Valence-selective local atomic structures on a YbInCu4 valence transition material by x-ray fluorescence holography
Shinya Hosokawa, Naohisa Happo, Kouichi Hayashi, Koji Kimura, Tomohiro Matsushita, Jens Rüdiger Stellhorn, Masaichiro Mizumaki, Motohiro Suzuki, Hitoshi Sato, Koichi Hiraoka
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[ c ond - m a t . m t r l - s c i ] S e p Valence-selective local atomic structures on a YbInCu valence transition material byx-ray fluorescence holography Shinya Hosokawa, ∗ Naohisa Happo, Kouichi Hayashi, Koji Kimura, Tomohiro Matsushita, Jens Rüdiger Stellhorn, † Masaichiro Mizumaki, Motohiro Suzuki, Hitoshi Sato, and Koichi Hiraoka Department of Physics, Kumamoto University, Kumamoto 860-8555, Japan Graduate School of Information Sciences Hiroshima City University, Hiroshima 731-3194, Japan Department of Physical Science and Engineering Nagoya Institute of Technology, Nagoya 466-8555, Japan Japan Synchrotron Radiation Research Institute (JASRI), Sayo 679-5198, Japan Hiroshima Synchrotron Radiation Center, Hiroshima University, Higashi-Hiroshima 739-0046, Japan Graduate School of Science and Engineering, Ehime University, Matsuyama 790-8577, Japan (Dated: September 17, 2019)An experimental technique of x-ray fluorescence holography for investigating valence-selectivelocal structures was established by employing the incident x-ray energy at a characteristic one nearan x-ray absorption edge, and it was adopted to discriminate environments around Yb and Yb ions in a YbInCu valence transition material below and above the transition temperature of 42 K.The reconstructed images of the neighboring atoms around Yb show a fcc structure as observedby diffraction experiments, whereas those around Yb have curious cross (+) features, indicatinga positional shift of the centered Yb ions from the fcc lattice point. An abrupt change was reported by Felner and Nowik[1] in 1986 in the temperature ( T ) dependence of mag-netic susceptibility of Yb x In − x Cu ( x ∼ . − . ). Asimple valence-fluctuation model was proposed, by whicha first-order Yb to Yb phase transition was pre-dicted with simply decreasing T . These compounds ex-hibit the sharpest T -dependent valence phase transitionin any metallic systems.Subsequent to this finding, Felner et al. [2] exhibitedseveral physical properties on this transition in mainlyYb . In . Cu alloy. An x-ray diffraction (XRD) experi-ment reveals a cubic Laves structure with the space groupof F d ¯3 m at all the temperatures from 300 to 4.2 K witha sudden increase in the unit cell size by about 0.15% at60-40 K ( T v at x = 0 . ). A neutron diffraction measure-ment proves the absence of magnetic order. An YbMössbauer study shows that the Yb ion is magnetic be-yond T v at 60 K, whereas it is non-magnetic below T v at4.2 K. An electrical resistivity exhibits a large decrease byabout 25% from 60 to 40 K. A specific-heat measurementreveals a characteristic increase around T v . Finally, Anx-ray absorption near edge structure (XANES) study atthe Yb L III edge shows a change in the f -electron occu-pancy at T v , and it was found that the valences of 2.9 and2.8 above and below T v , respectively, are independent of T in these temperature regions. In addition, substitution,pressure, and magnetic-field dependences of the valencephase transition were investigated by the same group indetail [3, 4].Then, the interests have moved to YbInCu ( x = 0 . )because the sample of x = 0 . is primarily in two phasesof YbInCu and InCu , which was found by Kojima etal. [5] using an electron-probe micro-analysis observa-tion. They measured XRD and found the cubic C15bcrystal type with the space group of F ¯43 m , in whichYb and In ions are ordered in a f cc site. The resis- tivity of a well-annealed sample shows a sudden changearound 40-45 K, which is narrower than the previouswork for Yb . In . Cu [2]. Their magnetic susceptibil-ity and In Knight shift results showed a sharp valencephase transition occurs at T v = 40 K and Yb ions arein the valence fluctuating state below T v . The structurewas refined by powder neutron diffraction (ND) data [6],and the lattice constant shows an abrupt change of 0.15%as was the previous study [2] at T v = 40 K without anychange in the crystal symmetry.Physical properties on a single crystal YbInCu weremeasured by Kindler et al. [7]. Mostly same values as thepolycrystalline ones were obtained in the above