Electronic structures of Yb intermetallic compounds studied by photoemission spectroscopy

PHYSICA[

Physica B 186-188 (1993) 26-30 North-Holland

Electronic structures of Yb intermetallic compounds studied by photoemission spectroscopy S.-J. Oh Department of Physics, Seoul National University, Seoul, 151-742, South Korea Electronic structures of mixed-valent and Kondo-like intermetallic Yb compounds YbAI 3, YbCu2Siz, Ybln 2, YbCu 2, Yb4As3, Yb4Sb 3 and Yb4Bi3 have been studied by photoemission spectroscopy, and they are all found to be well described by the Anderson impurity Hamiltonian with the hybridization strength A = ~rpV2 ranging between 15 and 80 meV. The high-resolution study of the 4ft4--->4f 13spectral weights in YbA13 and YbCu2Si z shows remarkable temperature-dependence between 10 and 300 K, which is consistent with the theoretical prediction for the behavior of the Kondo resonance.

I. Introduction

Electronic structures of mixed-valence and Kondolike compounds have been the subject of extensive study for a long time. Electron spectroscopic techniques such as photoelectron spectroscopy (PES) and Bremsstrahlung isochromat spectroscopy (BIS) are powerful tools to study electronic structures experimentally, and these techniques have revealed important information on this interesting class of materials. In particular, PES and BIS investigations were instrumental in elucidating the origin of anomalous physical properties of Ce mixed-valence and Kondolike compounds [1]. It is now widely accepted that the Anderson impurity Hamiltonian,

k,cr

m,tr

+ ~

m,m',~.c.'

(V~,,a~ a k ~ + H . C . ) ,

k . i n .o-

gives a good description of the electronic structures of Ce compounds, and equilibrium properties such as the magnetic susceptibility and specific heat and excitation properties such as PES, BIS and X-ray absorption can be understood on the same footing. The Kondo resonance near the Fermi level which can be observed in the PES and BIS spectral weights determines many physical properties [2], and the controlling parameter distinguishing a-like and y-like compounds is the hy-

Correspondence to: Se-Jung Oh, Department of Physics, Seoul National University, Seoul, 151-742, South Korea.

bridization strength between the localized 4f-level and itinerant conduction electrons. It is interesting to ask whether the same picture applies generally to electronic structures of rare-earth compounds other than Ce compounds. Yb compounds are particularly interesting in this respect because Yb in the last element in the lanthanide series and also theoretical formalisms used to study Ce compounds can be applied to Yb compounds directly by interchanging the role of the 4f electron and the 4f hole. In this paper, we report the valence band photoemission spectra of many mixed-valence and Kondo-like Yb intermetallic compounds including YbAI3, YbCu2Si2, Ybln2, YbCu 2, Yb4As3, Yb4Sb3, and Yb4Bi_~. We deduce the Anderson Hamiltonian parameter values of these Yb compounds from the PES spectra, and compare them with those of Ce compounds. We also compute the zero-temperature magnetic susceptibility Xm(0) expected from these parameters, and compare with the experimental values to see the consistency of Anderson Hamiltonian description for these compounds. Recently the observation of the Kondo resonance in the photoemission spectra of Ce compounds has been questioned [3]. Theoretically, the Kondo resonance in the 4f spectral weights of Ce compounds centers in the unoccupied region above the Fermi level, and therefore only its tail is expected to be observable in the photoemission spectra. On the other hand, because of the electron-hole symmetry, Yb compounds show the Kondo resonance below the Fermi level, which can be studied in detail by photoemission spectroscopy. In the latter part of this paper, we report the result of the

0921-4526/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

S.-J. Oh / Photoemission study of Yb compounds high resolution, temperature-dependent photoemission study of YbA13 and YbCu2Si2, and discuss the validity of the Kondo resonance interpretation for the 4f spectral weight observed by PES.

2. Anderson Hamiltonian parameters of Yb intermetallic compounds Figure 1 shows the valence band photoemission spectra of intermetallic Yb compounds YbPb2, Ybln2, YbCu 2, YbA13, Yb4As3, Yb4Sb3, and Yb4Bi 3 in the binding energy range of 0-5 eV. These spectra were

27

taken at beamline 11-D of the Photon Factory in Japan, equipped with a constant-deviation monochromator and a double pass cylindrical mirror analyzer. The YbPb2, Ybln2, YbCu 2 and YbA13 samples were polycrystalline ingots grown in a vacuum furnace with a tungsten heater, and the Yb4As3, Yb4Sb3, and Yb4Bi 3 samples were single crystals grown in a vacuum furnace with a SiC heater. Fresh surfaces for PES measurements were obtained by fracturing or scraping the samples in situ, and the sample cleanliness was checked by monitoring carbon and oxygen contamination in the spectra. We used photon energy of 60100 eV, in which range the Yb 4f emission dominates

r

(blYb~n2 hv :

IOOeV

,e,,°-C -,i •

......

