Bulk electronic structure of lanthanum hexaboride ($\mathrm{La}{\mathrm{B}}_6$) 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.

Figure 1

Experimental geometry used at BL15XU, Spring-8. The inset shows the crystal structure of $\mathrm{La}{\mathrm{B}}_6$. The crystal structure of $\mathrm{La}{\mathrm{B}}_6$ is simple cubic (space group $Pm\text{−}3m$), with ${\mathrm{B}}_6$ octahedra in body-centered positions and La atoms at the corners of the unit cell.

Figure 2

Survey spectra of $\mathrm{La}{\mathrm{B}}_6$, at 3237.5 eV (blue line) and at 5953.4 eV (red line) photon energies. The presence of O, C, and F atoms suggests surface contamination.

Figure 3

Core level spectra O $1s$ and C $1s$ normalized against La $4s$ measured at photon energies, 3237.5 eV (blue line) and 5953.4 eV (red line), respectively.

Figure 4

La $3d$ core level photoemission spectra of $\mathrm{La}{\mathrm{B}}_6$ measured at photon energies of 3237.5 eV (blue line) and 5953.4 eV (red line) compared to the calculated spectral weight of a cluster model calculation (thick black line is convoluted with a Voigt function, while the thin black line is the calculated unbroadened spectral weight). The calculated spectrum shows the final state effect of the photoemission core hole that leads to the poorly screened and well screened peaks in the experimental spectra.

Figure 5

XPS spectra (a) B $1s$ and (b) La $5p$ measured at photon energies, 3237.5 eV (blue line) and 5953.4 eV (red line), respectively.

Figure 6

(a) ARPES raw image collected at $h\nu =3237.5\mathrm{eV}$ and temperature 30 K; Fermi Energy is at $\mathrm{BE}=0\mathrm{eV}$; (b) ARPES image normalized by the density-of-states (DOS) and by the x-ray photoelectron diffraction (XPD) modulations; (c) free electron final state (FEFS) band structure calculation (gray solid lines) overlaid on the ARPES data from (b); (d) angle-resolved photoemission data calculated by the one-step theory at $h\nu =3238\mathrm{eV}$ and temperature 30 K; (e) experimental (HXPS at $h\nu =3237.5\mathrm{eV}, T=30\mathrm{K}$ ) and calculated ($h\nu =3238\mathrm{eV}, T=30\mathrm{K}$) angle-integrated valence band intensities.

Figure 7

Calculated Bloch spectral functions projected onto La and B sites, showing mixed character of bands throughout the valence band region.

Figure 8

(a) Mean square displacement of the La and B atoms, as a function of temperature; (b) one-step photoemission calculations at $h\nu =3238\mathrm{eV} T=0\mathrm{K}$; (c), (d) one-step calculations with different implementation of phonon excitations, either element resolved (c) or averaged (d). The wave-vector blurring is noticeably different, especially for bands around 10 eV, and stronger for the element resolved case.