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Nonoka U. Sakamoto, Hidenori Fujiwara, Takuya D. Nakamura, Kenshin Okazaki, Goro Nozue, Takayuki Kiss, Yasumasa Takagi, Souta Tanaka, [Yutaka Iwasaki](https://orcid.org/0000-0002-7317-4939), Yasuhiro Niwa, Asuka Ishikawa, Takafumi D. Yamamoto, Ryuji Tamura, Akira Yasui, Kiyofumi Nitta, Satoru Hamamoto, Masaki Oura, Akira Sekiyama

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[Orbital-Dependent Pseudogap Structure of an Al-Pd-Ru Quasicrystal Probed by X-ray Absorption and Core-Level Photoemission Spectroscopy](https://mdr.nims.go.jp/datasets/719e619f-f74b-4d51-b4bc-f2b8cee267f4)

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Orbital-Dependent Pseudogap Structure of an Al-Pd-Ru Quasicrystal Probed by X-ray Absorption and Core-Level Photoemission SpectroscopyOrbital-Dependent Pseudogap Structure of an Al-Pd-Ru Quasicrystal Probed byX-ray Absorption and Core-Level Photoemission SpectroscopyNonoka U. Sakamoto1,2,+1,+2, Hidenori Fujiwara1,2,3, Takuya D. Nakamura1,2,+2, Kenshin Okazaki1,2,+2,Goro Nozue1,2,+3, Takayuki Kiss1, Yasumasa Takagi4, Souta Tanaka5,+4, Yutaka Iwasaki6,Yasuhiro Niwa5,+4, Asuka Ishikawa5,+5, Takafumi D. Yamamoto5, Ryuji Tamura5, Akira Yasui4,Kiyofumi Nitta4, Satoru Hamamoto2, Masaki Oura2 and Akira Sekiyama1,2,31Division of Materials Physics, Graduate School of Engineering Science, The University of Osaka, Toyonaka 560-8531, Japan2RIKEN SPring-8 Center, Sayo 679-5148, Japan3Spintronics Research Network Division, Institute for Open and Transdisciplinary Research Initiatives, The University of Osaka,Suita 565-0871, Japan4Japan Synchrotron Radiation Research Institute, Sayo 679-5198, Japan5Department of Materials Science and Technology, Tokyo University of Science, Tokyo 125-8585, Japan6National Institute for Materials Science, Tsukuba 305-0047, JapanThe unoccupied electronic states of Al-Pd-Ru quasicrystal (QC) have been investigated by X-ray absorption spectroscopy (XAS). Inaddition, the core-level peak binding energies have been verified by hard X-ray photoemission spectroscopy. From the comparison of the XASspectra of the Al-Pd-Ru QC with those of single-element metals, the shift of the Al K edge can be explained by a shift in the Al 1s core level. Incontrast, the shifts of the Pd and Ru L3 edges cannot be explained solely by the shifts of the core levels. These differences are due to differencesin the orbital-dependent partial density of states near the Fermi level. [doi:10.2320/matertrans.MT-MD2025012](Received November 4, 2025; Accepted February 21, 2026; Published April 25, 2026)Keywords: quasicrystal, pseudogap, X-ray absorption spectroscopy, hard X-ray photoemission spectroscopy1. IntroductionAl-based icosahedral quasicrystals (QCs) and theirapproximants have attracted attention for their thermoelectricproperties due to suppression of the density of states (DOS)around the Fermi level (EF), which is so called pseudogapstructure [1, 2]. Therefore, many efforts have been madeto enhance their thermoelectric properties [3–5]. Sincesemiconducting QCs with energy gaps are expected to showhigh thermoelectric performance, various systems have beensurveyed for the discovery of them [6, 7]. Improvingthermoelectric performance of the Al-based QCs requiresenhancing Seebeck coefficient and electrical conductivity,both of which depend on the electronic structure in thevicinity of EF. Therefore, direct observation of the electronicstructure of the Al-based QCs is important for furtherinvestigations.Understanding the electronic structure on the unoccupiedside is just as important as that on the occupied side in Al-based quasicrystals. This insight is crucial for predictingchanges in physical properties with increasing e/a (electronsper atom) ratio, for example. X-ray absorption spectroscopy(XAS) is powerful to investigate the orbital-selectiveunoccupied electronic states. However, examples of XASstudies on Al-based quasicrystals remain limited at present.In addition, discussions of the absorption-edge shifts mustaccount for shifts in the core