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[Shigenori Ueda](https://orcid.org/0000-0001-9425-0614), Ikutaro Hamada

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[Polarization-dependent Bulk-sensitive Valence Band Photoemission Spectroscopy and Density Functional Theory Calculations: Part IV. 4<i>f</i> Rare-earths](https://mdr.nims.go.jp/datasets/0f0fdd9c-a8de-498c-891e-f842d06a723c)

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Polarization-dependent Bulk-sensitive Valence Band Photoemission Spectroscopy and Density Functional Theory Calculations: Part IV. 4f Rare-earthsPolarization-dependent Bulk-sensitive Valence Band Photoemission Spectroscopyand Density Functional Theory Calculations: Part IV. 4f Rare-earthsShigenori Ueda1,2+ and Ikutaro Hamada31Research Center for Electrical and Optical Materials, National Institute for Materials Science (NIMS),Tsukuba, Ibaraki 305-0044, Japan2Synchrotron X-ray Station at SPring-8, NIMS, Sayo, Hyogo 679-5148, Japan3Department of Precision Engineering, Graduate School of Engineering, The University of Osaka, Suita, Osaka 565-0871, Japan(Received February 4, 2025; accepted May 14, 2025; published online June 11, 2025)The valence band electronic structures of the elemental solids of 4 f rare-earths (REs: La, Ce, Pr, Nd, Sm, Eu, Gd, Tb,Dy, Ho, Er, Tm, Yb, and Lu) were studied by bulk-sensitive polarization-dependent hard X-ray photoemissionspectroscopy (HAXPES). Owing to the localized 4 f electrons in REs, the valence band (VB) region showed complicatedmultiplet structures reflecting the 4 f photoemission final states, except for La and Ce. The profiles of the 4 f multipletstructures did not depend on the X-ray polarization. In contrast, the VB spectra, which mainly consisted of the 5d and 6sstates, near the Fermi-level (EF) weakly depended on the X-ray polarization. The polarization-dependent VB spectra nearEF for La and Lu were reproduced by the 5d and 6s partial densities of states, which were obtained from the densityfunctional theory calculations for La and Lu, multiplied by photoionization cross-sections. The complicated multipletstructures were also observed in the 3d and 4d core-level HAXPES spectra via the exchange interaction between thecore–hole and 4 f electrons.1. IntroductionIn the elemental solids of 4f rare-earths (REs) or so-calledlanthanides (La–Lu), the number of electrons in the 4f orbital(n) changes with the atomic number (Z), where n is given byZ � 57 (Z ¼ 57 for La), except for Eu and Yb (n ¼ Z �57 þ 1). Many 4f RE elemental solids have a magneticground state due to the localized 4f orbital as well aselemental solids of 3d transition metal (TM), but Curie orNeel temperature (TC or TN) of 4f REs is lower than roomtemperature (RT) in contrast to that TC or TN of 3d TMs suchas Cr, Mn, Fe, Co, and Ni is higher than RT. The localized 4felectrons in REs have attracted in fundamental physics bymeans of various high-energy spectroscopies such as photo-electron spectroscopy (PES), inverse PES (called as IPESor BIS: bremsstrahlung isochromat spectroscopy), X-rayabsorption spectroscopy (XAS), and electron energy lossspectroscopy (EELS), since complicated multiplet structureshave been observed in many REs in these methods.1) Valencefluctuation and heavy fermion properties have also attractedin the studies of electronic states of RE alloys andcompounds by using PES.2) RE-TM intermetallic compoundshave been brought into the research field of advancedpermanent magnets.3) In addition, it is known that some ofRE alloys and compounds exhibit catalytic properties4) andsuperconductivity.5,6) Thus, 4f REs are of importance infundamental physics and applications.This paper is a series of X-ray polarization-dependentvalence band (VB) hard X-ray PES (HAXPES) studies ofelemental solids using 5.95 keV X-rays. HAXPES is wellknown as a bulk-sensitive probe of the electronic states ofsolids,7–10) since the kinetic energy of photoelectron reachesto several-keV. Such high-kinetic energy photoelectrons havea large inelastic mean-free-path (IMFP) in solids accordingto the TPP-2M equation.11) Therefore, HAXPES enables usto obtain the bulk-sensitive electronic states of solids withless containing surface-related electronic states in a suitableexperimental geometry.12) In the previous studies, wehave shown the experimental polarization-dependent VBHAXPES spectra for 3d, 4d, and 5d TMs with the simulatiedresults of VB spectra obtained by using the calculatedphotoionization cross-sections and partial densities of states(PDOSs) based on the density functional theory (DFT)calculations.13–15) In this work, we have performed thepolarization-dependent VB HAXPES measurements for 4fREs of La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb,and Lu elemental solids. The changes in the VB spectralshapes of the band originated from the 5d, 6s, and 6p statesshowed a clear X-ray