Reduction of Kondo lattice effects in Yb1−xLuxAl3 observed by soft x-ray photoelectron spectroscopy

We have carried out the bulk-sensitive and high-resolution soft x-ray photoelectron spectroscopy on Lu substituted intermediate-valence compound Yb1−xLuxAl3 (x = 0.4) at temperatures from 200 to 20 K. The temperature dependences of the bulk Yb 4f photoelectron spectra revealed in our preceding works on high purity YbAl3 have not been observed in this Lu substituted system. The temperature dependences of the bulk Yb 4f peak positions and the Yb valence in this system can be well reproduced by the single impurity Anderson model (SIAM), whereas the spectral behaviors in YbAl3 were not at all reproduced by the SIAM. These results confirm the importance of the Kondo lattice effects for YbAl3, for which the coherent lattice periodicity plays essential roles.


Introduction
The single impurity Anderson model (SIAM) could often explain the 4f spectral behavior observed by photoelectron (or photoemission) spectroscopy (PES) in rare-earth intermediatevalence (IV) compounds [1]- [4]. However, it has recently been revealed that the bulk 4f PES spectra of CeRu 2 , whose Kondo temperature T K is higher than 1000 K, cannot be well reproduced by the SIAM [5,6] (T K represents the hybridization strength between the 4f and conduction electrons). In addition, behaviors of the 4f electrons in the systems with lattice coherence (Kondo lattice effects or Anderson lattice effects) are also thought to deviate from the SIAM predictions, since the SIAM can be applicable only to an isolated 4f impurity ion with ignoring the influence of the periodicity of the lattice on the 4f state. In our preceding work [7], we have performed high-accuracy soft x-ray PES (SXPES) measurements of Yb-based IV compound YbAl 3 . This compound has the relatively high-T K (∼500 K) among Yb-based IV compounds and the Kondo lattice effects are suggested below the coherence temperature T coh ∼ 40 K [8,9] 7 . From the SXPES measurements, unusual temperature dependences of the Yb 4f spectra have been revealed for YbAl 3 . These temperature dependences of the Yb 4f spectra in YbAl 3 have not been reproduced within the framework of the SIAM. Thus, the limitation of the SIAM has been unambiguously clarified for the first time for YbAl 3 .
In Lu substituted compounds Yb 1−x Lu x Al 3 , the temperature T max of the broad maximum in the magnetic susceptibility shifts to higher temperatures with increasing x, i.e. T K (estimated as T K ∼ (4-6)T max ) increases with increasing x [10]. The anomalies in both susceptibility and specific heat below T coh attributed to the Kondo lattice effects in YbAl 3 are also suppressed for x 0.05 in Yb 1−x Lu x Al 3 [10,11]. By increasing x, the SIAM predictions are expected to be applicable to the Yb 4f spectra of Yb 1−x Lu x Al 3 in accordance with the suppression of the Kondo lattice effects. Therefore, SXPES studies of Yb 1−x Lu x Al 3 attract much attention to discuss the Kondo lattice effects.
In this paper, we present a SXPES study of Yb 0.6 Lu 0.4 Al 3 . We have confirmed that the temperature dependences of the Yb 4f spectra in Yb 0.6 Lu 0.4 Al 3 can be well reproduced by the non-crossing approximation (NCA) calculation based on the SIAM irrespectively from the increased T K induced by the Lu substitution.  [7] measured at 200 K. The Yb 3+ 4f multiplet structures are indicated by the vertical bars predicted by the atomic multiplet calculation [16]. For the spectrum of Yb 0.6 Lu 0.4 Al 3 , the two arrows show the Lu 3+ 4f 7/2 and 4f 5/2 peaks at 6.7 and 8.1 eV, respectively.

