Electronic structure of semiconducting CeFe$_4$P$_{12}$: Strong hybridization and relevance of single-impurity Anderson model

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by  M. Matsunami

Electronic structure of semiconducting CeFe P : Strong hybridization and relevance
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of single-impurity Anderson model
M. Matsunami,1,∗ K. Horiba,1 M. Taguchi,1 K. Yamamoto,1 A. Chainani,1 Y. Takata,1
Y. Senba,2 H. Ohashi,2 M. Yabashi,2,3 K. Tamasaku,3 Y. Nishino,3 D. Miwa,3 T. Ishikawa,2,3
E. Ikenaga,2 K. Kobayashi,2 H. Sugawara,4 H. Sato,5 H. Harima,6 and S. Shin1,7
1Soft X-Ray Spectroscopy Laboratory, RIKEN SPring-8 Center, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan
6 2JASRI/SPring-8, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan
0 3Coherent X-Ray Optics Laboratory, RIKEN SPring-8 Center, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan
0 4Faculty of Integrated Arts and Sciences, The University of Tokushima, Tokushima 770-8502, Japan
2 5Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
6Department of Physics, Kobe University, Kobe 657-8501, Japan
n
a 7Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
J (Dated: February 6, 2008)

6
Semiconducting skutterudite CeFe4P12 is investigated by synchrotron x-ray photoemission spec-

troscopy (PES) and x-ray absorption spectroscopy (XAS). Ce 3d core-level PES and 3d-4f XAS,
]
l in combination with single impurity Anderson model (SIAM) calculations, confirm features due to
e f0, f1 and f2 configurations. The Ce 4f density of states (DOS) indicates absence of a Kondo
-
r resonanceatFermilevel,butcanstillbeexplainedbySIAMwithasmallgapinnon-f DOS.While
t Ce 4f partial DOSfrom band structurecalculations are also consistent with themain Ce 4f DOS,
s
. theimportanceofSIAMforcoreandvalencespectraindicatesKondosemiconductingmixedvalence
t
a for CeFe4P12,derived from strong hybridization between non-f conduction and Ce 4f DOS.
m
PACSnumbers: 71.20.Eh,71.27.+a,79.60.-i
-
d
n
o Filled skutterudite compounds with a general formula gapsemiconductorswhich arealsoreferredto as Kondo-
c RT4X12 (R = rare earths; T = Fe, Ru, Os; X = P, As, semiconductors[12]. Inparticular,amongCe-filledskut-
[ Sb) exhibit a wide variety ofstronglycorrelatedelectron terudites,theCeT P seriesshowsemiconductingprop-
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1 phenomena, e.g., exotic superconductivity: PrOs4Sb12 erties and have much smaller lattice constants than the
v [1];heavyfermionbehavior: PrFe P [2];metal-insulator valueexpectedfromtrivalentlanthanidecontraction[13].
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4 transition: PrRu P [3]andSmRu P [4];unusualnon- This itself suggests that Ce 4f states have strong hy-
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1
metallicity: CeFe P and UFe P [5], etc. The filled bridization with c electron states, and hence the energy
1 4 12 4 12
skutterudites are also known to be important for ther- gap in CeT P may be a c-f hybridization gap. While
1 4 12
0 moelectric applications [6]. The properties depending a few studies on CeT4P12 [14, 15] support this picture,
6 on rare earth ion R in terms of its ionic size, electronic there is no direct experimental evidence for the strong
0 states, and its position in the unique bcc crystal struc- c-f hybridization in these compounds.
at/ ture(spacegroupIm¯3,withRionssurroundedbytwelve In this work, we use core-level photoemission spec-
X andeightT ions), suggesta tunable hybridizationbe-
m troscopy (CL-PES), 3d-4f resonant-PES (R-PES) and
tween the rare-earth f-electrons and non-f conduction
x-ray absorption spectroscopy (XAS) to investigate the
-
d (c) band states as primarily responsible for this variety electronicstructureofCeFe P . PESandXAS,incom-
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n of phenomena [7, 8].
