Bulk electronic structure of lanthanum hexaboride ($La\mathrmB_6$) by hard x-ray angle-resolved photoelectron spectroscopy

In the last decade rare-earth hexaborides have been investigated for their fundamental importance in condensed matter, and for their applications in advanced technological fields. Among these compounds, $\mathrm{La}{\mathrm{B}}_{6}$ has a special place, being a traditional $d$-band metal without additional $f$ bands. In order to understand the bulk electronic structure of the more complex rare-earth hexaborides, in this paper we investigate the bulk electronic structure of $\mathrm{La}{\mathrm{B}}_{6}$ using tender/hard x-ray photoemission spectroscopy, measuring both core-level and angle-resolved valence-band spectra. Furthermore, we compare the La $3d$ core level spectrum to cluster model calculations in order to understand the bulklike core-hole screening effects. The results show that the La $3d$ well-screened peak is at a lower binding energy compared to the main poorly screened peak; the relative intensity between these peaks depends on how strong the hybridization is between La and B atoms. We show that the recoil effect, negligible in the soft x-ray regime, becomes prominent at higher kinetic energies for lighter elements, such as boron, but is still negligible for heavy elements, such as lanthanum. In addition, we report the bulklike band structure of $\mathrm{La}{\mathrm{B}}_{6}$ determined by tender/hard x-ray angle-resolved photoemission spectroscopy (HARPES). We compare HARPES experimental results to the free-electron final-state calculations and to the more precise one-step photoemission theory including matrix element and phonon excitation effects. The agreement between the features present in the experimental ARPES data and the theoretical calculations is very good. In addition, we consider the nature and the magnitude of phonon excitations in order to interpret HARPES experimental data measured at different temperatures and excitation energies. We demonstrate that the one-step theory of photoemission and HARPES experiments provides, at present, the only approach capable of probing, both experimentally and theoretically, true ``bulklike'' electronic band structure of rare-earth hexaborides and strongly correlated materials.