polarization dependence mainly due tothe photoionization cross-section ratio of 5d=6s orbitals,which strongly depended on X-ray polarization and exper-imental geometry.13) In contrast, the spectral shapes ofmultiplet structures due to the 4f n�1 photoemission finalstates did not depend on X-ray polarization, which would beattributed to the use of polycrystalline 4f RE samples. Wehave also performed the 3d, 4d, and 4s core-level HAXPESmeasurements for 4f REs as a reference data set. Note thatconventional X-ray photoemission spectroscopy (XPS) usingAl-Kα (1486.7 eV) or Mg-Kα (1253.6 eV) cannot access toall the 3d core-levels in 4f REs owing to their high bindingenergy (830–1650 eV), while all the 3d core-level spectra for4f REs are observable in HAXPES at the photon energy of5.95 keV with higher bulk-sensitivity compared to conven-tional XPS. The 3d and 4d core-level HAXPES spectra for4f REs have revealed the complicated multiplet structuresdue to the c4f n photoemission final states (c denotes core–hole) because of high-resolution (HR) measurements.2. ExperimentalX-ray polarization-dependent VB HAXPES measurementsfor 4f RE elemental solids were conducted at the undulatorbeamline BL15XU9,16) of SPring-8. The polycrystallineingots of La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm,Yb, and Lu with purity better than 99.9% were in situfractured to obtain clean surfaces in a sample preparationchamber with the base pressure of 2:0 � 10�7 Pa. Then, thesamples were transferred to an analysis chamber, which wasequipped with a HR hemispherical electron analyzer (VGJournal of the Physical Society of Japan 94, 074703 (2025)https://doi.org/10.7566/JPSJ.94.074703Full Papers074703-1 ©2025 The Physical Society of Japanmaintain attribution to the author(s) and the title of the article, journal citation, and DOI.©2025 The Author(s)This article is published by the Physical Society of Japan under the terms of the Creative Commons Attribution 4.0 License. Any further distribution of this work mustJ. Phys. Soc. Jpn.Downloaded from journals.jps.jp by （研）物質・材料研究機構 on 06/26/25https://orcid.org/0000-0001-9425-0614https://orcid.org/0000-0001-5112-2452https://doi.org/10.7566/JPSJ.94.074703http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.7566%2FJPSJ.94.074703&domain=pdf&date_stamp=2025-06-11Scienta, R4000), with the base pressure of 3:0 � 10�8 Pa.The temperature of samples was kept at 15K during themeasurements. The photoelectrons were excited by horizon-tal (H-pol), vertical linear polarized (V-pol) X-rays or left- orright-handed circularly polarized (C-pol) X-rays. A near-normal emission geometry with a grazing incidence (approx-imately 2°) of X-rays with respect to a nominal samplesurface was applied to the HAXPES experiments. Theincident X-rays were firstly monochromatized by a Si 111double-crystal monochromator and then were further mono-chromatized by a Si 333 channel-cut monochromator. The X-ray polarization was switched by using a diamond phaseretarder, while the phase retarder was retracted from the X-ray axis for H-pol X-rays. The estimated degree of linear orcircular polarization (PL or PC) was ∼1.00, ∼0.70, and ∼0.95for H-, V-, and C-pol X-rays, respectively. PL correction to∼1.00 was done for the VB spectra measured with V-pol X-rays in this work as described elsewhere.13–15) The VBspectra for C-pol X-rays were obtained by the average of theVB spectra for left- and right-handed C-pol X-rays in eachelement. The 3d, 4d, and 4s core-level HAXPES measure-ments were performed with H-pol X-rays. Overall energyresolution (�E) of the HAXPES measurements was set to130meV, and the binding energy (EB) was calibrated by theFermi-level (EF) of a reference Au film. For Ce and Eu, wehave done HR HAXPES measurements of VB and Eu 4fstates with �E ¼ 85meV.3. DFT CalculationsDFT calculations were performed to obtain the electronicband structures (total DOS and PDOSs) for La and Lu. Theprojected augmented method17) as implemented in the VASPcode18,19) was used. The generalized gradient approximationof Perdew, Burke, and Ernzerhof 20) was applied to theexchange–correlation functional. The experimental structuresof La21) and Lu22) were used in the DFT calculations: doublehexagonal closed pack (dhcp) structure for La and hcpstructure for Lu. A kinetic energy cut-off of 750 eV was usedto expand the wave functions in terms of a plane-wave basisset. The tetrahedron method was used for the Brillouin-zoneintegration with the 36 � 36 � 12 and 36 � 36 � 24 k-pointgrids for La and Lu, respectively. We omitted to perform theDFT calculations of the other REs due to the strong final stateeffects in the partially filled 4f states in PES.23) The spin–orbitcoupling was not considered in the DFT calculations forsimplicity.4. Results4.1 Polarization-dependent VB HAXPES spectra of 4f REsFigures 1(a)–1(n) shows the polarization-dependent VBspectra of the 4f REs of