bination with single-impurity Anderson model (SIAM)
o
calculations, have played a major role in studying the
c Amongthe RFe P serieswithR belongingtothe 4f
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: electronicstructureofstronglycorrelatedmetallicf elec-
v series (R = La, Ce, Pr, Nd), only the Ce-compound is
tron systems exhibiting the Kondo effect, mixed valence
i semiconducting;the LaFe P isasuperconductor(T =
X 4 12 c and heavy fermion behavior [16, 17]. These techniques
4.1 K) while the PrFe P and NdFe P show metallic
4 12 4 12
r provide a quantification of electronic structure parame-
a behavior [5, 9, 10]. Even for single-crystals of CeFe4P12,
ters as well as the f-electroncount, n , whichis a direct
the fit to an activated behavior is valid only over a lim- f
ited temperature range and gives a gap value of ∼0.13 measure of hybridizationinduced mixed valency. Recent
work has also shown that soft x-ray (SX) 3d-4f R-PES
eV, consistent with a 0.15 eV gap-like structure in op-
[18] and hard x-ray (HX)-PES [19, 20, 21] are impor-
tical spectroscopy [11]. The temperature independent
tant for studying bulk-sensitive electronic structure of
magnetic susceptibility is also anomalous, with a value
solids, while 4d-4f R-PES probes surface sensitive elec-
approximately half of that of LaFe P . This fact indi-
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tronic structure due to lower escape depths.
cates a reduced magnetic moment for Ce ions, since the
metallic PrFe P and NdFe P exhibit typical triva- High-resolution low energy studies of Kondo semicon-
4 12 4 12
lent free-ion magnetic moments. The above described ductors have identified a clear pseudogap behavior at
behaviorofCeFe P isthus,similartothehybridization Fermilevel(E )inYbB [22],aswellasinCeRhAsand
4 12 F 12
2
&’( ;(cid:25)(cid:31)<= !> ?"@#(cid:16)$A% GODCFN y(cid:147){ bk[lcfdRm rstsuvwx
)*+,-. LM (cid:138)(cid:139)(cid:140)(cid:141)(cid:142)(cid:143)(cid:144)(cid:145)(cid:146)
K
J
(cid:13) I
(cid:5)(cid:2)(cid:1)(cid:4)(cid:12) /011-. GDCFH bnopq
E
(cid:10)(cid:7)(cid:8)(cid:9)(cid:11) 0,11-. BDC
(cid:6)
(cid:2) P(cid:134)R PQR PRR SPR SSR
(cid:5)(cid:1)(cid:4) (cid:135)(cid:136)Y(cid:137)(cid:136)Y]ZY[\]^_[‘a
(cid:2)(cid:1)(cid:3) 0/11-.
(cid:0) GODCF yz{ bk[lcfdRefmg hij rstsuvwx
2 3 2 4 2 52 3 2 4 2 5 N (cid:130) (cid:132) (cid:130)
67895 67:95 LIJKHM Z|}Xq (cid:132) (cid:132) (cid:133) (cid:132) (cid:133)
D
(cid:14)(cid:15)(cid:16) (cid:14)(cid:17)(cid:16) (cid:14)(cid:16)(cid:16) (cid:18)(cid:14)(cid:16) (cid:18)(cid:18)(cid:16) GF
C
(cid:19)(cid:20)(cid:21)(cid:22)(cid:20)(cid:21)(cid:23)(cid:24)(cid:21)(cid:25)(cid:26)(cid:23)(cid:27)(cid:28)(cid:25)(cid:29)(cid:30) DCE bnopq
B ~(cid:127)(cid:128)(cid:129)(cid:130) ~(cid:127)(cid:131)(cid:129)(cid:130)
STR SSR U SPR PRR PQR
FIG.1: (Coloronline)Ce3dcore-levelphotoemissionspectra VWXWYZY[\]^_[‘a
for CeFe4P12 measured at several excitation energies.