Experimental
Single-crystalline Yb 0.6 Lu 0.4 Al 3 samples (cubic AuCu 3 -type structure) were grown by the selfflux method with excess aluminium [9,12] and characterized by magnetic susceptibility and specific heat measurements [11]. The Kondo temperature suggested from T max ∼ 250 K in the magnetic susceptibility is T K ∼ 1000 K [10,11]. The bulk-sensitive and high-resolution SXPES measurements were performed with synchrotron radiation (hν = 700 eV) at beamline BL25SU of SPring-8 [13,14], by using the SCIENTA SES200 analyzer. The samples were fractured in situ in a vacuum with a base pressure of better than 3 × 10 −8 Pa and the SXPES were measured at temperatures from 200 to 20 K. The surface cleanliness was confirmed by the absence of the O 1s and C 1s SXPES signals. Energy calibration was performed for Au Fermi-edge at each measuring temperature. The total resolution of the SXPES measurement was set to 65 meV. Figure 1 compares the valence-band SXPES spectra of Yb 0.6 Lu 0.4 Al 3 and YbAl 3 [7] measured at 200 K. The spectra have been normalized by the integrated intensity of the Yb 3+ 4f multiplet structures. At hν = 700 eV, the cross-sections of the Yb and Lu 4f states are dominant while the contributions from the valence-bands are almost negligible [15]. Two groups of characteristic features derived from the Yb divalent (Yb 2+ ) and trivalent (Yb 3+ ) states for Yb-based IV 4 compounds are observed in both Yb 0.6 Lu 0.4 Al 3 and YbAl 3 . The Yb 3+ 4f 12 final-state multiplet structures (shown by the vertical bars after a proper energy scaling (∼1.1) for the calculated atomic multiplet structures [16]) are observed between 5 and 11 eV. Meanwhile two sharp peaks just below the Fermi level (E F ) and at 1.3 eV are derived from the Yb 2+ 4f 13 J = 7/2 (abbreviated as 4f 7/2 ) final-state and its spin-orbit partner J = 5/2 (4f 5/2 ) final-state from the Yb 2+ 4f 14 initial-state in the bulk. In addition, rather broad peaks centered around 0.9 and 2.2 eV in the Yb 2+ 4f region are observed, which are derived from the surface layer. Surface electronic configurations are often different from those of bulk in many strongly correlated electron systems [5,17]. In the present SXPES results, however, the spectral intensity of the surface components is much weaker compared with the previous low-energy (20 < hν < 130 eV) PES results [18]- [21]. Therefore, we can discuss the intrinsic peak energy positions in the bulk 4f spectra and the Yb valence with much higher accuracy. For Yb 0.6 Lu 0.4 Al 3 , one can see the prominent doublet peaks derived from the Lu 4f 13 final-states (shown by the two arrows) from the Lu 3+ 4f 14 initial-state overlapping with the Yb 3+ 4f multiplet structures. Figure 2(a) shows the temperature dependence of the first peak ( 3 H 6 ) of the Yb 3+ 4f 12 multiplet structures and the Yb 2+ 4f 13 7/2 peak (so-called Kondo peak) near E F in Yb 0.6 Lu 0.4 Al 3 . For comparison, the temperature dependence of the Yb 4f spectra of YbAl 3 [7] is reproduced in figure 2(b). Here, all spectra have been normalized by the integrated intensity of the 3 H 6 peak. As shown in figure 2(a), the 3 H 6 peak (and also the whole peaks of the Yb 3+ 4f multiplet structures) is found to shift toward higher binding energies (E B ) with decreasing the temperature from 200 to 20 K. On the other hand, the shift of the Yb 2+ 4f 7/2 peaks is found to be almost negligible (the Yb 2+ 4f 5/2 peaks also exhibit a similar behavior) in Yb 0.6 Lu 0.4 Al 3 . In contrast to Yb 0.6 Lu 0.4 Al 3 , however, the shift of the 3 H 6 peaks is found to be almost negligible in YbAl 3 . On the other hand, the Yb 2+ 4f 7/2 peak is found to shift toward lower E B with decreasing the temperature in YbAl 3 . Thus the temperature dependence of the Yb 4f spectra of Yb 0.6 Lu 0.4 Al 3 is in a strong contrast to that of YbAl 3 .