La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy,Ho, Er, Tm, Yb, and Lu. The VB spectra for H-, V-, and C-pol X-rays were normalized by the incident photon intensityin each element, and subtractions of an integrated-type-background were performed. The VB intensity was highest(lowest) for H-pol (V-pol) X-rays in each element and theintermediate VB intensity was found for C-pol X-rays, aswell as HAXPES for the elemental solids of 3d, 4d, and 5dTMs.13–15) The VB spectra were classified into two parts:5d6sp hybridized band near EF and multiplet structures dueto 4f photoemission final states. For La and Ce, the 4f derivedstructures cannot be found in Figs. 1(a) and 1(b). Theabsence of 4f photoemission in La is natural because of theempty 4f orbital (n ¼ 0). The absence of 4f photoemission inCe will be mentioned latter. For Yb and Lu, the spin–orbitdoublet (4f7=2 and 4f5=2) due to the fulfilled 4f orbital(n ¼ 14) can be seen in Figs. 1(m) and 1(n). The 4f multipletstructures strongly depended on n, and were similar to thosefor 4f REs reported in conventional XPS measurements.23)One sees that the 4f multiplet structures in Eu and Gd aresimilar each other, which is caused by same n in the initialstate of Eu and Gd. The multiplet structure becomescomplicate with increasing n up to 13. The assignment of4f multiplet states was described elsewhere.23,24)Although the profile of multiplet structure in Figs. 1(c)–1(l), does not depend on the X-ray polarization, the profilesof 5d6sp-derived band near EF in Figs. 1(a)–1(n) changewith the X-ray polarization. The changes in the 5d6sp-derived band profile are weak in peak structures (shoulderstructure in the case of La) immediately below EF and arestrong in broad peaks located at EB � 1:5 eV. According tothe previous polarization-dependent HAXPES work for 3dand 4d TMs,13,14) the photoionization cross-sections for satomic orbitals abruptly decrease in V-pol X-rays comparedto H-pol X-rays in our experimental configuration. Therefore,we see that the 5d-derived photoemission intensity isdominant in the observed band profile with a variedcontribution of 6s-derived one by the X-ray polarization inthe HAXPES spectra of 4f REs. For Eu and Yb, changes inthe observed band profile are unclear, since the band isoverlapped with 4f photoemission in both cases. A smallhump at EB � 5 eV shows the X-ray polarization dependencefor Eu and Gd in Figs. 1(f ) and 1(g), and the intensity of thehump reduces in the case of V-pol X-rays, suggesting that thesmall hump mainly originates from the 6s-derived states.Note that the contribution of 6p-derived intensity in 4f REsmight be quite small by considering the experimentalHAXPES results and calculated photoionization cross-sections for 6p atomic orbitals in 5d TMs.15)In Figs. 1(a)–1(n), a metallic Fermi edge was clearlyobserved in each RE regardless of X-ray polarization. Thisresult indicates that the recoil effect25–27) in 4f RE elementalsolids is sufficiently smaller than �E ¼ 130meV. In fact, thecalculated recoil energy of photoelectrons with the kineticenergy (EK) of 5.95 keV for the isolated 4f RE atomsaccording to Refs. 25–27 ranges from 23.5 to 18.7meV aslisted in Table I. A sufficiently small recoil energy wasfurther validated from the HR VB spectrum for Ce with�E ¼ 85meV, which also showed a clear Fermi edge, asshown in Fig. 1(o).4.2 3d core-level HAXPES spectra of 4f REsFigure 2 shows the 3d core-level HAXPES spectra of 4fRE elemental solids. The 3d core-level spectra have shownthe spin–orbit splitting (3d5=2 and 3d3=2) and complicatedmultiplet structures mainly due to the 3d94f n photoemissionfinal states via the exchange interaction between the core–hole and 4f electrons. In contrast, the spin–orbit splitting isdominant for n ¼ 0 (La) and 14 (Yb and Lu) due to emptyand fulfilled 4f orbitals, respectively. The broad structureslocated at the higher EB side of the 3d5=2 and 3d3=2 mainpeaks are due to the energy loss satellites for La, Yb, and Lu.J. Phys. Soc. Jpn. 94, 074703 (2025) Full Papers S. Ueda and I. Hamada074703-2 ©2025 The Physical Society of Japan©2025 The Author(s)J. Phys. Soc. Jpn.Downloaded from journals.jps.jp by （研）物質・材料研究機構 on 06/26/25Note that conventional XPS measured with Al-Kα (1486.7eV) or Mg-Kα (1253.6 eV) cannot access to all the 3d core-levels in 4f REs owing to their high EB (> 800 eV).In fact, Ref. 28, which presents the major and high-intensity core-levels in elemental solids, shows the limited 3dcore-level spectra (La, Ce, Pr, Nd, Sm, and Eu) in 4f REs.The observed La, Ce, Pr, Nd, Sm, and Eu 3d HAXPESspectra are similar to the reported XPS spectra measured withAl-Kα in Ref. 28 and are sharper than them owing to the HRmeasurements in this work. Note that in the case of light REelements, it is known that the experimental spectra areunderstood by the theoretical calculations based on theimpurity Anderson model with taking into