FIG. 2: (Color online) Comparison of (a) Ce 3d core-level
photoemission spectrum and (b) Ce 3d-4f x-ray absorption
CeRhSb [23]. Recent studies of 3d-4f R-PES [24] con-
spectrumwithcorrespondingspectracalculatedbytheSIAM.
cluded a bulk pseudogapin CeRhAs, while valence band Solid triangles mark energies at which off and on-resonant
HX-PES[25] with hν ∼ 6 keVof CeRhAs were analysed photoemission spectra in Fig. 3 were measured.
in terms of non-f DOS, since f-electron photoionization
cross-section is strongly reduced at hν∼ 6 keV. Thus,
methods of electron spectroscopy combined with SIAM
are well-establishedfor typical Kondo metals [16, 17], to and 3d3/2 energy ranges separated by about 18 eV. The
date. However,high-energyCL-PESincombinationwith 3d5/2f0 and 3d3/2f2 final states overlap. The 3-peak
3d-4f XASandR-PES,andtheirconsistencywithSIAM structure is typical of Ce-based Kondo or mixed valent
calculations for a hybridization gap semiconductor have metals and is thus surprising, as CeFe4P12 is a semi-
not been established. conductor. The presence of pronounced f0 and f2 fi-
CeFe P single crystals used in this work were grown nal states suggests that screening effects in CL-PES of
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by the tin-flux method [10]. SX-PES (both CL- and R- CeFe4P12 are qualitatively similar to Kondo metals. In
PES),x-rayabsorptionspectroscopy(XAS)andHX-CL- particular,sincethef2finalstateiscausedbyascreening
PES were performed at SPring-8. For all experiments, a ofthe coreholebyelectronsfromthevalencebandto4f
clean surface was obtained by fracturing in situ at low states, the f2 peak intensity is considered as an indica-
temperatures. The vacuum during measurements was tion of c-f hybridization strength. This evidence for va-
around2×10−8Pa. SX-PESandXASexperimentswere lence fluctuation derived from strong c-f hybridization,
performed at undulator beamline BL17SU. PES spectra is quantified in the following, using SIAM calculations.
were measured using a hemispherical electron analyzer, With increasing excitation energy, i.e., increasing bulk-
SCIENTA SES-2002. The overall energy resolution was sensitivity, the f2 and f0 peak intensities show a slight
set to ∼ 200 meV for the spectra of CL-PES and R- increasefromhν =1200eVto2100eV(asseenin3d5/2-
PES.XASspectrawererecordedusingthetotalelectron f2 peak), but negligible change for hν = 2100 eV and
yieldmethod. HX-PES(hν =5948eV)experimentswere 5948eV.Thisresultindicates thatthe spectraaredomi-
performedatundulatorbeamlineBL29XUusingahemi- natedbybulk-derivedstatesatandabovehν =2100eV.
spherical electron analyzer, SCIENTA SES-2002 [20] at A similar behavior has been reported in a series of Ce-
a total energy resolution of ∼ 300 meV. based Kondo metals [26].
Figure 1 shows Ce 3d CL-PES spectra of CeFe P In order to obtain the electronic structure parameters
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measured at excitation energies from 1200 to 5948 eV. of CeFe P , we use the modified SIAM with full multi-
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The excitation energy dependent spectra are normalized pleteffectstocalculatetheCe3dCL-PESspectrum. We
for the intensity of the 3d f1 peak. The spectra show usethebasissetconsisting4f0,4f1v,and4f2v2 configu-
5/2
common features, with a 3-peak structure labelled as rations to describe the groundstate, wherev is a hole in
f0, f1 and f2 states, for the spin-orbit split Ce 3d the c band below E . The hybridization strength V(ε)
5/2 F
3
(cid:223)
(cid:181)¶•¶ „” (cid:217)(cid:218)¥¥(cid:219)
‚ »
(cid:223)(cid:224)
…‰(cid:190)¿(cid:192)`´
ˆ˜¯˘˘˙(cid:192)¨ Æ(cid:226)
¡
(cid:152)
(cid:153)(cid:150)(cid:149) ª (cid:228) ª (cid:229) ª (cid:230)
(cid:160) —(cid:192)(cid:209)(cid:210) ˚(cid:211)(cid:212)(cid:213)˝
(cid:158)(cid:159)
(cid:157)
(cid:156)
(cid:155)
(cid:154) (cid:220)(cid:221)(cid:213)(cid:222)
(cid:153)(cid:150)(cid:152) FIG. 4: Schematic for the ground state configurations in
(cid:149) the SIAM with an energy gap at Fermi level. Dashed lines :
(cid:151)
(cid:150)(cid:149) normal metal DOS(no energy gap).
