Photoelectron diffraction for probing valency and magnetism of 4 f -based materials: A view on valence-fluctuating EuIr 2 Si 2

We present and discuss the methodology for modeling $4f$ photoemission spectra, $4f$ photoelectron diffraction (PED) patterns, and magnetic dichroism effects for rare-earth-based materials. Using PED and magnetic dichroism in photoemission, we explore the electronic and magnetic properties of the near-surface region of the valence-fluctuating material ${\\mathrm{EuIr}}_{2}{\\mathrm{Si}}_{2}$. For the Eu-terminated surface, we found that the topmost Eu layer is divalent and exhibits a ferromagnetic order below 10 K. The valency of the next Eu layer, that is the fifth atomic layer, is about 2.8 at low temperature that is close to the valency in the bulk. The properties of the Si-terminated surface are drastically different. The first subsurface Eu layer (fourth atomic layer below the surface) behaves divalently and orders ferromagnetically below 48 K. Experimental data indicate, however, that there is an admixture of trivalent Eu in this layer, resulting in its valency of about 2.1. The next deeper lying Eu layer (eighth atomic layer below the surface) behaves mixed valently, but the estimated valency of 2.4 is notably lower than the value in the bulk. The presented approach and obtained results create a background for further studies of exotic surface properties of $4f$-based materials, and allow us to derive information related to valency and magnetism of individual rare-earth layers in a rather extended area near the surface.