High-resolution photoemission study of the valence transition in YbInCu4

Abstract We have performed a photoemission study of YbInCu4, which undergoes a first-order phase transition at Tv≃40 K between the low-temperature intermediate-valence state and the high-temperature local-moment state. The Yb 4f photoemission peak (Kondo peak) just below the Fermi level, which probably originates from the subsurface region of the YbInCu4 samples but tracks the valence transition in the bulk YbInCu4, has been studied above and below Tv. It has been found that the 4f photoemission peak is shifted from ∼− 35 meV at 75 K to −40 meV at 7 K.By analyzing the 4f peak position and the Yb valence in the two phases using the Anderson impurity model, we find that the bare 4f level, which is located close to the Fermi level, is shifted downward and the hybridization strength decreases in going from the high-temperature to low-temperature phases.

The isostructural ®rst-order transition in YbInCu 4 , which was ®rst found by Felner and Nowik in 1986 [1], has attracted much attention due to sudden changes in the transport and thermodynamic properties within a very narrow temperature range around T v 40±70 K [1±4]. A collection of Yb 31 local moments in the high±temperature phase is transformed to a Pauli±paramagnetic state with an intermediate Yb valence in the low±temperature phase. The Curie±Weiss magnetic susceptibility above T v changes sharply to the temperature-independent Pauli paramagnetism and the electrical resistivity is reduced by about one order of magnitude. While Felner et al. [2]reported the ®rstorder transition in Yb 0.4 In 0.6 Cu 2 with the disordered C15 Laves-phase structure (Fd3m), subsequent studies have con®rmed that the sharp transition occurs in YbInCu 4 , which has the ordered C15B structure (F4 Å 3m) both above and below T v [5]. Since the ionic radius of Yb 21 is larger than that of Yb 31 , the lattice constant increases by 0.15% on cooling across T v . From the change in the lattice constant the decrease in the Yb valence through the transition has been estimated to be ,0.1 [2]. Yb L III -edge X-ray absorption studies [2,6] have shown that the Yb valence decreases from ,2.9 to ,2.8 on cooling. A neutron powder diffraction study [5] con®rmed the lattice expansion below T v and detected no change in the crystal symmetry between the two phases.
Photoemission spectroscopy (PES) is a direct probe of occupied electronic states and is expected to give clear information especially for Yb compounds, where the 4f level is mostly occupied and signals from the outermost atomic layer are energetically well separated from bulk signals [12]. So far, several groups [7±11] have performed photoemission studies of YbInCu 4 and have found the decrease of the Yb valence on cooling. However, the absolute value of the valence of`bulk' Yb deduced from the photoemission spectra is much smaller than that deduced from the magnetic susceptibility and the lattice constant.
According to Reinert et al. [9], the valence deduced from PES changes continuously across T v , i.e. from 2.56 at 20 K to 2.85 at 220 K. In order to explain the difference in the Yb bulk' valence between PES and the other more bulk-sensitive experiments, it has been proposed that apart from the outermost layer, the subsurface region within the photoelectron escape depth may also be different from the bulk [7,9]. Although not completely bulk sensitive, PES studies of YbInCu 4 may give useful information about the valence transition in bulk YbInCu 4 because the valence change across T v in the subsurface region of YbInCu 4 re¯ects the valence transition in the bulk. Indeed, Moore et al. [11] found a sudden change in the 4f photoemission intensity at T v . So far, except for the reported small Yb valence compared to the bulk [7,9±11] little is known about the subsurface electronic structure of YbInCu 4 .
In the present work, we have focused on the 4f peak position just below the Fermi level (E F ), i.e. the Kondo peak. Sarrao et al. [4]estimated the Kondo temperature in YbInCu 4 to be T K . 20 K above T v and 430 K below T v by ®tting the J 7/2 Coqblin±Schrieffer model to the measured magnetic susceptibility. Lawrence et al. [13] analyzed the inelastic neutron spectrum of YbInCu 4 using the Anderson impurity model (AIM) and deduced T K to be 25 K above T v and 405 K below it. According to AIM, the Kondo peak appears at 2k B T K in the photoemission spectrum and thus an energy shift of the peak as large as ,35 meV would be expected through T v in YbInCu 4 if one could measure bulk-sensitive PES spectra. Although the previous PES measurements have revealed a strong temperature dependence in the spectral weight of the Kondo peak [8±10] such an energy shift has not been reported yet.The increase in the 4f electron number below T v should be accompanied by a decrease in the number of conduction electrons, which would lower the Fermi level. Such a shift may change possibly the bare 4f-level position (e f 0 ) measured from E F and the DOS at E F , r(E F ), both of which determine the 4f electronic states.