(cid:148) …(cid:201)(cid:201)(cid:190)¿(cid:192)`´˚¸(cid:204)˙˝
ˆ˜¯˘˛ˇ(cid:192)¨
(cid:214)(cid:192)(cid:215)(cid:216) ˚(cid:211)(cid:212)(cid:213)˝ Figure 3 shows the off- and on-R valence band PES
spectra of CeFe P , measured at hν = 876 eV and
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882 eV, respectively. The photon energies used are
¢ £ ⁄ ¥ ƒ § ¤ƒ
'“«‹“«›fi«fl(cid:176)›–†fl‡· marked in the XAS spectrum shown in Fig. 2 (b). The
spectra are normalized to the incident photon flux. The
large increase (about twelvefold) in spectral intensity of
FIG.3: (Coloronline)Ce3d-4f resonantphotoemissionspec- on-R PES spectrum compared to off-R PES spectrum
traforCeFe4P12 incomparisonwiththeLDAbandstructure represents the Ce 4f partial density of states (pDOS).
calculation (Ce4f pDOS)andSIAM.Off-resonantspectrum In typical Ce-based Kondo metals, the Ce 4f pDOS ob-
is compared with LDA Fe3d pDOS.
tained from the on-RPES spectrum is well-describedby
SIAM calculations [16, 17, 18]. In this model, the Ce 4f
pDOSin the occupiedDOS is composedoff0 finalstate
at high binding energy (∼3 eV), and f1 final state cor-
between the 4f and c band depends on the c band en- responding to the so-called Kondo resonance peak just
ergy ε. The c band states are logarithmically discretized at and above E [16, 17, 18]. The intensity of f1 peak
F
[27], witha semi-ellipticalformofV(ε)2 anda smallgap at and near E is enhanced by electron-hole pair excita-
F
(0.2 eV) at E (Fig. 4), because CeFe P is a semicon- tions[27]. Incontrast,theexperimentallyobtainedCe4f
F 4 12
ductor. Details of the model calculations are standard pDOS exhibits a main peak significantly below E , po-
F
and are described in earlier work [16, 27, 28]. Figure 2 sitioned at 0.7 eV binding energy. Thus CeFe P does
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(a) shows a comparison of the Ce 3d CL-PES spectrum not behave like a regular Kondo metal as seen by the
measuredathν = 5948eV withthe calculatedspectrum absence of the Kondo resonance at E , although Ce 3d
F
obtained using the SIAM. The calculated spectra match CL-PES can be described by the SIAM. We believe this
the experimental spectra fairly well and the estimated is in accord with its semiconducting property. Figure 4
parameters are: on-site Coulomb repulsion U = 7 eV, schematically shows f-level and c states for a regular
ff
core-hole potential U = 11.78 eV, charge-transfer en- Kondo metal andits modification due to a semiconduct-
fc
ergy ∆ = −0.9 eV, hybridization strength V = 0.44 eV, inggap. Thepresenceofasmallgapstillallowsscreening
bandwidth W = 2.0 eV and n = 0.86. These values of a core-hole from occupied valence band states giving
f
are similar to those of α-Ce investigated by bulk sensi- characteristicfeaturesobservedinCL-PESandXAS,but
tivespectroscopy[29]. Theresultsclearlyindicatemixed does not give the Kondo resonance peak. Consequently,
valencydue tothe strongc-f hybridizationinCeFe P . theCe4f featuresresultinqualitativelydifferentbehav-
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Usingthesameparametersetwithasmallchangeonlyin ior, unlike a conventional SIAM calculation for a Kondo
