Electronic structure of YbXCu₄ (X = In, Cd, Mg) investigated by high-resolution photoemission spectroscopy†

The valence-band electronic structure of YbXCu₄ (X = In, Cd, Mg) has been investigated by means of temperature-dependent high-energy-resolution photoemission spectroscopy using a He I resonance line (hν = 21.22 eV) and synchrotron radiation (hν = 800 eV). Intensities of the structure due to the Yb²⁺ 4f_7/2 states in the He I spectra of YbInCu₄ and YbCdCu₄ gradually increase with decreasing temperature from 300 to 10 K, and Yb²⁺ 4f_7/2 structures are clearly observed as peaks near the Fermi level (E_F) at 10 K. The enhancement of the Yb²⁺ 4f_7/2 peak from 50 to 10 K is much greater for YbInCu₄ than for YbCdCu₄. On the other hand, the Yb²⁺ 4f_7/2 states of YbMgCu₄ are observed as a broad structure near E_F. In the synchrotron radiation photoemission spectra of YbInCu₄ and YbCdCu₄, the structures due to the Yb²⁺ and Yb³⁺ 4f states are recognized at all temperatures. The intensity ratio Yb²⁺/Yb³⁺ gradually increases with decreasing temperature. The energy separations between the Yb²⁺ and Yb³⁺ 4f structures of YbInCu₄ increase from 50 to 20 K. For YbMgCu₄, on the other hand, almost only the Yb²⁺ structures are observed and little temperature dependence has been detected.

1. Introduction

Among the cubic C15b-type compounds YbXCu₄ (X = In, Ag, Au, Cd, Mg, Tl, Pd, Zn), YbInCu₄ has been the most extensively studied so far. This compound exhibits a first-order phase transition at T_v = 42 K (Felner et al., 1987; Sarrao et al., 1996). In the high-temperature phase of YbInCu₄, Yb is almost trivalent, displaying Curie–Weiss susceptibility with a paramagnetic moment near the free-ion value of 4.5μ_B. At T_v, the Yb valence is reduced to 2.8 (Cornelius et al., 1997) and the compound shows a temperature-independent Pauli paramagnetism below T_v. The lattice volume changes by 0.5% at T_v with no change in the crystal structure (Lawrence et al., 1996). Furthermore, the Kondo temperature changes from T_K+ ≃ 25 K in the high-temperature phases to T_K− ≃ 400 K in the low-temperature phases (Lawrence et al., 1999). The mechanism of the valence transition has not clearly been revealed yet.

Direct investigation of the electronic structure of YbInCu₄ has been carried out by means of temperature-dependent photoemission spectroscopy (Reinert et al., 1998; Joyce et al., 1999; Moore et al., 2000). On the other hand, the photoemission experiments for the other YbXCu₄ compounds, such as YbCdCu₄ and YbMgCu₄, have not been performed so far. The purpose of the present study is to investigate the X-dependence of the electronic structure of YbInCu₄, YbCdCu₄ and YbMgCu₄ by means of temperature-dependent high-energy-resolution photoemission spectroscopy. Valence electrons of elements X contribute to the Fermi level (E_F) of YbXCu₄ compounds and play an important role in determining a wide variety of their physical properties. A comparison of experimental results of YbInCu₄ with those of YbCdCu₄ and YbMgCu₄ is fruitful for revealing the electronic structure peculiar to YbInCu₄ and, furthermore, is expected to provide a clue to understanding the mechanism of the valence transition of YbInCu₄.

YbCdCu₄ and YbMgCu₄ have so far been studied relatively less. Hiraoka et al. performed ¹¹³Cd NMR and ⁶³Cu NQR experiments on YbCdCu₄ and concluded that the Yb 4f states change gradually from the Fermi liquid to localized states from low to high temperature (Hiraoka et al., 1995, 2000). The Kondo temperatures T_K of YbCdCu₄ and YbMgCu₄ are estimated to be ∼220 and ∼850 K, respectively, from the magnetic susceptibility experiments (Sarrao et al., 1999).