account themultiplet states and the charge transfer between 4f andconduction electrons and that in the case of heavy REelements, the ionic model is often applied due to negligiblecharge transfer effect as described in Ref. 29. In this paper,we do not discuss the charge transfer effects for simplicity,since details of them are described in Ref. 30.The Eu 3d HAXPES spectrum shows several sharp peaksin the 3d5=2 and 3d3=2 main structures. A resemblancebetween the Gd and Eu 3d HAXPES spectra is observed,because the spectra mainly reflect the 3d94f 7 photoemissionfinal states in both Gd and Eu cases. A higher photo-excitation (5.95 keV in this work) enables the observation ofthe all 3d core-level photoemission with high intensity andlong probing depth in 4f REs. The probing depth (3 � IMFP)for the 3d core-level HAXPES in 4f REs ranges from 31.8(La) to 17.1 nm (Lu), where IMFP is calculated by the TPP-2M equation.11) By utilizing the large probing depth (i.e.,high bulk-sensitivity), temperature-induced valence transi-tions in YbInCu4 and EuNi2(Si1�xGex)2 have been analyzedFig. 1. Continued on next page.J. Phys. Soc. Jpn. 94, 074703 (2025) Full Papers S. Ueda and I. Hamada074703-3 ©2025 The Physical Society of Japan©2025 The Author(s)J. Phys. Soc. Jpn.Downloaded from journals.jps.jp by （研）物質・材料研究機構 on 06/26/25from the Yb and Eu 3d core-level HAXPES spectra,respectively.31,32)The observation of the Ce 3d core-level spectrum is usefulto determine the crystal phase of Ce metal, because α- and γ-Ce shows the different Ce 3d XPS spectral shapes.33) Theobserved Ce 3d HAXPES spectrum in Fig. 2(b) showssimilarity to the Ce 3d XPS spectrum for α-Ce rather thanγ-Ce according to Ref. 33. For the spectrum of α-Ce,characteristic peaks located at EB of ∼894.7 and ∼913.2 eVwas found in both the HAXPES and XPS spectra, while thesepeaks were absent in the 3d XPS spectrum of γ-Ce. It isreasonable to assume that the used Ce sample in this work isin the low-temperature α-phase, since the sample was kept at15K during the measurements. For Pr metal, the observed 3dFig. 1. (Color online) (a)–(n) X-ray polarization-dependent VB HAXPES spectra of La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lupolycrystalline samples for H-pol (red), V-pol (blue), and C-pol (green) X-rays. In each element, the VB spectra were normalized by the incident X-rayintensity. The insets in (m) and (n) show the enlarged view of the VB spectra near EF. (o) HR Ce VB HAXPES spectrum and (p) Eu 4f spectrum in the case of�E ¼ 85meV. Vertical bars (red) in (p) indicate the multiplet states with different J in the final states.Table I. Recoil energy of photoelectrons with EK of 5.95 keV for La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu atoms.Recoil energy (meV)La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu23.5 23.3 23.2 22.6 21.7 21.5 20.7 20.5 20.1 19.8 19.5 19.3 18.9 18.7J. Phys. Soc. Jpn. 94, 074703 (2025) Full Papers S. Ueda and I. Hamada074703-4 ©2025 The Physical Society of Japan©2025 The Author(s)J. Phys. Soc. Jpn.Downloaded from journals.jps.jp by （研）物質・材料研究機構 on 06/26/25Intensity (arb. units)(a) (b)(c) (d)(e) (f)(g) (h)(i) (j)(k) (l)(m) (n)Fig. 2. (Color online) RE 3d core-level HAXPES spectra measured with H-pol X-rays.J. Phys. Soc. Jpn. 94, 074703 (2025) Full Papers S. Ueda and I. Hamada074703-5 ©2025 The Physical Society of Japan©2025 The Author(s)J. Phys. Soc. Jpn.Downloaded from journals.jps.jp by （研）物質・材料研究機構 on 06/26/25core-level HAXPES spectrum was similar to the spectrameasured with the photon energies of 1253.6, 2450, and5450 eV in Refs. 34 and 35, suggesting that the EKdependence on the spectral shape is very weak in Pr metalas well as La, Ce, and Nd metals, which show theresemblance between the HAXPES and the conventionalXPS spectra in the 3d core-level regions. In contrast, the EKdependence on the spectral shape for Sm metal is large. Theweak peaks located at EB of ∼1073.5 and ∼1100.7 eV in theSm 3d core-level HAXPES spectrum increase in the conven-tional XPS spectra measured with Al-Kα (1486.7 eV) andMg-Kα (1253.6 eV). Furthermore, as seen in Ref. 28, thesepeaks are larger in the spectrum for Mg-Kα than that for Al-Kα. Lower EK for Mg-Kα than Al-Kα corresponds to shorterIMFP for Mg-Kα than Al-Kα according to Ref. 11. Thisresult indicates that these two peaks originate from electronicstates near surface of Sm metal, which has been alreadyreported in the take-off-angle dependent Sm 4d XPS spectraof Sm metal.1)4.3 4d core-level HAXPES spectra of 4f REsFigure 3 shows the 4d core-level HAXPES spectra of 4fRE elemental solids. Owing to higher energy resolution inHAXPES in this work compared to conventional XPS, the 4dcore-level HAXPES spectra shows fine and complicatedmultiplet structures mainly due to 4d94f n photoemissionfinal states. The observation of these fine structures is due toless core–hole lifetime broadening in the shallower 4d core-levels than the 3d core-levels and relatively larger exchangeinteractions between the core–hole and 4f electrons in the 4dcore-level photoemission process. For La, Yb, and Lu, thespin–orbit doublet (4d5=2 and 4d3=2) is clearly seen inFigs. 