V (= 0.4eV),wehavealsocalculatedthe Ce 3d-4f XAS metal. Therefore, we introduce a modified SIAM model,
spectrum and compared with experiments, as shown in which has a narrow energy gap at E (Fig.4). The pa-
F
Fig. 2 (b). For the XAS spectrum, weak satellite struc- rameters used for the calculation of on-R PES spectrum
tures at 888 eV and 907 eV are clearly observed, with a are the same as that of XAS. The calculated spectrum
slightlylowerintensityintheexperimentcomparedtothe shows a reasonable agreement with experimental on-R
calculation. Nonetheless,theseweaksatellites aredue to PES spectrum, except for a weak structure just below
the3d94f1 finalstateoriginatingfromthe4f0configura- E . Note that while the Ce 3d CL-PES is like α-Ce,
F
tion, and indicate the importance of the f0 contribution the Ce 4f states are very different from α-Ce. The weak
inthe groundstate ofCeFe P . AsmallreductioninV structure in on-R PES spectrum also has 4f character
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is known for XAS of Ce-based Kondo metals from early as its spectral intensity is suppressed in the off-R PES
work [16]. spectrum (Fig. 3).
4
We have also compared the on- and off-R PES spec- terudite” (Nos. 15072203and 15072206)of the Ministry
tra with band structure calculations using the local den- of Education, Culture, Sports, Science and Technology,
sity approximation (LDA) [31], as shown in Fig. 3. The Japan.
valence and conduction bands around E in CeFe P
F 4 12
are composed of Ce 4f, Fe 3d and P 3p states. Tak-
ing into account the photoionization cross sections [30],
∗
Electronic address: [email protected]
the off-R PES spectrum is expected to be dominated by [1] E. D.Bauer et al., Phys.Rev.B 65, 100506(R) (2002).
Fe 3d pDOS, while the on-R data is dominated by Ce [2] H. Sugawara et al., Phys.Rev. B 66, 134411 (2002).
4f pDOS. Except for a weak feature around EF in the [3] C. Sekine et al., Phys. Rev.Lett. 79, 3218 (1997).
on-R PES spectrum, the Ce 4f spectral shape is also [4] C. Sekine et al., Science and Technology of High Pres-
well reproduced by the LDA calculation. It is surpris- sure, Universities Press, Hyderabad,India,826 (2000).
ing that the Ce 4f electronic states are similarly repro- [5] G. P.Meisner et al., J. Apple.Phys.57, 3073 (1985).
[6] B. C. Sales, D. Mandrus and R. K. Williams, Science
duced by both SIAM and LDA calculations, since the
272, 1325 (1996).
calculations are generally incompatible with each other
[7] B. C. Sales, in Handbook of Physics and Chemistry of
[32]. The off-R PES spectrum is nicely reproduced by
theRareEarths,Vol.33Ch.211, eds.K.A.Gschneidner,
the calculated Fe 3d pDOS. The main peaks of the Fe J. -C. Bunzli and V. K.Pecharsky (2003).
3d and Ce 4f appear at ∼ 1 eV and ∼ 0.7 eV, respec- [8] Y. Aokiet al., J. Phys.Soc. Jpn.74, 209 (2005).
tively,andthisdifference inthe peakpositions isquanti- [9] M. S.Torikachvili et al., Phys.Rev.B 36, 8660 (1987).
tativelyagreewiththeFe3dandCe4f calculatedpDOS. [10] H. Sato et al., Phys. Rev.B 62, 15125 (2000).
[11] S. V. Dordevic et al., Phys. Rev.B 60, 11321 (1999).
