Crystal electric field splitting and $f$-electron hybridization in heavy-fermion ${\mathrm{CePt}}_2{\mathrm{In}}_7$

We use high-resolution angle-resolved photoemission spectroscopy to investigate the electronic structure of the antiferromagnetic heavy fermion compound ${\mathrm{CePt}}_2{\mathrm{In}}_7$, which is a member of the ${\mathrm{CeIn}}_3$-derived heavy fermion material family. Weak hybridization among $4f$ electron states and conduction bands was identified in ${\mathrm{CePt}}_2{\mathrm{In}}_7$ at low temperature much weaker than that in the other heavy fermion compounds like ${\mathrm{CeIrIn}}_5$ and ${\mathrm{CeRhIn}}_5$. The Ce $4f$ spectrum shows fine structures near the Fermi energy, reflecting the crystal electric field splitting of the $4f_{5/2}^1$ and $4f_{7/2}^1$ states. Also, we find that the Fermi surface has a strongly three-dimensional topology, in agreement with density-functional theory calculations.

Figure 1

(a) ${\mathrm{CePt}}_2{\mathrm{In}}_7$ on-resonance valence band structure at 10 K and 123 eV. (b) Angle-integrated photoemission spectroscopy of the intensity plot in (a). Inset: A 3D Brillouin zone with high-symmetry momentum points (red dots) marked. The locations of $\mathrm{\Gamma }, M, N$, and $X$ points are at the $k_z=0$ plane while the $Z, A$, and $R$ points are at $k_z=2\pi /c$ plane. (c) Calculated Ce $4f$, Pt $5d$, and In $4p$ density of state (DOS) vs energy $E$.

Figure 2

CEF splitting of ${\mathrm{CePt}}_2{\mathrm{In}}_7 4f$ states. (a) High-energy resolution of on-resonance valence band structure plot along [110] direction near Fermi energy is taken at 10 K with 123 eV. (b) Measured structure reduced with the 2D second derivative to enhance the weak bands while maintaining band dispersion. (c) EDCs of the spectral show in (a). The purple and aqua shadows are indicated the positions of the $f_{5/2}^1$ and $f_{7/2}^1$ states, respectively. The red curve represents the EDC at the M point. (d) EDCs at different momentum locations in (a). The brown, cyan, black, red, and green curves are obtained by integrating the regions between two brown, cyan, black, red, and green dashed lines, as indicated in (a), respectively.

Figure 3

FS and corresponding ${\mathrm{CePt}}_2{\mathrm{In}}_7$ band structure. (a) Symmetrized FS in the $k_x-k_y$ plane of ${\mathrm{CePt}}_2{\mathrm{In}}_7$ measured at 10 K with 100 eV (close to $\mathrm{\Gamma }$ point). The intensity is integrated over [$-10$ meV, 10 meV] energy window with respect to the Fermi level $E_F$. [(b1)–(b3)] Measured band structures along the $N^{\prime }-X^{\prime }-N^{\prime }$ direction, indicated by the dashed yellow arrow in (a). [(c1)–(c3)] Measured band structure along $X^{\prime }-{\mathrm{\Gamma }}^{\prime }-X^{\prime }$ direction, indicated by the dashed green arrow in (a). (b1) and (c1) are the original data. (b2) and (c2) are second-derivative images from the original data with respect to energy. [(b3) and (c3)] Second-derivative images from the original data with respect to momentum. Red dashed lines in (b2) and (c2) represent DFT band structure. Green dashed lines represent DFT band structure along $R-Z-R$ line.

Figure 4

Band structure of ${\mathrm{CePt}}_2{\mathrm{In}}_7$ at 10 K. [(a1) and (a2)] Original photoemission image and corresponding EDC second derivative image measured along the $N^{\prime }-X^{\prime }-N^{\prime }$ direction with 80-eV photon energy. [(b1) and (c1)] Photonemission data taken along $X^{\prime }-{\mathrm{\Gamma }}^{\prime }-X^{\prime }$ direction with 80- and 34-eV photon energies, respectively. [(b2) and ( c2)] Corresponding EDC second derivative images of (b1) and (c1), respectively. Red dashed lines in (a2), (b2), and (c2) represent DFT band structure. (d) Calculated FS of ${\mathrm{CePt}}_2{\mathrm{In}}_7$. The 3D FS is presented in the body-centered tetragonal Brillouin zone, in which one unit cell contains one Ce atom. (e) DFT-calculated Fermi surface contours in the $\mathrm{\Gamma }XRZ$ plane ($k_x-k_z$). The colors used for different Fermi surfaces are consistent with (d). The red, green, and brown arcs indicate the final-state arcs for 100-, 80-, and 34-eV photon energies, respectively.