Single crystals of YbInCu 4 were grown from high-purity constituent materials with InCu¯ux [4]. The prepared samples showed a sharp jump in the magnetic susceptibility and the electrical resistivity at T v 42 K with a narrow temperature range of 2 K. Photoemission measurements were performed using an Omicron EA 125 HR analyzer and a VG He discharge lamp. Samples with a cleavage post were transfered from a preparation chamber into the analyzer chamber in the 10 211 Torr range and were cleaved in situ. The acceptance angle of the electron analyzer was set to^88, which corresponds to one third of the Brillouin zone area of YbInCu 4 for the He I radiation (hn 21.2 eV), and the cleaved surfaces were irregular, probably making the measured spectra angle integrated ones. Photoemission spectra between 219 eV and E F were almost reproducible between different cleaving as reported by Reinert et al. [9] 1 . The measurements were made at 75 and 7 K, bracketing Surface' indicates the Yb 4f 14 ! 4f 13 7/2 transition in the outermost layer. Fig. 2. Yb 4f spectra near E F corresponding to the 4f 14 ! 4f 13 7/2 transition. The solid and dashed curves represent the spectra taken at 75 and 7 K, respectively. The solid curve is the sum of the time-dependent raw spectra (1) and (3), which are shown in the inset, and the dashed curve is the sum of (2) and (4). The vertical bars in the ®gure are a guide to eyes.
T v 42 K. Since the cleavage at 7 K requires cooling of the sample with the post across T v , at which the sample shows the lattice expansion, all the samples were cleaved at 75 K. We evaporated Au onto each sample to determine the E F position and the energy resolution. The energy resolution thus deduced was 20±22 meV for the He I spectra and ,60 meV for the He II (hn 40.8 eV) spectra. As Reinert et al. discussed in detail [9], the 4f peak intensity just below E F decreased with time after the cleavage. Thus we took the 4f spectra near E F while changing the temperature as 75 K ! 7 K ! 75 K ! 7 K for each in situ cleaved sample to subtract extrinsic time dependence. Those spectra were measured within ,5 h after the cleavage. Fig. 1 shows an He II wide energy-range scan of the valence band of YbInCu 4 taken just after cleavage. The sharp signals just below E F and at 21.3 eV correspond to the 4f 14 ! 4f 7/2 13 and 4f 14 ! 4f 5/2 13 transition, respectively. The broad peak around 21 eV, on the other hand, corresponds to the 4f 14 ! 4f 7/2 13 transition at the Yb atoms in the outermost layer. The other outermost Yb 21 signal of the 4f 14 ! 4f 5/2 13 transition is overlapped by the Cu 3d band, which extends from 22 to 25 eV. Between 25 and 213 eV appears the multiplet structure of the 4f 13 ! 4f 12 transition. The In 4d core level is observed around 217 eV. Fig. 2 shows the He I photoemission spectra near E F taken with higher energy resolution. We have normalized the spectra to the average intensity between 20.25 and 20.20 eV. The spectra consist of the 4f peak just below E F , which corresponds to the 4f Kondo peak, and the conduction band with a¯at density of states (DOS). Such a¯at conduction-band DOS near E F has been observed in the non-f reference compound LuInCu 4 [7,10]. The inset shows a series of spectra taken in a sequence after a cleavage. They show that the Yb 4f spectral weight decreases with time, but the intensity change between the two phases was reproducible and the peak position in each phase did not change.
On cooling from 75 to 7 K across T v , the Kondo peak becomes remarkably stronger in accordance with the decrease in the Yb 4f valence. At the same time, the intensity maximum of , 2 35 meV at 75 K is shifted by about 5 meV away from E F . This value is much smaller than what the bulk magnetic measurements predict according to AIM. Note that the Fermi±Dirac (FD) function at 75 K is 0.99 at 235 meV and therefore does not affect the peak position appreciably 2 . Such a shift was not observed in the previous work [8±11], probably due to insuf®cient energy resolution. Joyce et al. [10] measured a shift of the spin-orbit replica of the Kondo peak (4f 14 ! 4f 5/2 13 signal) at , 2 1.3 eV across T v but found no shift in their spectra taken with the energy resolution of ,45 meV. We note that the spin-orbit replica is further broadened due to the shorter life time of the photohole in comparison with the Kondo peak just below E F .
