Electronic structure of the intermediate-valence compound ${\mathrm{EuNi}}_2{\mathrm{P}}_2$ studied by soft x-ray photoemission spectroscopy

We carried out angle-resolved photoemission (ARPES) experiments using soft x rays to investigate the electronic structure of the intermediate-valence compound ${\mathrm{EuNi}}_2{\mathrm{P}}_2$. Both the ${\mathrm{Eu}}^{2+}$ and ${\mathrm{Eu}}^{3+}$ components arising from the $4f^6$ and $4f^5$ final states were observed in the valence spectra, directly confirming an intermediate-valence character of Eu ions. The three-dimensional band structure was studied by ARPES measurements, and the ARPES results were compared with calculations based on the density-functional theory for the non-4$f$ reference compounds ${\mathrm{SrNi}}_2{\mathrm{P}}_2$ and ${\mathrm{YNi}}_2{\mathrm{P}}_2$. We found that the ARPES spectra up to just below the Fermi level are better reproduced by the calculation of ${\mathrm{SrNi}}_2{\mathrm{P}}_2$ rather than that of ${\mathrm{YNi}}_2{\mathrm{P}}_2$. The heavy-fermion bands in ${\mathrm{EuNi}}_2{\mathrm{P}}_2$ are thus considered to be formed through the hybridization between the dispersive valence bands, which resemble those for ${\mathrm{SrNi}}_2{\mathrm{P}}_2$, and the ${\mathrm{Eu}}^{2+}$ components located at the very vicinity of the Fermi level.

Figure 1

(a) AIPES spectrum of ${\mathrm{EuNi}}_2{\mathrm{P}}_2$ measured at $h\nu =500$ eV. The vertical bars show the calculated $4f^6$ and $4f^5$ final state multiplets cited from Refs. [15, 29], which correspond to the ${\mathrm{Eu}}^{2+}$ and ${\mathrm{Eu}}^{3+}$ components, respectively. These calculated multiplets are shifted to match the experimental ${\mathrm{Eu}}^{2+}$ and ${\mathrm{Eu}}^{3+}$ peaks. (b) AIPES spectra of ${\mathrm{EuNi}}_2{\mathrm{P}}_2$ measured with various photon energies ranging from 500 to 1200 eV. (c) Fitted AIPES spectrum for $h\nu =800$ eV. In (c), the solid red and blue lines are results of fitting, and the dashed lines represent the spectral components. (d) Photon energy dependence of the intensity ratio between ${\mathrm{Eu}}^{2+}$ and ${\mathrm{Eu}}^{3+}$ components.

Figure 2

(a) ARPES spectra of ${\mathrm{EuNi}}_2{\mathrm{P}}_2$ along the high-symmetry lines measured at $h\nu =580$ eV. (b),(c) The corresponding calculated band structures for ${\mathrm{SrNi}}_2{\mathrm{P}}_2$ and ${\mathrm{YNi}}_2{\mathrm{P}}_2$. The color of each band represents the contribution of the Ni $3d$ states. (d) Brillouin zone of ${\mathrm{EuNi}}_2{\mathrm{P}}_2$, which has a body-centered tetragonal crystal structure. (e),(f) Three-dimensional shapes of the calculated FSs of ${\mathrm{SrNi}}_2{\mathrm{P}}_2$ and ${\mathrm{YNi}}_2{\mathrm{P}}_2$.

Figure 3

(a) ARPES spectra of ${\mathrm{EuNi}}_2{\mathrm{P}}_2$ measured at around $h\nu =650$ eV along the X-$\mathrm{\Gamma }$-X line. The red dashed lines are guides to eyes. The upper panel shows the MDC spectrum obtained by integrating the ARPES data within 0.2 eV to $E_{\mathrm{F}}$. (b),(c) The corresponding calculated band structures of ${\mathrm{SrNi}}_2{\mathrm{P}}_2$ and ${\mathrm{YNi}}_2{\mathrm{P}}_2$. The color scale shows the contribution of Ni $3d$ states.

Figure 4

(a) ARPES spectra of ${\mathrm{EuNi}}_2{\mathrm{P}}_2$ measured at $h\nu =580$ eV along the X-Z-X line. The red dashed lines are guides to eyes. (b),(c) The corresponding calculated band structures of ${\mathrm{SrNi}}_2{\mathrm{P}}_2$ and ${\mathrm{YNi}}_2{\mathrm{P}}_2$. The contribution of Ni $3d$ states is represented by the color scale.

Figure 5

(a) The photoemission intensity near $E_{\mathrm{F}}$ region in the $k_x\text{−}{k}_y$ plane for ${\mathrm{EuNi}}_2{\mathrm{P}}_2$. This intensity map is obtained by integrating ARPES spectra at $h\nu =580$ eV over $E_{\mathrm{F}}\pm 50$ meV. (c) Same intensity map in the $k_{xy}\text{−}{k}_z$ plane obtained by $h\nu$-dependent ARPES measurements. (b),(d) Corresponding calculated FSs of ${\mathrm{SrNi}}_2{\mathrm{P}}_2$ in these planes.