level, yet such discussions havebeen largely absent to date. While Al-Pd-Re QCs, Al-Pd-MnQCs and Al-Cu-Fe QCs have been the main targets for XASstudy [8–10], observing the 2p levels of 5d TMs (TransitionMetals) or the 1s levels of 3d TMs using photoemissionspectroscopy is not easy due to their high binding energies.Study on Al-Pd-4d TM QC has been suitable systems for thisdiscussion since the binding energy of the 2p3/2 orbital in 4dTM is approximately 2–3.3 keV.Recently Al-Pd-Ru QCs with the largest thermoelectricpower factor S2· of 780 µW/(m·K2) among QCs has beendiscovered [11]. The Al-Pd-Ru QC exhibits nonmetallicbehavior in the temperature dependence of electrical con-ductivity [12], where the Al71.5Pd19Ru9.5 QC is ³360/(³·cm)at ³300K and ³910/(³·cm) at ³870K. This is due to thedeep pseudogap structure, which is directly observed byhard x-ray photoemission spectroscopy (HAXPES) in ourprevious study [13]. On the other hand, the unoccupied statesabove EF remain still unclear, which is also important forimproving the thermoelectric properties in future. Al K-edgeXAS (Pd and Ru L3-edge XAS) provides the informationabout unoccupied Al 3p (Pd and Ru 4d) states owing to thedipole selection rule in the X-ray absorption process with the1s ¼ 3p (2p ¼ 4d) transition.In this paper, we report on the unoccupied Al 3p, Pd andRu 4d states of the Al-Pd-Ru QC investigated by the Al K-edge, Pd and Ru L3-edge XAS. For Pd and Ru L3-edge XAS,the spectra have been obtained in the total-electron-yield(TEY), partial-fluorescence-yield (PFY) and Transmissionmode simultaneously on powder samples to evaluate thedependence on yield mode and the influence of the self-absorption effect. We have also performed the core-levelHAXPES. The combination of the XAS and core-level+1Corresponding author, E-mail: nsakamoto@decima.mp.es.osaka-u.ac.jp+2Graduate Student, The University of Osaka+3Present address: Physikalisches Institut and Würzburg-Dresden Cluster ofExcellence ct.qmat, Julius-Maximilians-Universität, Würzburg, Germany+4Graduate Student, Tokyo University of Science+5Present address: Institute of Engineering Innovation, School of Engineer-ing, The University of TokyoMaterials Transactions, Vol. 67, No. 5 (2026) pp. 626 to 630Special Issue on Frontiers in Hypermaterials Research©2026 The Japan Institute of Metals and Materialshttps://doi.org/10.2320/matertrans.MT-MD2025012HAXPES allow us to reveal the orbital-dependent pseudogapstructure, for which the gap would be opened for the Pd andRu d-orbital partial density of states (PDOS) whereas thepseudogap is narrower for the Al sites.2. Experimental ProceduresPolycrystalline sample of Al71.5Pd19Ru9.5 QC was preparedby the arc-melting method. The process of the synthesishas been described elsewhere [13]. As reference materials,the spectra of polycrystalline Al, Pd and Ru metals were alsomeasured under the same conditions as those for the Al-Pd-Ru QC. All X-ray spectroscopic experiments describedbelow were conducted at room temperature.The Al K-edge XAS and photoemission spectroscopy(PES) for the Al-Pd-Ru QC and Al metal were performedat BL17SU in SPring-8 [14–16]. The XAS spectra wereobtained in the TEY mode. The clean surface of the Al-Pd-Ru QC was obtained by fracturing in situ. The surface ofthe Al plate was scraped in situ with a diamond file. Surfacecleanliness was checked with the weakness of the shoulderstructure caused by the oxidation in PES spectra.The Pd and Ru L3-edge XAS measurements for the Al-Pd-Ru QC, Pd and Ru metals were performed at BL27SU inSPring-8 [17]. The experimental geometry is shown in Fig. 1.For the Al-Pd-Ru QC, bulk and powder samples were used.The bulk sample of the Al-Pd-Ru QC and the plate of Pdmetal were polished in air. The Pd foil, the Ru plate and thepowder sample of the Al-Pd-Ru QC were measured withoutsurface treatment. The XAS spectra of the samples except forthe powder sample were measured in PFY mode. The powdersample of the Al-Pd-Ru QC was uniformly covered onto thecarbon tape and measured in PFY, TEY and transmissionmodes simultaneously. These three methods