3(a), 3(m), and 3(n), while it is not clear in the other 4fREs due to their complicated multiplet structures. The broadstructure (shoulder) located at the higher EB side of the 4d5=2and 4d3=2 main peaks is due to the energy loss satellites forLa (Yb and Lu). Since EB of 4d core-level region for 4f REsis sufficiently lower than the energies of Al-Kα (1486.7 eV)and Mg-Kα (1253.6 eV), conventional XPS can access the all4d core-levels for REs and many 4d core-level spectra of theRE elements and oxides have been reported in the early stageof XPS.28,29,36–38) In Ref. 29, the experimental 4d core-levelXPS spectra for Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lumetals have been compared with the theoretical multipletcalculations based on the ionic model. The observed 4d core-level HAXPES spectra shown in Fig. 4 are much sharperthan the reported experimental 4d core-level XPS spectra inRefs. 29 and 37 due to the HR HAXPES measurements.Fig. 3. (Color online) RE 4d core-level HAXPES spectra measured with H-pol X-rays.J. Phys. Soc. Jpn. 94, 074703 (2025) Full Papers S. Ueda and I. Hamada074703-6 ©2025 The Physical Society of Japan©2025 The Author(s)J. Phys. Soc. Jpn.Downloaded from journals.jps.jp by （研）物質・材料研究機構 on 06/26/25Note that for Sm, the small peak located at EB of ∼123 eVoriginates from the electronic state near surface, because ofstrong reduction in the HAXPES spectrum compared to theXPS one37) and absence of the small peak in the theoreticalcalculation,29) as mentioned above.In the 4d XPS spectra for Ce, Sm, and Eu metals with�E ¼ 0:55 eV, fine multiplet structures were observed,37) butour results on Ce, Sm, and Eu metals with �E ¼ 130meVdetected further fine structures. For Eu metal, the impact of�E in the spectral shape is apparent; the structure located atEB of ∼130 eV was observed as a broad peak with �E ¼0:7 eV in Ref. 29, that was observed as several peaks with�E ¼ 0:55 eV in Ref. 37, and that was clearly resolved asseveral sharp peaks in HAXPES with �E ¼ 130meV in thiswork. Due to the 4d94f 7 final states in both Eu and Gdmetals, the 4d core-level HAXPES spectral shapes aresimilar each other as well as the 3d core-level HAXPEScases as shown in Fig. 2. The observed 4d core-levelHAXPES spectra with �E ¼ 130meV allow the directcomparison with the theoretical multiplet structures indicatedby the vertical bars for Sm, Gd, Tb, Dy, Ho, Er, and Tmin Ref. 29. These results indicate the importance of HRmeasurements of core-level as well as valence band inHAXPES.4.4 4s core-level HAXPES spectra of 4f REsFigure 4 shows the 4s core-level HAXPES spectra of 4fRE elemental solids. It is known that the multiplet structuresdue to photoemission final states are simplified in the s core-level PES spectra and that the spin exchange splitting appearsin the s core-level spectra due to the interaction between the score–hole and valence electrons.39) Therefore, the compli-cated multiplet structures like 3d and 4d core-level HAXPESspectra are absent in the 4s core-level HAXPES spectra for 4fREs, and most 4s core-level spectra shown in Fig. 4 show thetwo peaks due to the configuration of core–hole spin parallelor antiparallel to the spin of 4f electrons.40,41) As mentionedin Sect. 1, many RE elemental solids have a magnetic groundstate so that the local spin magnetic moment is non-zero,except for La (empty 4f orbital) and Yb and Lu (fulfilled 4forbital). Therefore, the peak splitting in the 4s spectra due tothe spin exchange interaction between the 4s core–hole and4f electrons can be clearly seen in Sm, Eu, Gd, Tb, Dy, andHo metals, while the peak splitting is unclear or small in Ce,Pr, Nd, Er, and Tm metals due to their small spin magneticmoments. One sees that the 4s core-level HAXPES spectra of4f RE metals in Fig. 4 show clear shoulder structures at thehigher EB side of two peaks (Nd, Sm, Eu, Gd, Tb, Dy, Ho,and Er) or main peak (La, Ce, Pr, Tm, Yb, and Lu). Note that(a) (b) (c)(d) (e) (f)(g) (h) (i)(j) (k) (l)(n)Intensity (arb. units)(m)Fig. 4. (Color online) RE 4s core-level HAXPES spectra measured with H-pol X-rays.J. Phys. Soc. Jpn. 94, 074703 (2025) Full Papers S. Ueda and I. Hamada074703-7 ©2025 The Physical Society of Japan©2025 The Author(s)J. Phys. Soc. Jpn.Downloaded from journals.jps.jp by （研）物質・材料研究機構 on 06/26/25a small peak at EB of ∼531 eV is oxygen-related surfacecontaminations for Lu. The shoulder structures in Fig. 4 seemto be absent in the 4s XPS for insulating RE trifluoride.41)Thus, the shoulder structures in the 4s HAXPES spectra for4f RE metals originate from the energy loss satellites due toplasmon excitations. The relatively large intensity of theenergy loss satellite in