In order to interpret the above temperature dependence of the photoemission spectra in the subsurface region, we have calculated the 4f photoemission spectra using AIM to the second order in 1/N f , where N f is the degeneracy of the J 7/2 4f level. The model consists of the degenerate J 7/2 4f level of N f 8 at e f 0 and the continuum extending from 2B ; 2 0.15 eV to 1B ; 0.15 eV with the J 5/2 level being neglected. We have calculated both I(4f 14 ! 4f 13 ) and I(4f 13 ! 4f 12 ), where I(4f n ! 4f n21 ) is the 4f n ! 4f n21 photoemission intensity, using a ®nite Coulomb repulsion U 7 eV to compare n f,I ; I(4f 13 ! 4 f 12 )/[I(4f 13 ! 4f 12 ) 1 7/8I(4f 14 ! 4f 13 )] and the groundstate 4f-hole occupancy n f 3 . Basis states in the calculation are lowest-order f 14 , f 13 , and f 12 states and second-order f 14 state [16,18] for the initial ground state and lowest-order f 13 , f 12 , and f 11 states and second-order f 14 and f 13 states for the ®nal states. Here, the second-order states include one electron-hole pair in the continuum. We de®ne the 4f hole occupancy in the ground state n f as |c(13)| 2 1 2|c(12)| 2 , where the ground state |c l is expressed as |c l c(14)|4f 14 l 1 c(13)|4f 13 l 1 c(12)|4f 12 l. Since the 4f peak appeared in the energy region where the FD function is almost unity at the measurement temperatures, we did not take into account the effect of the FD function.
We have reproduced the photoemission peak position observed in the present experiment and n f,I deduced by Reinert et al. [9]as shown by curves (a) and (b) in Fig. 3. We note that recent PES study by Moore et al. [11] has given similar values of n f,I . We have convoluted all the calculated spectra with a Gaussian of 22 meV FWHM. From the experimentally determined peak position and n f,I , e f 0 and the 4f-conduction band hybridization strength D p=2B R B 2B reuVu 2 de in the AIM [17], where V(e ) is the hybridization matrix element and r(e ) is the conductionband DOS, are uniquely determined. We obtained e f 0 0.120 eV and D 0.042 eV to reproduce the 75 K spectrum (a) and e f 0 0.067 eV and D 0.030 eV to reproduce the peak position of the 7 K spectrum (b) 4 . Here, we have adjusted only these two parameters to reproduce both the peak position and n f,I . Owing to the weak hybridization strength D, the discrepancy between n f and n f,I is negligibly small: n f (n f,I ) is 0.67 (0.66) at 75 K and 0.58 (0.57) at 7 K. This con®rms that the Yb valence in the subsurface region is indeed smaller than that in the bulk in Since the Hall coef®cient |R H | at 7 K is smaller than that at 75 K by one order of magnitude in YbInCu 4 [6], the DOS around E F would be higher below T v than that above it, which would increase D in the low-temperature phase. On the other hand, the expansion of the lattice below T v would reduce V(e) and hence D below T v . The present result of the decrease in D below T v indicates that the effect of the reduction of V(e) exceeds the effect of the increase in the carrier number. We note that e f 0 0.067±0.120 eV is very small in comparison with typical values of e f 0 0.3±1.0 obtained or assumed in the previous photoemission studies of Yb compounds [10,14±16]. We have calculated photoemission spectra with e f 0 1.0 eV [10] by varying D to reproduce the peak position of 240 meV as shown by curve (c) in Fig. 3. We have found that n f,I 0.86 (n f 0.90), which is much larger than the experimentally observed value, as pointed out by Joyce et al. [10]. Therefore, the proximity of the bare 4f level to E F and the smallness of D is responsible for the small 4f hole occupancy (n f,I p 1) with the 4f peak position relatively close to E F , which is characteristic of the photoemission spectra of YbInCu 4 . The small value of e f 0 may be the origin of the 4f instability because a small change in e f 0 or D, which is negligible in the case of large e f 0 and D, may vary n f dramatically. Presumably the present PES results for the subsurface region would therefore be qualitatively correct in the bulk and would be useful to understand the valence instability in bulk YbInCu 4 .
In summary, we have studied the photoemission spectra of YbInCu 4 with high energy resolution. We have observed that the divalent 4f peak is shifted away from E F on cooling across T v . The 4f peak position and the Yb valence were analyzed using AIM with a ®nite U. We have shown that the proximity of e f 0 to E F and the smallness of D are characteristic of YbInCu 4 and are responsible for the valence instability because n f changes sensitively for a small change in e f 0 or D. We have also shown that the discrepancy between n f,I and n f is small for YbInCu 4 owing to the weak hybridization strength D.