complementeach other in probing depth, ensuring a reliable discussion[18]. The advantage of TEY and PFY mode is that themeasurement can be performed on thick samples. Thedisadvantage of TEY is that it is relatively sensitive tosurface conditions. PFY is relatively bulk-sensitive but can beaffected by self-absorption effect or diffraction. In the Pd andRu L3-edge PFY-XAS, luminescence including Pd Lα1 lineand Ru Lα1 line, respectively, were detected as signals usinga silicon drift detector (SDD) with four channels.The HAXPES measurements for the Al-Pd-Ru QC, Al, Pdand Ru metals were performed at BL09XU [19] in SPring-8with SCIENTA OMICRON R4000 photoelectron spectrom-eter. The photon energy was set to 7.2 keV, and the overallenergy resolution was set to 180meV. The Fermi energy wasdetermined by the Fermi edge of Au. The clean surface ofthe Al-Pd-Ru QC was obtained by fracturing in situ at themeasuring temperature. The surface of the Al and Pd plateswere scraped in situ with a diamond file. The Ru metal wasevaporated onto Si(100) and then transferred to the measure-ment chamber after exposure to air. The thickness of theevaporated Ru layer is estimated to be about 65 nm by XRR(X-Ray Reflectivity) measurements. Sample cleanliness waschecked with the weakness of the shoulder structure causedby the oxidation.3. Results and DiscussionsFigure 2 shows the Pd and Ru L3-edge XAS spectra forthe powder sample of the Al-Pd-Ru QC. The PFY- and TEY-XAS spectra were normalized by the intensity of the incidentX-rays (I0). The background signals have been subtractedfrom the TEY-XAS spectra. The spectra in the transmissionmode are defined as ¹ln(I1/I0), where I1 is the intensity ofthe transmitted X-rays. We have determined the absorptionedge of each spectrum by the first inflection point (FIP). TheFIP has been defined as the point where the second derivativeof the spectrum becomes zero for the first time. The FIP ofeach spectrum is shown in Table 1. The difference of FIP isat most about «0.1 eV, indicating that differences in surfacestate or measurement mode have little influence fordetermining the absorption edges. Also note that the possibleeffect of the self absorption in the PFY mode can be includedin the above difference of FIP as <«0.1 eV. Furthermore,these differences are much smaller compared to thedifferences between the absorption edges of the Al-Pd-RuQC and the reference single-element metals as discussedbelow.Figure 3 shows the Al K-edge and Pd and Ru L3-edgeXAS spectra of the Al-Pd-Ru QC and reference single-element metals. The spectra were normalized by I0 and thenaligned by intensity in the EXAFS (Extended X-rayAbsorption Fine Structure) region well above the absorptionSide view(a)Sample e-ASDD (4 channel)PFY-XASX-ray (I0)I1TEY-XASTransmissionFig. 1 (a) Experimental geometry for the XAS measurements in SPring-8 BL27SU. (b) Picture of the XAS instruments. (online color)Orbital-Dependent Pseudogap Structure of an Al-Pd-Ru Quasicrystal Probed by X-ray Absorption and Core-Level Photoemission Spectroscopy 627edge. When we compare the spectra of the bulk Al-Pd-RuQC with those of the powder QC, it is found that thedifference of the spectra is negligible between the bulk andpowder. The absorption edges of the Al-Pd-Ru QC shifts tohigher energy than those of single-element metals. Thistendency, where the absorption edges of a QC are observed athigher energy sides than those of simple metals in all XASspectra, has also been reported for the Al-Pd-Re QCs [10]with deep pseudogap structures [20]. The relative absorption-edge shifts are estimated as 0.5 eV and 0.6 eV for the Al Kand Ru L3 edges, respectively. In contrast, the shift isrelatively large as 3.1 eV at the Pd L3 edge. This difference islarger than the difference between Pd metal and Pd(II) oxide[21]. On the other hand, the absorption-edge shift originatesfrom both unoccupied partial density of states and core levelsto be excited. For discussion of the difference in theabsorption-edge shifts, it is necessary to investigate the corelevels of the Al-Pd-Ru QC and single-element metals.Figure 4 shows the Al 1s, Pd and Ru 2p3/2 core-levelHAXPES spectra of the Al-Pd-Ru QC and reference single-element metals. The shoulder structure observed around³2 eV higher binding energy side from the main peak inFig. 