ebook img

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

0.3 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

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

Electronic structure of semiconducting CeFe P : Strong hybridization and relevance 4 12 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- 4 12 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]. 4 12 4 transition: PrRu P [3]andSmRu P [4];unusualnon- This itself suggests that Ce 4f states have strong hy- 4 12 4 12 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- 4 12 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 4 12 : 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- 4 12 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 4 12 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 4 12 measured at excitation energies from 1200 to 5948 eV. of CeFe P , we use the modified SIAM with full multi- 4 12 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 4 12 882 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 4 12 (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- 4 12 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 4 12 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). 4 12 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 4 12 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-

See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.