Resonant 4f photoemission from lanthanides at the 4d edge: Analysis for individual |MJ⟩ states

Rapid development of material systems containing lanthanides (Ln) highlights the need for a thorough evaluation of Ln-driven properties, for which Ln-sensitive resonant photoelectron spectroscopy (RPES) can be particularly useful. Employing RPES in combination with theoretical modeling, we investigate in detail the ${\mathrm{LnRh}}_{2}{\mathrm{Si}}_{2}$ compound family, particularly to examine how photoelectron diffraction (PED) and the crystal electric field (CEF) influence the resonantly enhanced $4f$ emission associated with individual $|{M}_{J}\ensuremath{\rangle}$ ground states. The presence of two well-defined Ln- and Si-terminated surfaces together with the pronounced reorientation of $4f$ moments at the surface due to change of CEF makes ${\mathrm{LnRh}}_{2}{\mathrm{Si}}_{2}$ particularly well suited for this study, which was performed for the region of Ln $4d\stackrel{}{\ensuremath{\rightarrow}}4f$ excitations. High-quality data for Tb, Tm, and Ho enabled detailed analysis of the effects of PED and CEF on the RPES $4f$ spectra for individual $|{M}_{J}\ensuremath{\rangle}$ states, revealing excellent agreement between experiment and theory. Based on this, we discuss theoretical results for other ${\mathrm{LnRh}}_{2}{\mathrm{Si}}_{2}$ systems. The resulting overview of resonant $4f$ photoemission spectra and PED patterns provides a solid platform for investigating a wide range of Ln-based systems, from molecules to solids, with a particular focus on evaluating properties arising from $4f$ magnetic moments and their orientation.