25 tc)

Yb,A=3

;~

/%,

C

"E I-4

4.0

:5.0

2.0

I.O

EF

Binding Energy (eV)

5.o

4.0

:5.0

2,o

LO

EF

Binding Energy (eV)

Fig. 1. Valence band photoemission spectra of (a) YbPb 3 (b) Ybln 2 (c) Yb4As 3 (d) YbCu 2 (e) YbAI3 (f) Yb4Sb 3 and (g) Yb4Bi3 using synchrotron radiation (dots) and their fit with the bulk and the surface 4f spin-orbit pairs (solid lines). The higher binding energy peak represents the emission from the surface. Backgrounds due to inelastic electrons are also shown.

28

S.-J. Oh / Photoemission study o f Yb compounds

the spectra because of the cross section and the large number of Yb 4f electrons. (YbCu 2 is an exception where strong Cu 3d emissions can be seen in the 2-5 eV binding energy range.) In all of these spectra, we can see two pairs of spin-orbit peaks for the divalent 4f 14---->4f 13 transition, as indicated by the least squares fitted curves shown with the solid line. (The transition from the trivalent component 4f13---.4f ~2 shows up in the binding energy range 5-12 eV.) We interpret the pair closer to the Fermi level as due to the bulk transition, and the other pair with deeper binding energy as due to the divalent surface layers. This identification was based on the sensitivity of the higher binding energy peaks to oxygen contamination and their peak widths, which tend to be larger than that of the bulk because usually many crystallographic orientations and more than one surface layer contribute to surface peaks. The surface peaks are shifted to the higher binding energy by 0.52-0.94 eV relative to the bulk peaks, which can be understood as the result of the reduced number of neighboring atoms at the surface. The direction and magnitude of these surface core-level shifts are in good agreement with the predictions of Johansson and Mhrtensson's fully screened core hole model [4] using Miedema's empirical scheme [5] for the cohesive energy estimation of intermetallic compounds. Having identified surface peaks, we can extract spectral features from the bulk 4f emissions to study the bulk electronic structure of these Yb compounds. First, we determine the valence v from the intensity ratio of the bulk 4f divalent peak IB(+2 ) and the bulk 4f trivalent peak I s ( + 3 ) in the wide range valence band spectra (not shown here) using the relation v =2+

Is(+3) ~41B(+2) + 1 , ( + 3 ) "

The number of 4f holes nf is then given by nf = v - 2. We have neglected here the effect of spectral weight transfer due to hybridization, but this is expected to be small in Yb compounds. Secondly, we can determine the characteristic temperature To, which sets the temperature scale of many physical properties and is loosely called the "Kondo temperature", from the binding energy position of the 4f peak. According to theoretical calculations [6-8] utilizing the large degeneracy Nf of the 4f level, the 4f spectral weight has a peak ("Kondo resonance") at ~f = k T o from the Fermi level. In the case of Yb compounds, this "Kondo resonance" is located below the Fermi level, and we can determine e~ experimentally from the position of the bulk 4f 14---->4f7/2 x3 transition peak in the photoemission spectra. The values of nf and ef determined this way are listed in table 1 for each Yb compound studied. The large Nf theory gives the following relations [6-8] for the Anderson impurity Hamiltonian in the U---~~ limit: n~ l

--

-n

f

N l 'IT

~ X -- , Ef

/~ff nf Xm(0 ) ~- ~ X -Ef

where zl = .rrpV 2 ( p is the conduction band density of states) is the average hybridization strength between the 4f level and conduction electrons, Xm(O) is the magnetic susceptibility at 0 K, and p~f, = / ~ j + l ) g t x B = 4 . 5 4 / ~ B for the 4f~7~2 configuration. Using the values of n~ and Ef determined from the PES spectra, and taking Nf = 8 since the spin-orbit splitting energy for the Yb 4f level is ~1.3 eV, we can calculate ,~ and Xm(0) from the above relations. In table 1, we list the values of A and Xm(0) obtained in this way for each Yb compound. To see if the Anderson Hamiltonian parameter description is appropriate for these Yb

