Valence transition induced changes of the electronic structure in ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$

We present the results of hard x-ray angle-resolved photoemission spectroscopy and photoemission diffraction measurements performed on high-quality single crystals of the valence transition compound ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ for temperatures $25\text{K}\le T\le 300$ K. At low temperatures, we observe a Eu $4f$ valence $v=2.5$, which decreases to $v=2.1$ for temperatures above the valence transition around $T_V\approx 160$ K. The experimental valence numbers resulting from an evaluation of the Eu(III)/Eu(II) $3d$ core levels, are used for calculating band structures using density functional theory. The valence transition significantly changes the band structure as determined by angle-resolved photoemission spectroscopy. In particular, the Eu $5d$ valence bands are shifted to lower binding energies with increasing Eu $4f$ occupancy. To a lesser extent, bands derived from the Si $3p$ and Pd $4d$ orbitals are also affected. This observation suggests a partial charge transfer between Eu and Pd/Si sites. Comparison with ab initio theory shows a good agreement with experiment, in particular concerning the unequal band shift with increasing Eu $4f$ occupancy.

Figure 1

(a) Sketch of the direct space crystal structure of ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ and coordinate system used in this article. Red arrows denote the lattice expansion with increasing temperature in the ab-plane caused by the valence transition. Green arrows denote the partial charge transfer from the Si/Pd-planes to the Eu crystal plane. (b) Corresponding Brillouin zone in reciprocal space indicating the high-symmetry points.

Figure 2

(a) Temperature dependence of the Eu $3d$ core spectra obtained with a photon energy of 3.4 keV at 300 (red) and 25 K (blue) for a ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ single crystal. The mean valence number $n$ results is derived from the ratio of the areas of the corresponding $3d$ core orbitals. The specified binding energies are referred to the Fermi level. The marks indicate the interatomic exchange interaction splitting (IEX) and the multiplet splitting (MP) of the Eu $3d$ core spectra. (b) Corresponding simulation using charge transfer multiplet calculations. (c) Valence band energy distribution curves for 25 and 300 K. The photoemission intensity was integrated over a planar section of the full Brillouin zone.

Figure 3

(a) X-ray photoelectron diffraction patterns measured for a photon energy of 3.4 keV at the Eu(II) $3d_{5/2}$ core level at low temperature. Dark straight lines indicated by blue lines mark Kikuchi lines. The distance between a pair of Kikuchi lines corresponds to $2G_{110}$. (b) Similar data measured at room temperature. (c) Line profiles averaged along the yellow thick lines in (a) and (b) (Blue full line for low temperature and red full line for room temperature). Fits to Gaussian functions of two corresponding intensity maxima reveal an increase of the reciprocal lattice in the $ab$ plane by $(3\pm 1)\%$ at low temperature as compared to room temperature.

Figure 4

(a) Final state model where the sphere defined by the final state momentum intersects the repeated Brillouin zone scheme. The field-of-view of the parallel momentum and the coverage of the perpendicular momentum range are indicated by the light-blue rectangle. Due to the translational symmetry a perpendicular momentum range of $G_{001}/4$ is sufficient to reconstruct the entire Brillouin zone. (b) Photoemission intensity (white: high intensity) for an $E$-vs-$k$ section measured at 25 K. (c) The same data processed with a Laplacian operator (second derivative in horizontal and vertical directions), emphasising the negative curvature of the dispersing band intensities.

Figure 5

[(a)–(h)] Constant energy maps of the photoemission intensity $I(E_B,k_x,k_y)$ for the indicated binding energies $E_B$ measured at 25 [(a)–(d)] and 300 K [(e)–(h)]. The photon energy is 3.4 keV. The photoemission intensity has been symmetrized according to the crystal symmetry. [(i)–(p)] Binding energy vs parallel momentum sections of the photoemission data array along the indicated high-symmetry directions measured at 25 [(i)–(l)] and 300 K [(m)–(p)]. The photoemission intensity is normalized on the valence band energy distribution curve shown in Fig. 2 and color coded on the indicated linear orange-hot scale.

Figure 6

Full-potential local-orbital calculations of the ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ compound for high-symmetry directions in momentum space for valence numbers $n=6.5$ (a) and 6.9 (b), corresponding to the low- (a) and high-temperature (b) phases. For the definition of the high-symmetry points see Fig. 1. Orbital projections shown in the fat band representation. Orange bands correspond to Eu $5d$-derived bands, green to Pd $4d$-derived bands, and purple to Si $3p$-derived bands. The horizontal dotted line indicates the band minimum of the band Si2 at low temperature. Orbital-projected density-of-states functions (PDOS) for $n=6.5$ and $n=6.9$ for (c) Eu $5d$, (d) Pd $4d$, and (e) Si $3p$.

Figure 7

Experimental photoemission intensity sections along the measured high-symmetry directions for the (a) low- and (b) high-temperature data (Same color scales as in Fig. 5). Overlay of orbital-projected bands from full-potential local-orbital calculations of the ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ compound for selected high-symmetry directions in momentum space for valence numbers $n=6.5$ (a) and 6.9 (b), corresponding to the low- (a) and high-temperature (b) phases.

Figure 8

[(a) and (b)] Momentum distribution curves along the indicated high-symmetry directions and binding energies, measured at 25 K. [(c) and (d)] Similar data measured for 300 K. The 300 K data have been smoothed along the momentum axis by a Gaussian profile with radius $0.03(2\pi /a)$. Data for different binding energy are shifted along the vertical axis for clarity.

Figure 9

(a) Experimentally determined photoemission intensity $I(E_B=0,k_x,k_y,k_z)$ at the Fermi level (grey) within the Brillouin zone (red lines) at low temperature. Blue color shows one out of four constant energy sections in the extended Brillouin zone scheme. (b) Calculated Fermi surface for the corresponding Fermi surface sheets at low temperature. (c) Same calculated Fermi surface data in the extended Brillouin zone scheme. (d) Top view of the data shown in (b).