parame-ters although T v is a higher value of 66.9 K. Owing to thesingle crystal sample, elastic constants can be measuredin different directions, and a pronounced softening of thebulk modulus and an anomalous decrease in the Poissonratio occur in the vicinity of T v . Detailed comparisons ofthe structures of single and polycrystalline samples werecarried out using neutron diffraction [8], and the sharpestsingle transition was found in the single crystal near 40 K.They also concluded that the neutron diffraction patternsmeasured above and below T v are identical to be C15bcrystal type, and the increases of T v and gradual transi-tions are originated from a site-disorder between the Yband In atoms. A similar argument was performed on asite-disorder between the In and Cu atoms by XRD usingthe k dependence of x-ray atomic form factors [9].Concerning the f -electron occupancy across T v , theXANES analysis gave a small change of . → . [10].However, a bulk-sensitive hard x-ray electronic study ofYb d core-level and valence band photoemission mea-surements reveals a quite large change of . → . [11]. The valency change was also observed by Yamaokaet al. [12] using bulk-sensitive methods of high-resolutionx-ray absorption spectroscopy with partial fluorescenceyields mode and resonant x-ray scattering spectroscopyat the Yb L III absorption edge, and a change of approxi-mately . → . was reported. Thus, a valence changeof ∼ . is the consensus value for the valence transition,which causes large changes in physical properties as men-tioned above. The charge transfer at T v was suggested tobe between the Cu-derived conduction band and the Yb f states by Cu p / soft x-ray absorption spectroscopyby Utsumi et al. [13].The atomic radius of Yb is larger than that of Yb by about 17% even depending on the coordination num-bers around the Yb ions [14]. So, the increase of the aver-aged atomic radii of Yb ions can be estimate to be ∼ . %on the valence transition, which is extremely larger thanthe increase of the lattice constants of ∼ . % at T v .Thus, the Yb ions with the large atomic size shouldhighly squeeze into a rigid crystal lattice below T v , andlarge lattice distortions are expected around the Yb ions.A detailed XRD measurement using synchrotron ra-diation (SR) revealed an increase in the inter-Cu -tetrahedron below T v by about 0.2% together with smallincreases of Yb-Cu and In-Cu distances, while intraCu-Cu distance in the tetrahedron remains mostly un-changed [15]. It would be an indirect structural effect forthe change of Yb valency. Very recently, Tsutsui et al.found a small splitting of Bragg peaks in high-order re-flections by a high-energy XRD experiment below T − v ,and concluded that a structural change occurs from acubic to a tetragonal phase at T v [16], which contradictsthe previous conclusions of unchanged crystal type [2, 5–9, 15].For the further structural investigation on the valencetransition material, valence-selective method is essential.However, XRD has a small difference with valence, i.e.,atomic form factors are slightly different owing to theelectron numbers, and ND has no difference. X-ray ab-sorption fine structure (XAFS) data shows an overlapof oscillations with different valencies with energy shifts.Therefore, a reliable valence-selective methods is highlyrequired for evaluating the structural information on dif-ferent valencies in YbInCu .For this, we propose valence-selective x-ray fluores-cence holography (XFH), which recently applied to Y ox-ide thin film [17] in which the valence is different betweenthe surface and bulk, and to an Fe O mixed valence ma-terial [18]. XFH is a method for atom-resolved structuralcharacterizations, and enables to draw three-dimensional(3D) atomic images around a specific element emittingfluorescent x-rays [19, 20]. When the incident x-rays havean energy higher than an absorption edge of an element,the target atom emits fluorescent x-rays. In addition, x-rays scattered by surrounding atoms also reach the targetatom. The direct incident waves (reference wave) andthe scattered waves (object wave) interfere each other,and the intensity of fluorescent x-rays is proportional to I n t en s i t y ( A r b . un i t s ) /Yb Yb L III
FIG. 1. Yb L III