This result suggests that the majority of states near E
F [12] G.AeppliandZ.Fisk,CommentsCondens.MatterPhys.
in CeFe4P12 has Ce 4f character. According to c-f hy- 16, 155 (1992).
bridizationmodel[12]forKondosemiconductors,thehy- [13] F.Grandjeanetal.,J.Phys.Chem.Solids45,877(1984).
bridization between the narrow f band positioned just [14] I.Shirotanietal.,J.SolidStateChem.142,146(1999).
below E anda broadc band producesanenergygapat [15] C. H.Lee et al., Phys. Rev.B 60, 13253 (1999).
F
E . The CL-PES and XAS results give convincing evi- [16] O. Gunnarsson and K. Sch¨onhammer, Phys. Rev. B 31,
F
dence for stronghybridization in CeFe P , with a n = 4815 (1985); Phys.Rev. B 28, 4315 (1985).
4 12 f [17] J. W. Allen et al., Adv.Phys. 35, 275 (1986).
0.86 typical of mixed valent α-Ce type systems. A clus-
[18] A. Sekiyamaet al., Nature403, 396 (2000).
termodelanalysisofPESspectraforPrFe4P12 [33],con- [19] K. Kobayashi et al., Appl.Phys. Lett.83, 1005 (2003).
cluded a heavy fermion metallic behavior due to strong [20] Y. Takata et al., Appl.Phys. Lett. 84, 4310 (2004).
hybridization with an nf count of 2.07, corresponding [21] M. Taguchi et al., Phys. Rev.Lett. 95, 177002 (2005).
to divalent admixture [34]. Therefore, CeFe P is ever [22] T. Susakiet al., Phys. Rev.Lett. 82, 992 (1999).
4 12
more mixed valent and has stronger hybridization than [23] H. Kumigashira et al., Phys. Rev. Lett. 87, 067206
PrFe P . The experimental data lends strong credence (2001).
4 12 [24] A. Sekiyamaet al., Physica B 359-361, 115 (2005).
to the gap in CeFe P being a c-f hybridization gap.
4 12 [25] K. Shimada et al., Nucl. Inst. Methods Phys. Res. 547,
Thus,whileSIAMandLDAcalculationsdescribetheCe
169 (2005).
4f pDOS equally well, the features derived from f0, f1 [26] L. Braicovich et al., Phys. Rev.B 56, 15047 (1997).
and f2 configurations in CL-PES and XAS indicate a [27] M.NakazawaandA.Kotani,J.Phys.Soc.Jpn.71,2804
Kondo semiconducting ground state for CeFe P . (2002).
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In summary,we have performedsynchrotronPESand [28] In the calculations, the c-f hybridization is reduced by
XAS on the filled skutterudite CeFe P . The Ce 3d a factor RC (=0.7) in the presence of a core hole and
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CL-PES and XAS, in combination with SIAM calcula- enhanced by a factor 1/RV (RV = 0.7) in the presence
of an extra 4f electron. The framework is discussed in
tions, indicate mixed valency in CeFe P due to strong
4 12 detail in O. Gunnarsson and O. Jepsen, Phys. Rev. B
c-f hybridization. Ce 3d-4f R-PES reveals the absence 38, R3568 (1988).
of a Kondo resonance, consistent with a semiconducting [29] C. Dallera et al., Phys.Rev. B 70, 085112 (2004).
ground state. While band structure and SIAM calcula- [30] J. J.YehandI.Lindau,At.DataNucl.DataTables32,
tions show qualitative agreement with the main peak of 1 (1985).
Ce4f pDOS,featuresderivedfromf0,f1 andf2 config- [31] H. Harima, unpublished.
[32] R.-J. Jung et al., Phys. Rev.Lett. 91, 157601 (2003).
urations in CL-PES and XAS clearly indicate a Kondo
[33] A. Yamasaki et al., Phys. Rev. B 70, 113103 (2004);
semiconducting ground state of CeFe4P12. A. Yamasaki et al., J. Phys.Soc. Jpn. 74, 2045 (2005).
The authors thank Drs. T. Takeuchi and R. Eguchi [34] Y. Kucherenkoet al., Phys.Rev.B 66, 165438 (2002).
for technical support. This work was supported by a
Grant-in-AidforScientificResearchPriorityArea”Skut-