching ratio in transition-metal and rare-earth compounds. A specific example is given for the influence of second-order spin-orbit interactions in high-spin Ni compounds.