Energy Dispersion of $4f$-Derived Emissions in Photoelectron Spectra of the Heavy-Fermion Compound ${\mathrm{YbIr}}_2{\mathrm{Si}}_2$

Angle-resolved photoemission spectra of the heavy-fermion system ${\mathrm{YbIr}}_2{\mathrm{Si}}_2$ are reported that reveal strong momentum ($\mathbf{k}$) dependent splittings of the $4f^{13}$ bulk and surface emissions around the expected intersection points of the $4f$ final states with valence bands in the Brillouin zone. The obtained dispersion is explained in terms of a simplified periodic Anderson model by a $\mathbf{k}$ dependence of the electron hopping matrix element disregarding clearly interpretation in terms of a single-impurity model.

Figure 1

PE spectra of ${\mathrm{YbIr}}_2{\mathrm{Si}}_2$ taken at 25 (hatched) and 110 eV (dots) photon energy integrated in the range of angles from $-5°$ to $+25°$ to the normal emission along the $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ direction. Subspectra reflect results of a least-squares fit using atomic Yb $4f^{12}$ and $4f^{13}$ final-state multiplets [18].

Figure 2

Angle-resolved PE spectra of ${\mathrm{YbIr}}_2{\mathrm{Si}}_2$ taken along the $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ direction. Note that the surface-to-bulk ratio of the $4f$ signal is larger and the BE of the $4f$ surface component is smaller than that in the $4f$ spectrum shown in Fig. 1, indicating surface termination by an almost closed Yb layer [23].

Figure 3

Energy bands calculated along the $\Gamma \mathrm{\text{−}}M$ direction of the Brillouin zone for the nine-atomic layer ${\mathrm{YbIr}}_2{\mathrm{Si}}_2$ slab (left) and for the slab, where Yb atoms are substituted by Ba in the surface layer and by La in the bulk (right). For comparison, experimental PE data taken at $h\nu =25\mathrm{eV}$ are shown in a color-scale representation, where lighter colors correspond to higher PE intensities.

Figure 4

Angle-resolved $4f$ emission of ${\mathrm{YbIr}}_2{\mathrm{Si}}_2$ simulated by means of the simplified PAM: contribution from the bulk (top, multiplied by factor 3.5), the surface layer (middle), and the total intensity distribution in the PE spectra (bottom).