the 4s HAXPES suggests that thepresence of the energy loss satellite at the higher EB side ofthe main structure in the 3d and 4d HAXPES spectra in thecase of 4f RE metals. A series of 3d, 4d, and 4s core-levelHAXPES measurements, thus, provides information on theenergy loss satellite in the core-level spectra for 4f RE metalsand suggests the necessity of considering the energy losssatellite in the analysis of core-level spectra based on theionic model in metallic RE alloys and compounds.5. DiscussionTo understand the electronic structures of 4f RE elementalsolids from the VB HAXPES measurements, we haveperformed the DFT calculations to obtain the total DOSand PDOSs as shown in Fig. 5. Since the DFT calculationsgenerally do not give the photoemission final states, wefocused on the RE elements with n ¼ 0 (La) and 14 (Lu) toexclude the 4f contribution to the DOS. As seen in Fig. 5, the5d PDOS mainly contributes to the DOS in each case. The 4fcontribution to the occupied states in La is negligibly small asseen in Fig. 5(a), while the 4f states are localized as a shallowcore-level at EB of ∼4.9 eV in Lu as seen in Fig. 5(b).Figure 6 shows the simulated VB HAXPES spectra forvarious X-ray polarization for La and Lu. In the simulations,the sum of the 5d and 6s PDOSs multiplied by thephotoionization cross-sections per electron with taking theorbital-dependent angular distributions with respect to the X-ray polarizations into account was used, while the 6p PDOSwas ignored probably due to a quite small cross-section in REatoms as expected from a quite small 6p cross-section in 5dTMs.15) In addition, the 4f PDOSs for La and Lu obtained bythe DFT calculations were not used in the simulations. Thesimulated VB HAXPES spectra for La and Lu in Figs. 6(a)and 6(b) reproduced well the experimental polarization-dependent VB HAXPES spectra in Figs. 1(a) and 1(n),respectively. Therefore, the X-ray polarization-dependent VBspectral shape can be understood by the changes in the cross-section ratio with considering the angular distribution of 5dorbital to 6s one. The calculated 6s and 4f cross-sections withrespect to 5d one for RE atoms for 6 keV photoexcita-tion42–44) with taking the angular distributions with respect tothe X-ray polarizations into account are summarized inTable II. The calculated 5d cross-section ratios of RE atomswith respect to La 5d one are also summarized in Table III.The drastic changes in the 6s cross-section between H- andV-pol in our experimental geometry seen in Table II reflectthe changes in the VB profile at EB of ∼1.5 eV (2.2 eV) forLa (Lu). This result is consistent with the fact that the PDOScalculations show that the broad 6s states locate at around EBof ∼1.5 eV (∼2.2 eV) for La (Lu) and that the relativelynarrow 5d states locate near EF in both La and Lu. Thesechanges in the experimental band profiles derived from the5d and 6s states for the other REs were also reproduced bytentative simulations as mentioned in Appendix, except forEu and Yb.Next, we discuss the 4f states in the VB region of Cemetal. In Fig. 1(b), it is hard to find the 4f photoemissionsignal for Ce in HAXPES, although a small hump at EB of∼3.3 eV due to the 4f photoemission signal for Pr can be seenFig. 5. (Color online) Total DOSs and 5d, 6s, 6p, and 4f PDOSs for(a) dhcp La and (b) hcp Lu obtained from the DFT calculations.Fig. 6. (Color online) Simulated X-ray polarization-dependent VB spectrafor (a) La and (b) Lu. The red (blue) [green] solid curves indicate H-pol (V-pol) [C-pol] X-rays. Note that in the simulation for Lu, the peak positions ofthe Lu 4f7=2 and 4f5=2 were obtained from Fig. 1(n), and the branching ratiowas set to 8 : 6 as indicated by black vertical bars in (b). The inset of (b)shows the enlarged view of the VB spectra near EF.J. Phys. Soc. Jpn. 94, 074703 (2025) Full Papers S. Ueda and I. Hamada074703-8 ©2025 The Physical Society of Japan©2025 The Author(s)J. Phys. Soc. Jpn.Downloaded from journals.jps.jp by （研）物質・材料研究機構 on 06/26/25in Fig. 1(c). If the 4f photoemission signal for Ce isdetectable in HAXPES, a sharp peak structure located nearEF can be found as observed in Ref. 45. To clarify whetherthe 4f photoemission signal is detectable, we have performedthe HR HAXPES measurement for Ce using H-pol X-rays asshown in Fig. 1(o). The observed spectrum with �E ¼ 85meV was sharper than that with �E ¼ 130meV for H-polX-rays, but a peak at EB � 2 eV due to the 4f 1-to-4f 0photoemission process and a sharp peak (a tail of Kondoresonance peak) in the vicinity of EF in α-Ce (low-temperature phase) reported in Ref. 45 cannot be found. Onthe other hand, these two structures can be seen in the XPSspectrum for Ce (high-temperature γ-phase), even thoughtheir intensities are weak compared to the photoemissionintensity derived from the Ce 5d states.23) This fact suspectsthat the photoionization cross-section ratio of 4f=5d orbitalsin HAXPES (5.95 keV) is much smaller than that in XPS(1486.7 eV). The calculated cross-section ratios of 4f=5dorbitals are ∼0.19 and ∼1.16 for HAXPES and XPS in thesame experimental geometry, respectively.46) The absence ofthe 4f related peaks even in HR-HAXPES might lead that thecalculated cross-section ratio of 4f=5d orbitals for 6 keV isoverestimated, since the 4f=5d ratio of ∼0.19 is not so smallto detect the 4f related peaks. These results suggest that thedirect observation of Ce 4f photoemission is in a difficultsituation for HAXPES due to a quite smaller 4f cross-sectioncompared to 5d one and the condition of n ¼ 1 for Ce.Finally, we mention the impact of the HR measurement inHAXPES. Figure 1(p) shows the Eu 4f HAXPES spectrumwith �E ¼ 85meV for H-pol X-rays. The fine multipletstructures due to the 4f 7-to-4f 6 photoemission process wereobserved. The multiplet states for J ¼ 6, 5, and 4 deducedfrom the theoretical calculations24) were found as distinguish-able peaks in the experimental spectrum, while that for J ¼ 3appeared as a shoulder structure. These peaks were notresolved in the VB spectrum with �E ¼ 130meV as seen inFig. 1(f ) and the simulated Eu 4f spectrum for �E ¼ 130meV as shown in Fig. A·1(e) for H-pol X-rays. Whetherthe recoil effects25–27) in high EK photoelectrons exist (e.g.,the energy shift as listed in Table I and broadening of spectralshape) in 4f RE elemental solids, the result of the Eu 4fHAXPES spectrum shown in Fig. 1(p) strongly suggests theimportance of HR measurements in HAXPES to elucidate theelectronic states of materials at least photo-excitation (or EKof photoelectrons) up to 6 keV, which is also supported bythe fine and complicated multiplet structures for 4f REs inthe 3d and 4d core-level HAXPES spectra as seen in Figs. 2and 3.6. SummaryWe have conducted the VB, 3d, 4d, and 4s core-levelmeasurements of the elemental solids of 4f REs (La, Ce, Pr,Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu) by meansof bulk-sensitive HAXPES with �E ¼ 130meV. The VBspectra for 4f REs were separated by 5d6sp-derived bandlocated near EF and multiplet structure due to the 4fphotoemission final states, while the 4f photoemissionintensity was not found for La and Ce. The absence of the4f signal in La is due to n ¼ 0 (the empty 4f level), but theabsence of the 4f signal in Ce with n ¼ 1 even in the HRmeasurement (�E ¼ 85meV) is due to the quite lowphotoionization cross-section ratio of 4f=5d orbitals. ForYb and Lu, the spin–obit doublet (4f7=2 and 4f5=2) was founddue to the fully occupied 4f level in these metals. The profilesof band near EF depended on the X-ray polarization in ourexperimental geometry, while those of the 4f n�1 multipletTable II. Polarization-dependent cross-sections per electron of 5d, 4f, 6s orbitals for isolated La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu atomsfor H-, V-, and C-pol X-rays at the photon energy of 6 keV. The 5d cross-sections were obtained by the interpolation of those for La, Gd, and Lu. The 6s cross-section for Ce was obtained by the extrapolation of those for the other REs. The values were normalized by that of the 5d orbital in each element for H-pol X-rays. Note that the orbital-dependent angular distributions with respect to the X-ray polarizations were taken into account in the polarization-dependent cross-sections in the table.ElementH-pol. V-pol. C-pol.5d 4f 6s 5d 4f 6s 5d 4f 6sLa 1.000 — 1.4935 0.2405 — 0.01880 0.6086 — 0.7483Ce 1.000 0.1917 1.1898 0.2336 0.0899 0.01549 0.6056 0.1351 0.5962Pr 1.000 0.2273 1.1306 0.2247 0.1047 0.01518 0.6017 0.1594 0.5667Nd 1.000 0.2670 1.0807 0.2170 0.1201 0.01328 0.5983 0.1858 0.5409Sm 1.000 0.3558 0.9868 0.2043 0.1557 0.01443 0.5927 0.2461 0.4948Eu 1.000 0.4069 0.9476 0.1990 0.1754 0.01438 0.5904 0.2808 0.4753Gd 1.000 0.4942 1.0516 0.1994 0.2097 0.01637 0.5905 0.3397 0.5276Tb 1.000 0.5244 0.8799 0.1900 0.2188 0.01415 0.5864 0.3588 0.4416Dy 1.000 0.5915 0.8504 0.1861 0.2426 0.01413 0.5847 0.4030 0.4269Ho 1.000 0.6645 0.8232 0.1826 0.2680 0.01411 0.5832 0.4508 0.4134Er 1.000 0.7435 0.7980 0.1793 0.2951 0.01421 0.5818 0.5024 0.4009Tm 1.000 0.8297 0.7747 0.1764 0.3238 0.01431 0.5805 0.5583 0.3894Yb 1.000 0.9219 0.7531 0.1737 0.3546 0.01441 0.5793 0.6182 0.3787Lu 1.000 1.0950 0.8898 0.1690 0.4154 0.01762 0.5773 0.7318 0.4477Table III. Relative per-electron cross-sections of the La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu 5d orbitals to that of the La 5d orbital forH-pol X-rays at the photon energy of 6 keV. Note that the cross-section ratio (Ti 3d=La 5d) is 0.01481.Relative cross-section of 5d orbitalsLa Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu1.0000 1.0997 1.1829 1.2662 1.4328 1.5160 1.6324 1.6826 1.7658 1.8491 1.9324 2.0157 2.0989 2.1658J. Phys. Soc. Jpn. 94, 074703 (2025) Full Papers S. Ueda and I. Hamada074703-9 ©2025 The Physical Society of Japan©2025 The Author(s)J. Phys. Soc. Jpn.Downloaded