Results and discussion
In order to estimate the temperature dependence of the accurate peak positions of the Yb 4f spectra and the Yb valence of Yb 0.6 Lu 0.4 Al 3 , we have carried out a numerical fitting. For simplicity, calculated PES line spectra are convoluted with the Gaussian function for the instrumental resolution and the Lorentzian function for the lifetime broadening. The Yb valence can be estimated from the intensity ratio of the bulk Yb 2+ and Yb 3+ 4f components after subtraction of the surface components (the Yb valence of which is assumed to be 2+) observed in the Yb 2+ 4f region. In addition, it has been reported that a subsurface layer with more Yb 2+rich properties than the bulk exists in some Yb-based IV compounds [19], [22]- [25]. Thus, two structures (split by the spin-orbit interaction) are assumed for the surface and subsurface components in order to extract the intrinsic contribution of the bulk Yb 2+ 4f components. From the numerical fitting, the integrated intensity ratio for the bulk, subsurface and surface Yb 2+ 4f components is estimated as I b : I ss : I s = 0.77 : 0.07 : 0.16. The thicknesses of the surface (d s ) and subsurface (d ss ) layers are given by where λ is the mean free path of the photoelectrons (λ ∼ 15.8 Å at hν = 700 eV) [26]. Then, d s ∼ 2.8 Å and d ss ∼ 1.3 Å are roughly evaluated as the thicknesses of the surface and subsurface layers. d s + d ss ∼ 4.1 Å is comparable to the lattice constant of Yb 0.6 Lu 0.4 Al 3 (a ∼ 4.20 Å) [11]. The Yb 3+ 4f multiplet structures in the SXPES spectra are fitted as mentioned before [16]. The Lu 3+ 4f spin-orbit split components are subtracted from the Yb 3+ 4f components. The temperature independent Mahan's asymmetry parameters [27] are assumed as α = 0.12 and 0.18 for the bulk Yb 2+ and Yb 3+ components, respectively. As an example, the fitting result of   [11] are added in figure 3(b). The Yb valences estimated from the Yb L III XAS spectra for Yb 0.7 Lu 0.3 Al 3 and Yb 0.5 Lu 0.5 Al 3 are larger than those estimated by the SXPES spectra for Yb 0.6 Lu 0.4 Al 3 . In the case of the Yb L III XAS, the Yb 2+ and Yb 3+ components strongly overlap and the separation of the XAS spectrum into the two components has some ambiguities. Thus, the accuracy of the valence evaluation from the Yb L III XAS spectra is rather limited. In the SXPES, on the other hand, the Yb 4f spectra can be clearly separated into the Yb 2+ and Yb 3+ components, facilitating accurate estimation of the Yb valence. Figures 3(c) and (d) show the temperature dependence of the bulk Yb 2+ 4f 7/2 peak position and the center of gravity (COG) of the Yb 3+ 4f multiplet structures, respectively. In Yb 0.6 Lu 0.4 Al 3 , the peak positions of the bulk Yb 2+ 4f 7/2 spectra stay at 57-55 meV below 200 K. In contrast, the whole peaks of the    (c), respectively. The parameter set (C) reproduces best the experimental results. Estimated T K 's are also given. In order to discuss the temperature dependence of the bulk Yb 4f spectra for Yb 0.6 Lu 0.4 Al 3 , we have carried out the NCA calculation based on the SIAM. In this calculation, the 4f 14 , 4f 13 (J = 7/2, 5/2) and 4f 12 initial-states are considered. Possible crystal field splitting of the 4f 7/2 state below 10 meV [28] is neglected. The degeneracy of the 4f 13 7/2 , 4f 13 5/2 and 4f 12 states are considered as 8, 6 and 91, respectively. The spin-orbit splitting of the 4f 13 states (the energy difference between the 4f 13 7/2 and 4f 13 5/2 states) is adjusted to 1.27 eV. The hybridization of the 4f states with a conduction-band extending within ±6 eV from E F with trapezoidal shape is assumed. The calculated spectral functions are convolved with the Fermi-Dirac function and the Gaussian function (the full width at half maximum (FWHM) is 65 meV) for the instrumental resolution. Other optimized parameters are the bare 4f energy level ε f (<0) (ε f is the binding energy of the 4f electron corresponding to the 4f 14 → 4f 13 process), the Coulomb repulsive energy U ff