4(a) was caused by the oxidation. Even as surfaceoxidation progresses, the main peak binding energy has beenhardly shifted. The Al 1s and Pd 2p3/2 core-level peaks of theAl-Pd-Ru QC are shifted toward the higher binding energyside by about 0.2 eV and 2.0 eV, respectively, compared tothose of the simple metals. On the other hand, the Ru 2p3/2core-level peak of the Al-Pd-Ru QC is located on the lowerbinding energy side by about 0.4 eV compared to that of theRu metal. The different tendency of the peak shifts wouldreflect the degree of the charge transfer among the sites aspointed out elsewhere [13]. Possible intrinsic charge-transfersatellite structure due to electron correlations is not seen inall core-level HAXPES spectra, which indicates that thecore-level peak binding energy directly reflects the core levelenergy.In order to discuss the unoccupied electronic states near EFbased on the XAS spectra, we need to take both shifts of theabsorption edge in the XAS spectra and the core-level peakin the HAXPES spectra, which has been lacking in previousstudies, into account. When ¦ is defined as the differencebetween the absorption edge and the peak binding energy EBto be excited, it is evaluated as about ¹0.5, ¹2.3 and ¹1.7 eVfor the Al, Pd and Ru sites of the single-element metals fromTable 2. These negative values are due to the attractiveCoulomb interactions between the outer valence electronsTable 1 Values of the first inflection point (FIP) determined as theabsorption edge for each XAS spectrum of the powder Al-Pd-Ru QCin Fig. 2.Fig. 2 (a) Pd and (b) Ru L3-edge XAS spectra of the powder Al-Pd-Ru QCin the TEY, Transmission (Trans.) and PFY modes. Each spectrum hasbeen normalized by the intensity of the incident X-ray. The backgroundsignal has been subtracted from the TEY-XAS spectra. The dashed linesindicate the absorption edge determined by the first inflection point (FIP)for each spectrum. (online color)Fig. 3 (a) Al K-edge TEY-XAS, (b) Pd and (c) Ru L3-edge PFY-XASspectra of the Al-Pd-Ru QC and reference single-element metals. Thedashed lines indicate the absorption edge determined by FIP of eachspectrum. The gray arrows indicate the direction of the absorption-edgeshift in the XAS spectra of the Al-Pd-Ru QC compared with those of thesingle-element metals. (online color)N.U. Sakamoto et al.628(including excited electrons) and the core hole created inthe X-ray absorption process. If these attractive Coulombinteractions were negligible, ¦ = 0 eV would be expectedfor conventional metals. Note that the attractive Coulombinteractions depend on element and orbital but are essentiallyindependent on material since these are intraatomicquantities. On the other hand, ¦ is estimated from Table 2as about ¹0.2, ¹1.2 and ¹0.7 eV for the Al, Pd and Ru sitesof the Al-Pd-Ru QC. Thus, the differences in ¦ between theAl-Pd-Ru QC and single-element metals are evaluated as³0.3 eV for the Al sites and ³1 eV for the Pd and Ru sites.When we assume that the element-dependent attractiveCoulomb interactions are essentially equivalent between theQC and single-element metals, the differences in ¦ reflectthe pseudogap electronic structure in the unoccupied side forthe Al-Pd-Ru QC.Figure 5 summarizes the element-dependent energy-leveldiagrams of the Al-Pd-Ru QC compared to those of thesingle-element metals based on our XAS and core-levelHAXPES results. In the Pd and Ru sites, the 2p ¼ 4dtransitions to the absorption edges correspond to thetransitions to the 4d unoccupied states at ³1 eV above EFfor the Al-Pd-Ru QC while those are due to the transitionsto the unoccupied states at EF for the single-element metals.This indicates the opening of the pseudogap in the 4d PDOSTable 2 Values of the absorption edge of the XAS spectra in Fig. 3 andmain peak binding energies (EB) in the HAXPES spectra in Fig. 4. Thesevalues have been obtained