2. Experimental

High-resolution photoemission experiments on YbXCu₄ (X = In, Cd, Mg) were carried out using a hemispherical analyzer (GAMMADATA-SCIENTA ESCA-200) with a He I resonance line (hν = 21.22 eV) from an intense He lamp (GAMMADATA-SCIENTA VUV-5010). Soft X-ray photoemission experiments using synchrotron radiation were carried out with hν = 800 eV at the BL-25SU beamline of SPring-8 (Saitoh et al., 2000). Typical values of total energy resolutions of the He I and synchrotron radiation photoemission experiments were below 10 meV (10 K) and 100 meV (20 K), respectively. The experiments were carried out from room temperature to 10 K (He I) or 20 K (synchrotron radiation). Clean surfaces of samples were prepared by scraping with a diamond file every 30–60 min.² The binding energy of the photoemission spectra is defined with respect to E_F of the respective samples.

The YbInCu₄ and YbCdCu₄ samples used for the present experiments were single crystals prepared by the flux growth method (Sarrao et al., 1996). The constituent elements with stoichiometric ratios in InCu or CdCu fluxes were put in an alumina crucible and sealed in an evacuated quartz ampoule. The sample was then heated to 1373 K and cooled slowly to 1073 K. After keeping at 1073 K for 20 h, the flux was removed. YbMgCu₄ samples were polycrystals. An appropriate amount of the elements was melted in an arc-furnace. After the reaction, the product in the quartz ampoule was annealed at 873 K for two weeks. The crystal structures of all samples were confirmed to be the C15b-type by X-ray powder diffraction. For YbInCu₄, the temperature width of the valence transition at T_v was below 2 K from the measurements of the magnetic susceptibility.

3. Results and discussion

Fig. 1 shows the photoemission spectra near E_F of YbXCu₄ (X = In, Cd, Mg) with the He I resonance line measured at 10 K. The spectra are normalized using intensities in the binding-energy region of 300–700 meV, where we assume a dashed line from 350 to 550 meV for YbInCu₄ and YbCdCu₄. The prominent peaks near E_F in the spectra of YbInCu₄ and YbCdCu₄ are ascribed to the Yb²⁺ 4f_7/2 states. The peak intensity of YbInCu₄ is stronger than that of YbCdCu₄, suggesting that the Yb ion in YbInCu₄ is more divalent than that in YbCdCu₄ at 10 K. The peak energies of YbInCu₄ and YbCdCu₄ are around 50 and 30 meV, respectively. On the other hand, the Yb²⁺ 4f_7/2 states in YbMgCu₄ are extremely broad compared with those in YbInCu₄ and YbCdCu₄, which implies that the electronic structure near E_F of YbMgCu₄ is substantially different from YbInCu₄ and YbCdCu₄, and the Yb²⁺ 4f_7/2 states have a large dispersion due to the hybridization between the Yb²⁺ 4f_7/2 and conduction-band states.

Figure 1 He I photoemission spectra near EF of YbXCu4 (X = In, Cd, Mg) measured at 10 K.

Fig. 2 shows the temperature dependence of the Yb²⁺ 4f_7/2 peak of YbInCu₄ and YbCdCu₄. Roughly speaking, the peak intensity is reduced with increasing temperature and the peak almost disappears at 300 K for both compounds. Similar temperature dependence has also been observed for YbAgCu₄ (Weibel et al., 1993). One notices, however, the slight differences between the spectra of both compounds. For YbCdCu₄, the energy position of the Yb²⁺ 4f_7/2 peak gradually shifts to the deeper side with increasing temperature. On the other hand, the peak energy for YbInCu₄, which is around 50 meV at 10 K, first shifts toward the E_F side at 50 K and then to the deeper side above 100 K, in contrast with the results of YbCdCu₄. Furthermore, the enhancement of the peak intensity from 50 to 10 K for YbInCu₄ is much greater than that for YbCdCu₄.

Figure 2 Temperature-dependent He I photoemission spectra near EF of (a) YbInCu4 and (b) YbCdCu4.

In order to estimate the peak energy and intensity with accuracy, the photoemission spectra are fitted with the summation of the Yb²⁺ 4f_7/2 conduction bands and the background due to secondary electrons. We assume the Yb²⁺ 4f_7/2 feature with the asymmetric Doniach–Sunjic line shape and conduction bands with constant density of states at all temperatures. The background contribution is estimated from the integrated method. Finally, we convolute the obtained curve with the Gaussian function to represent the experimental resolution, taking into account the thermal effect using the Fermi–Dirac function. The derived curves reproduce well the experimental results for all temperatures, and for YbCdCu₄ the curve-fitting procedure also works successfully.