Table 1 Anderson impurity Hamiltonian parameter values of Yb compounds along with the calculated and cxpcrimcntal zero-temperature magnetic susceptibility Xm(0). Here n, is the num0er of 4f holes, e~ is the 4f7/2 level binding energy of the bulk, A is the hybridization parameter. We also included the values of YbAl2 from the data of Kaindl et al. [12]. compound

nI

Ef

YbPb 3 YbAI 3 Ybln~ YbCu 2 YbAI 2 Yb4As3

0 0.65 0.10 0.18 0.40 0.37 0.39 0.13

700 30 550 260 240 300 310 290

YbaSb 3

Yb4Bi3

(meV) A (meV) Xm(0)× 10-3 (emu/mol))¢~,xp(0) × 10-3 (emu/mol) 21.9 24 22 63 69 78 17

4.98 0.041 0.16 0.37 0.28 0.28 0.10

4.62 0.070 0.17 0.41 n/a n/a n/a

29

S.-J. Oh / Photoemission study of Yb compounds

compounds, we compare the predicted /~m(0) value with the experimentally measured value x~P(0) of Klaasse et al. [9]. We can see that these two values are in good agreement, supporting the Anderson Hamiltonian description for the electronic structures of Yb compounds. The BIS study [10] and the Yb 3d corelevel X-ray photoelectron spectroscopy study [11] for some Yb compounds also supports this conclusion. The hybridization parameter A ranges between 17 and 78 meV, which is smaller than most Ce compounds as expected from the lanthanide contraction of the 4f wave function, but still large enough to be important for determining the physical properties of these compounds.

3. Temperature-dependent high-resolution PES study of Yb compounds Recently the observation of Kondo resonances in the PES spectra of mixed-valent or Kondo-like Ce compounds has been questioned [3]. The main reasons for this argument are: (1) there is no temperaturedependence other than the thermal broadening factor in the spectral weight near the Fermi level; and (2) the width of the spectral weight near the Fermi level is much broader than expected from the "Kondo temperature" combined with crystal field splittings. However, as mentioned in the Introduction, Yb compounds are a much better system to study the behavior of the Kondo resonance by photoemission spectroscopy, since the Kondo resonance is expected to lie below the Fermi level. This is in contrast to the case of Ce compounds where it is necessary to look at the BIS spectra [13] to study the whole Kondo resonance, and presently the resolution of BIS is not as good as that of PES. In this section, we report the results of the high-resolution PES study of YbA13 and YbCu2Si 2 as a function of temperature to see the behavior of the 4f spectral weight near the Fermi level. The experiment was performed in beamline U4B (Dragon) of the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory, USA, in collaboration with Dr. L.H. Tjeng of A T & T Bell Laboratories• The samples were scraped in situ to obtain a clean surface, and the high resolution PES spectra were taken with a photon energy of 102 eV at temperatures of 10, 100, 200 and 300K. Figure 2 shows the divalent 4f]4----~4fa3 transition region of the YbA13 spectra at various temperatures taken with the resolution (full width at half maximum) of --70 meV. The broad features are surface peaks as identified earlier, and two sharp features near the Fermi level and at about 1.3 eV below are the bulk 4fa4~ 4f 713/2

• • •

: 1OK : lOOK : 200 K

A

® 4f

3

~

4f

2

1

Binding

E n e r g y (eV)

EF

Fig. 2. The divalent 4f TM~ 4f 13 spectra of YbAI3 at temperatures of 10, 100, 200 and 300 K. The photon energy was 102 eV, and the total instrumental resolution (FWHM) was --70 meV. and 4 f 14 ~ 4f~% transition peaks, respectively• We can see the weight and the width of these bulk peaks change substantially with temperature in contrast to the surface peaks which hardly show any temperature dependence• This is qualitatively as expected from the Kondo resonance [8] with the characteristic temperature T O= 300 K of YbA13. To see the behavior of this bulk 4f spectral weight in 14 13 more detail, we have taken the 4f -,4f7/2 feature only with - 4 0 meV resolution, as shown in fig. 3. We first note that the position of this peak is - 3 5 meV below the Fermi level, consistent with the Kondo temperature of this compound. This is also in agreement with the result of the previous independent measurement done at the Wisconsin Synchrotron Radiation Laboratory [14]. The width of the peak is difficult to estimate because the peak shape is not

• • •

: 10 K : 100K : 200 K

EF tll I

I

.5

m m

_c

4

0.4

0.3

(bulk)

0.2 Binding

0.1

0.0

-0.1

-0.2

E n e r g y (eV)

Fig. 3. The 4f 14----~4f7/2 13 spectral feature of YbA13 at temperatures of 10, 100, 200 and 300 K. The photon energy was 102 eV, and the total instrumental resolution (FWHM) was - 4 0 meV.