between two 4f electrons on the same lattice site (the binding energy in 4f 13 → 4f 12 process is represented as ε f + U ff ) and the averaged hybridization strength = (π/B)   The temperature dependence of the best-fit NCA spectra is shown in figure 4(c) for which the NCA parameter set (C) is given in table 1. In this case, the COG of the 4f 12 multiplet structures shifts from ∼7.030 eV at 200 K to ∼7.055 eV at 20 K. Therefore, the peak shift is predicted to be ∼25 meV toward higher E B with decreasing the temperature. On the other hand, the peak position of the 4f 13 7/2 spectra stays at ∼60 meV even with changing the temperature. The Yb valence predicted by the present NCA calculation decreases gradually from 2.66 at 200 K to 2.57 at 20 K ( figure 3(b)). These theoretical results are in good agreement with the temperature dependences evaluated from the bulk Yb 4f spectra of Yb 0.6 Lu 0.4 Al 3 . In addition, we have simulated the magnetic excitation spectrum using this NCA calculation with the same parameter set (C) in order to estimate T K (T K for (A) and (B) are given for reference in table 1). T K is estimated as ∼840 K from the peak position of the predicted magnetic excitation spectrum. This value is comparable to that of T K ∼ 1000 K estimated from the magnetic susceptibility [10,11]. Thus the results of Yb 0.6 Lu 0.4 Al 3 are well explained by the SIAM. Our new results for Yb 0.6 Lu 0.4 Al 3 indicate that the lattice periodicity of the Yb ions is responsible for the Kondo lattice effects.
We compare the Yb valence and T K of Yb 0.6 Lu 0.4 Al 3 to those for YbAl 3 . The Yb valence of Yb 0.6 Lu 0.4 Al 3 (decreasing from 2.65 at 200 K to 2.58 at 20 K) is smaller than that of YbAl 3 (decreasing from 2.71 at 200 K to 2.65 at 20 K), i.e. the bulk Yb divalent component is larger by ∼20% for the Lu concentration of x = 0.4. T K increases also from ∼500 K for YbAl 3 to ∼840 K for Yb 0.6 Lu 0.4 Al 3 . These differences of the Yb valence and T K are not due to a simple chemical pressure effect since the lattice parameter decreases by only ∼0.3% from YbAl 3 to LuAl 3 [11]. In Yb 1−x Lu x Al 3 , the Lu substitution into YbAl 3 is predicted to induce the electron doping due to the addition of the Lu 5d 1 electron as conduction electrons. This is related to the decreasing electrical resistivity from YbAl 3 to LuAl 3 [12]. The electron doping raises E F and moreover strengthens the effective hybridization ρV 2 between the Yb 4f and conduction electrons near E F , resulting in the decrease of the Yb valence and the increase in T K [29]. Although T K is increased by the Lu substitution, the temperature dependences of the bulk Yb 4f spectra in Yb 0.6 Lu 0.4 Al 3 are well interpreted within the SIAM. This indicates that the Kondo lattice effects are suppressed due to the random potential by the substituted Lu ions.

Conclusions
In conclusion, we have studied the Lu substituted compound Yb 1−x Lu x Al 3 by the soft x-ray photoelectron spectroscopy. In Yb 0.6 Lu 0.4 Al 3 , it is found that the peak positions of the bulk Yb 2+ 4f spectra are found to be almost independent of temperatures while the whole peaks of the Yb 3+ 4f multiplet structures are found to shift by ∼20 meV toward higher E B with decreasing the temperature from 200 to 20 K. The bulk Yb valence decreases gradually from 2.65 at 200 K to 2.58 at 20 K. These thermal behaviors in Yb 0.6 Lu 0.4 Al 3 are well understood in the framework of the SIAM whereas T K is obviously higher than for YbAl 3 . These results are qualitative different from those for YbAl 3 , suggesting that the Kondo lattice effects are important for describing the bulk electronic states of YbAl 3 . Thus, we understand that the lattice periodicity of the Yb ions without randomness besides the strong hybridization is responsible for the Kondo lattice effects. Concrete analyses of YbAl 3 within the framework of the periodic Anderson model will be really required in the near future to discuss the temperature dependence of the bulk Yb 4f spectra.