From the curve-fitting procedure, the peak energies of YbInCu₄ and YbCdCu₄ at 10 K are estimated to be 46 and 31 meV, respectively. According to the single-impurity Anderson model, these values correspond to k_BT_K (Blyth et al., 1993) and provide T_K ≃ 534 and 360 K. The deeper peak energy for YbInCu₄ is thus qualitatively explained by the higher T_K: ∼430 K for YbInCu₄ (Sarrao et al., 1996) and ∼220 K for YbCdCu₄ (Sarrao et al., 1999). The energy shift about 3 meV to the deeper side from 50 to 10 K for YbInCu₄ is also qualitatively explained by the change of T_K at T_v.

Fig. 3 shows the peak intensities of the Yb²⁺ 4f_7/2 lines, derived from the fitting procedure for the photoemission spectra, as a function of temperature. One notices that the peak intensity of YbCdCu₄ increases continuously with decreasing temperature. For YbInCu₄ from 300 to 50 K the intensity also increases continuously, while from 50 to 10 K the intensity is remarkably enhanced compared with YbCdCu₄. The drastic enhancement is peculiar to YbInCu₄ and would reflect the change of the electronic structure of YbInCu₄ at T_v. For YbMgCu₄, little temperature dependence has been observed.

Figure 3 Intensities of the Yb^2+ 4f7/2 peak in the photoemission spectra of YbInCu4 and YbCdCu4 as a function of temperature.

The photoemission spectra using the He I resonance line discussed above provide information only on the Yb²⁺ 4f states. In addition, at hν = 21.22 eV (He I) the photoionization cross section of the Yb 4f states is significantly small compared with the other states forming the conduction bands such as the In 5p and Yb 5d states (Yeh & Lindau, 1985). In order to observe the Yb 4f states clearly and to investigate the temperature-dependence of the Yb³⁺ states as well as the Yb²⁺ states, we have measured the synchrotron radiation photoemission spectra at hν = 800 eV for YbXCu₄ (X = In, Cd, Mg). At hν = 800 eV, contributions to the photoemission spectra from the other valence electrons, except for the Cu 3d and Cd 4d states, are almost negligible. The ratios of the photoionization cross sections are [Cu 3d]/[Yb 4f] ≃ 0.14 and [Cd 4d]/[Yb 4f] ≃ 0.22 (Yeh & Lindau, 1985).

Fig. 4 shows the synchrotron radiation photoemission spectra of YbXCu₄ (X = In, Cd, Mg) measured at 20 K. The remarkable structures at 3–5.5 eV in all the spectra are assigned to the Cu 3d states, and the structure around 10 eV in YbCdCu₄ are assigned to the Cd 4d states. In the spectrum of YbInCu₄ the prominent doublet peaks due to the Yb²⁺ 4f_7/2 and 4f_5/2 states are observed at 0.1 and 1.4 eV, respectively, which probe the Yb²⁺ 4f states in the bulk. On the other hand, one also notices some structures in the Yb²⁺ 4f region at 0–3 eV other than the doublet peaks. A structure at 2.7 eV and a weak shoulder at the shallower binding-energy side of the Yb²⁺ 4f_5/2 peaks, which are denoted by `S' in the figure, are known to be contributions from the surface layer. The weak structures just below the Yb²⁺ 4f_7/2 and 4f_5/2 peaks (dashed lines in the figure) also come from the second surface layer. The Yb³⁺ 4f states contribute to the spectrum from 5.5 to 12 eV as multiplet structures. These are well reproduced by atomic calculations (Gerken, 1983). It should be noted that the photoemission spectra of YbInCu₄ and YbCdCu₄ are quite similar including the relative intensity of the Yb²⁺ and Yb³⁺ 4f structures. The Yb ions in YbInCu₄ and YbCdCu₄ are in the mixed divalent and trivalent states.

Figure 4 Synchrotron radiation photoemission spectra of YbXCu4 (X = In, Cd, Mg) measured at 20 K.