30

S.-J. Oh / Photoemission study of Yb compounds

Lorentzian, but the experimental width seems to be close to the theoretical prediction [8] of - 1 . 4 T 0 ~ 50meV. The valence change deduced from the 14 13 4f ---->4f7/2 peak weight change is from v =2.65 at 10K to v = 2.74 at 300K. This amount of valence change is also confirmed by the 3d--->4f X-ray absorption spectra taken at the same time. The direction and the magnitude of the valence change are again consistent with the predictions of the non-crossing approximation calculation [8]. Theoretically the valence increases with temperature because low-lying excited states with predominantly f~-hole character becomes thermally populated at high temperature. Hence, we conclude that most of the characteristics of the 4fla-"->4f71~2 transition peak in YbAI3, including its temperature dependence and the width, are consistent with the predicted behavior of the Kondo resonance. The results for YbCu2Si 2 are also similar. This is taken as evidence for the observation of the Kondo resonance in the photoemission spectra of Yb compounds.

4. Conclusion The results of a valence band photoemission spectroscopy study of many mixed-valent intermetallic Yb compounds are consistent with the Anderson impurity Hamiltonian description for their electronic structures. The 4f14---->4f1732 spectral weight near the Fermi level shows most of the features consistent with the Kondo resonance. This work is the result of collaboration with many people. Among them I especially appreciate Drs. EnJin Cho, L.H. Tjeng, S. Suga, T. Suzuki, J.W. Allen, Y.S. Kwon, T. Kasuya, A. Fujimori and C.G. Olson. This work is supported in part by the Ministry of Education of Korea.

References [1] J.W. Allen, S.-J. Oh, O. Gunnarsson, K. Sch6nhammer, M.B. Maple, M.S. Torikachvili and I. Lindau, Adv. Phys. 35 (1986) 275. [2] N.E. Bickers, D.L. Cox and J.W. Wilkins, Phys. Rev. Lett. 54 (1985) 230. [3] J.J. Joyce, A.J. Arko, J. Lawrence, P.C. Canfield, Z. Fisk, R.J. Bartlett and J.D. Thompson, Phys. Rev. Lett. 68 (1992) 236. [4] B. Johansson and N. Mfirtensson, Phys. Rev. B 21 (1980) 4427. [5] A.R. Miedema, P.F, de Chfitel and F.R. de Boer, Physica B 100 (1980) 1. [6] O. Gunnarsson and K. Sch6nhammer, Phys, Rev. B 28 (1983) 4315. [7] Y. Kuramoto and E. Miiller-Hartmann, J. Magn. Magn. Mater. 52 (1985) 122. [8] N.E. Bickers, D.L. Cox and J.W. Wilkins, Phys. Rev. B 36 (1987) 2036. [9] J.C.P. Klaasse, F.R. de Boer and P.F. de Chfitel, Physica B 106 (1981) 178. [10] S.-J. Oh, S. Suga, A. Kakizaki, M. Taniguchi, T. Ishii, J.-S. Kang, J.W. Allen, O. Gunnarsson, N.E. Christensen, A. Fujimori, T. Suzuki, T. Kasuya, T. Miyahara, H. Kato, K. Sch6nhammer, M.S. Torikachvili and M.B. Maple, Phys. Rev. B 37 (1988) 2861. [111 Jin-Seok Chung, En-Jin Cho and S.-J. Oh, Phys. Rev. B 41 (1990) 5524. [12] G. Kaindl, B. Reihl, D.E. Eastman, R.A. Pollak, N. Mfirtensson, B. Barbara, T. Penny and T.S. Plaskett, Solid State Commun. 41 (1982) 157. [13] D. Malterre, M. Grioni, P. Weibel, B. Dardel and Y. Baer, Phys. Rev. Lett. 68 (1992) 2656. [14] En-Jin Cho, S.-J. Oh, C.G. Olson, J.-S. Kang, R.O, Anderson, L.Z. Liu, J.H. Park and J.W. Allen, Physica B 186-188 (1993) 70.