from the spectra for the bulk samples. Theerror of the core-level peak fitting is ³0.03 eV.22Fig. 4 (a) Al 1s, (b) Pd 2p3/2 and (c) Ru 2p3/2 core-level HAXPES spectraof the Al-Pd-Ru QC and reference single-element metals. The dashedlines indicate main peak binding energies (EB). The gray arrows indicatethe directions of shift for the main peaks in the HAXPES spectra of theAl-Pd-Ru QC relative to that of the single-element metals. (online color)EFAl 1s(a)    Al K-edge XAS (b)    Pd L3-edge XAS (c)    Ru L3-edge XASPd 2p3/2~0.3 eVAl-Pd-Ru QC Al metalAl 3p Al 3p~0.2 eVEFAl-Pd-Ru QC Pd metalPd 4dPd 4d~2 eV~1 eVRu 2p3/2EFAl-Pd-Ru QC Ru metalRu 4d Ru 4d~0.4 eV~1 eVFig. 5 Schematic energy-level diagrams of (a) Al 1s¼ Al 3p, (b) Pd 2p3/2 ¼ Pd 4d and (c) Ru 2p3/2 ¼ Ru 4d transitions in the Al-Pd-Ru QC and reference single-element metals. (online color)Orbital-Dependent Pseudogap Structure of an Al-Pd-Ru Quasicrystal Probed by X-ray Absorption and Core-Level Photoemission Spectroscopy 629near EF for the Al-Pd-Ru QC. In the Al sites, the 1s ¼ 3ptransitions to the absorption edge are due to the 3punoccupied state at ³0.3 eV above EF for the Al-Pd-RuQC, which suggests the narrower pseudogap states. Thesemean that the Al 3p states contribute predominantly to theDOS near EF while the Pd and Ru 4d contributions are muchless near EF, which is consistent with the finding obtainedfrom our previous study for the occupied electronic states ofthe Al-Pd-Ru QC [13]. Although the precise discussion onthe pseudogap electronic structure in a meV scale is difficultfrom the XAS spectra of which the lifetime broadening isof the order of 1 eV, we can clarify the orbital-dependentpseudogap electronic structure of the Al-Pd-Ru QC from theXAS and core-level HAXPES spectra compared to those ofthe single-element metals as discussed here.Our results show that analysis of the XAS spectrum ofAl-based QCs requires consideration of both core-level shiftsand unoccupied states since the suppression of the PDOSnear EF affects the absorption-edge shift in the XAS spectraas we have discussed here. In addition, the bottom of thepseudogap structure of the Al-Pd-Ru QC is largely ascribedby the Al sites. Identifying the origin of this residual Al stateand controlling it would be important for improvingthermoelectric performance of the Al-Pd-Ru QCs.4. ConclusionWe have performed the XAS and HAXPES of the Al-Pd-Ru QC and the Al, Pd and Ru metals. In the XAS, theabsorption edges in the spectra of the Al-Pd-Ru QC havebeen all observed at the higher energy side compared tothose of the simple metals. The shift in the core-level peaks inthe HAXPES have shown the different tendency dependingon element. We have concluded that this difference is due tothe difference in the contribution from each site to DOS nearthe EF in the Al-Pd-Ru QC.AcknowledgementsWe acknowledge Y. Torii, M. Sakaguchi, S. Kaneko andM. Togawa for supporting the experiments. The XASexperiments at BL27SU and BL17SU in SPring-8 wereperformed under the approvals of JASRI (ProposalNo. 2024B1957) and RIKEN (Proposal No. 20250096),respectively. The HAXPES experiment at BL09XU inSPring-8 was performed under the approvals of JASRI(Proposal. Nos. 2024B1899 and 2025A1986). This workwas financially supported by a Grant-in-Aid for InnovativeAreas (JP22H04594), a Grant-in-Aid for TransformativeResearch (JP23H04867), a Grant-in-Aid for ScientificResearch (JP22K03527 and JP24K03202), from JSPS andMEXT, Japan, and CREST (JPMJCR22O3) from JST, Japan.This work was also supported by the Thermal & ElectricEnergy Technology Foundation, Japan. G. Nozue wassupported by the Osaka University fellowship program ofSuper Hierarchical Materials Science Program and by theJSPS Research Fellowship for Young Scientists.REFERENCES[1] K. Kirihara and K. Kimura: Covalency, semiconductor-like andthermoelectric properties of Al-based quasicrystals: icosahedral clustersolids, Sci. Technol. Adv. Mater. 1 (2000) 227–236.[2] K. Kirihara, T. Nagata, K. Kimura, K. Kato, M. Takata, E. Nishiboriand M. 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