On the other hand, the spectrum of YbMgCu₄ is completely different from the other two compounds. The Yb²⁺ 4f peaks at 0.2 and 1.5 eV are considerably broad, consistent with the He I photoemission spectrum. In addition, the intensity of the Yb³⁺ 4f multiplet structures is considerably weak, indicating that the Yb ion in YbMgCu₄ is in the almost divalent state. These experimental results for the Yb valence of YbXCu₄ (X = In, Cd, Mg) are in qualitative agreement with those of the Yb L_III-edge absorption experiments, although the intensity of the Yb³⁺ 4f structures in the photoemission spectrum of YbMgCu₄ is too small (Felner et al., 1987; Sarrao et al., 1999).

The energy separation between the centre of gravity of the Yb²⁺ and Yb³⁺ 4f structures roughly provides ∊_f + U_ff, where ∊_f and U_ff represent the energy level of an f electron and the averaged Coulomb interaction energy between the Yb 4f electrons in the compounds, respectively. One notices that ∊_f + U_ff is largest in YbInCu₄ among the three compounds and decreases as X goes from In to Cd to Mg. The smallest ∊_f + U_ff values of YbMgCu₄ would qualitatively be understood from the small U_ff value because of the Yb 4f states hybridizing with the conduction-band states, which are also supported from the broad Yb²⁺ 4f_7/2 peak in both He I and synchrotron radiation photoemission spectra of YbMgCu₄.

Fig. 5 shows the temperature-dependent synchrotron radiation photoemission spectra of YbInCu₄ measured at 20, 50, 100, 200 and 300 K. The Yb²⁺ 4f_7/2 and 4f_5/2 peak intensities increase continuously with decreasing temperature down to 20 K, in agreement with the results of the He I photoemission spectra. On the other hand, the intensity of the Yb³⁺ 4f structures decreases. A remarkable change in the spectra between 20 and 50 K owing to the valence transition is not clearly observed. The photoemission spectra of YbCdCu₄ exhibit a similar temperature dependence as YbInCu₄, indicating that the electronic structures of the two compounds are similar. For YbMgCu₄, on the other hand, little temperature dependence has been observed.

Figure 5 Temperature-dependent synchrotron radiation photoemission spectra of YbInCu4.

Fig. 6 shows the synchrotron radiation photoemission spectra of YbInCu₄ measured at 20 and 50 K, in comparison with those of YbCdCu₄. The binding-energy region of the Cu 3d states is removed from the figure. It should be noted that the energy separation between the Yb²⁺ and Yb³⁺ 4f structures, i.e. ∊_f + U_ff, increases by about 0.2 eV in the spectrum of YbInCu₄ at 20 K, while that of YbCdCu₄ is almost unchanged. Since the U_ff value is considered to be almost unchanged, this suggests that the ∊_f value changes critically through the valence transition of YbInCu₄.

Figure 6 Comparison of the synchrotron radiation photoemission spectra of YbInCu4 and YbCdCu4 measured at 20 and 50 K.

In summary, although the temperature-dependent He I and synchrotron radiation photoemission spectra of YbInCu₄ and YbCdCu₄ are similar, the enhancement of the Yb²⁺ 4f_7/2 peak from 50 to 10 K for YbInCu₄ is greater than that for YbCdCu₄, and the energy separation between the Yb²⁺ and Yb³⁺ 4f structures of YbInCu₄ changes between 20 and 50 K. These results reflect the valence transition of YbInCu₄. On the other hand, the electronic structure of YbMgCu₄ is different from YbInCu₄ and YbCdCu₄, and little temperature dependence has been observed.

Footnotes

†Presented at the `International Workshop on High-Resolution Photoemission Spectroscopy of Correlated Electron Systems' held at Osaka, Japan, in January 2002.

²For YbInCu₄, the photoemission spectra for the sample surfaces prepared by scraping and cleavage are compared by Reinert et al. (1998). The temperature dependence of the spectra is the same for both sample surfaces, though the peak intensity is slightly reduced for the scraped surface. In this paper we limit the discussion to the temperature dependence and X dependence of the photoemission spectra. Experiments for the cleaved surfaces are in progress.