from journals.jps.jp by （研）物質・材料研究機構 on 06/26/25structure did not depend on the X-ray polarization. Thechanges in the observed band profiles were understood by theX-ray polarization-dependent cross-section ratio of 6s=5dorbitals.We have performed the simulations of the polarization-dependent VB spectra near EF for La and Lu by using the5d and 6s PDOSs, which were obtained from the DFTcalculations for La and Lu, multiplied by the calculatedphotoionization cross-sections with considering the angulardistributions with respect to the X-ray polarizations. Thesimulated spectra including the polarization dependenceagreed with the experimental spectra for La and Lu. WeFig. A·1. (Color online) (a)–(l) Simulated X-ray polarization-dependent VB spectra for Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb with 4fmultiplet final states. For Ce, 4f photoemission was excluded, while for Eu and Yb, 5d6s band photoemission was excluded, for simplicity.J. Phys. Soc. Jpn. 94, 074703 (2025) Full Papers S. Ueda and I. Hamada074703-10 ©2025 The Physical Society of Japan©2025 The Author(s)J. Phys. Soc. Jpn.Downloaded from journals.jps.jp by （研）物質・材料研究機構 on 06/26/25have tentatively performed the simulations of the polar-ization-dependent VB spectra for the other REs by using thePDOSs for La or Lu and photoionization cross-section andthe calculated 4f multiplet states as shown in Appendix.The observed 3d and 4d core-level HAXPES spectra for 4fREs showed the complicated multiplet structures via theexchange interaction between the core–hole and 4f electrons.In particular, the 4d core-level spectra showed fine andcomplicated structures owing to the HR measurements(�E ¼ 130meV), smaller lifetime broadening effects, andrelatively large exchange interactions with the core–holecompared to the 3d spectral region. The clear spin exchangesplitting in the 4s core-level spectra were also observed.Further HR measurement (�E ¼ 85meV) for the Eu 4fphotoemission revealed that the clear separation of J ¼ 6,5, and 4 states. These results strongly suggest the importanceof HR measurements in HAXPES to elucidate the electronicstates of materials at least photo-excitation up to 6 keV.Acknowledgements The HAXPES measurements were performed withthe approval of NIMS Synchrotron X-ray Station at SPring-8 (Proposal No.2019B4606). This work was partially supported from Tokodai Institute forElemental Strategy (TIES: Grant No. JPMXP0112101001) and Data Creation andUtilization Type Material Research and Development Project (Grant No.JPMXP1122683430) funded by MEXT, Japan.Appendix: Tentative Simulations of Polarization-dependent VB HAXPES Spectra of REsIn this Appendix, the simulated polarization-dependent VBspectra of Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, andYb were shown in Fig. A·1. For Ce, Pr, Nd, and Sm, thePDOSs of dhcp La were tentatively used to calculate the VBphotoemission intensity for simplicity. For Gd, Tb, Dy, Ho,Er, and Tm, the PDOSs of hcp Lu were tentatively usedto calculate the VB intensity for simplicity. The energyseparation and relative photoemission intensity of multipletsstates in 4f photoemission final states were referred to thetheoretical calculation in Ref. 24, except for Ce, Pr, and Yb,and were used in the simulations. Note that the energyseparation of the multiplet states was adjusted to theexperimental 4f spectra. In the case of Ce, the experimentalVB spectra did not show the signature of 4f photoemissiondue to lower 4f orbital cross-section than 5d one asmentioned in Sect. 5. In addition, we tentatively used the5d and 6s PDOSs of dhcp La in the simulation for dhcp Ce,while the used Ce sample was in the α-phase. For Pr (Yb), theenergy position of single (double) peak(s) due to the 4fphotoemission was obtained from the experimental VBspectra. The multiplet states were indicated by vertical barsin Fig. A·1. The VB intensity simulation for the 5d and 6sstates was not performed for Eu and Yb by using the 5d and6s PDOSs of La or Lu, since the band structure calculationsfor La and Lu with the ð5d6spÞ3 configuration were notsuitable for Eu and Yb with the ð5d6spÞ2 configuration. Thesimulated spectra for the 5d6sp-derived band agreed with theexperimental spectra except the spectral width of 5d6sp-derived band in later REs probably due to the differencein lattice constant. Overall 4f multiplet structures in theexperimental spectra agreed with the calculations based onthe intermediate coupling model,24) but the deviation of theintensity ratio between the multiplet components in thepresent experiments and theory remained, which was alsofound in later RE elements in Ref. 23, although we did notconsider the multiplet-dependent lifetime broadening effectsin the simulations. In addition, the agreement between theexperiment and calculation for Nd [Figs. 1(d) and A·1(c)]was found to be poor. 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