XANES spectra of YbInCu at 7 K (closedsquares) and 300 K (empty squares). the interfered x-ray intensity. Thus, the fluorescent x-rays give a modulation of some 0.1% with the incidentx-ray angles with respect to the crystal axes of the sam-ple, which is referred as a hologram. Then, the 3D im-ages of the neighboring atoms can, in principle, be re-constructed via simple Fourier transform-like approachwith no special atomic models. Thus, XFH can observelocal atomic arrangements in the short and intermedi-ate ranges around the target atoms emitting fluorescentx-rays.The important attempt for XFH to comprise thevalence-selective character is to employ the incident x-ray energy, E , at an energy specific to a valence near theXANES region. Figure 1 shows Yb L III
XANES spectraof YbInCu used for the present study at 7 and 300 Kmeasured in fluorescence mode, the feature of which isin very good agreement with the previous results [2] onYb . In . Cu . At 7K, a shoulder is observed at about8.939 keV, which is characteristic to the Yb . When E are employed at this energy, Yb p / electrons inonly Yb ions excite and emit the fluorescent x-rays,and those in Yb ions do not. Thus, the obtained holo-gram at this energy composes valence-selective structuralinformation around mainly Yb ions.A single crystal YbInCu was grown by a flux growthmethod. Constituent elements with stoichiometric ratiosin InCu flux were put in an alumina crucible and sealedin an evacuated quartz ampoule. The sample was thenheated to 1100 ◦ C and cooled slowly down to 800 ◦ C. Afterkeeping at 800 ◦ C for 20 h, the flux was removed. Thecrystal was cleaved so as to have a flat (001) surface withan area larger than × mm . The crystallinity of thesample was examined by taking a Laue photograph, andthe concentration and homogeneity over the sample wereconfirmed within the experimental errors by an electron-probe microanalysis.Yb Lα XFH measurements were carried out at 7 and300 K using a cryostat designed solely for XFH ex-periments (Pretech Co. Ltd., Type XFME-RR4K) atBL39XU of the SPring-8, Sayo, Japan. The sample wasplaced on a rotatable table in the cryostat head part.The incident x-rays were focused with a size of . × . mm on the (001) surface of the sample. The measure-ment was performed in inverse mode [20] by changing theazimuthal angle ◦ ≤ φ ≤ ◦ in steps of ∼ . ◦ of thecryostat head and the incident angle ◦ ≤ φ ≤ ◦ insteps of ◦ of the whole cryostat. The Yb Lα fluores-cent x-rays with an energy of 7.414 keV were collectedusing an avalanche photodiode detector via a cylindricalgraphite crystal energy-analyzer. The XFH signals wererecorded at E of 8.939 and 8.947 keV as indicated byarrows in Fig. 1.The holographic oscillation data were obtained by sub-tracting the backgrounds from the fluorescent x-ray in-tensities and normalized them with the incident x-rayintensities measured with an ion chamber. Extensions ofthe holographic data were carried out using the measuredx-ray standing wave lines in the hologram. Since theholograms are obtained at a single energy in the presentstudy, a usual Fourier transform-like analysis producesunphysical twin and false images owing to too less inputexperimental data for the requested unknown atomic con-figurations. Thus, we employed a sophisticated analysisof a "scattering pattern matrix extraction algorithm us-ing an L regularized linear regression" (SPEA-L1) byMatsushita [21], which is based on inverse problem andrepresents a sparse modeling approach to the experimen-tal holographic data.The holographic oscillation χ ( k ) is given as, χ ( k ) = − Z g ( r ) f ( θ r , k ) cos( kr − k · r )d r , (1)where g ( r ) is the atomic distribution function and f ( θ r , k ) is the atomic form factor at an angle between r and k , θ r , k . when voxels are introduced for describing g ( r ) , Eq. (1) is modified as, χ ( k j ) = − X g ( r i ) f ( θ r i , k j ) cos( k j r i − k j · r i ) , (2)where i and j are the numbers of the voxels and pixelof the holograms, respectively. Since g ( r i ) is sparse inreal space, a L -regularized regression is applicable. Toobtain g ( r i ) , its evaluation function is given by, E = X j | χ ( k j ) − ˆ χ ( k j ) | + λ X i | g ( r i ) | , (3)where ˆ χ ( k j ) is the experimental hologram and λ is apenalty parameter. For the present analysis, the voxelsize was set to be 0.01 nm cubic in the total range of ± . nm for each direction from the central Yb atoms.Figure 2(a) shows 3D atomic images measured at 300K and E = 8 . keV, where mainly Yb ions emit flu-orescent x-rays. The threshold value is set at 20% of the maximum intensity in (c). For the reference, the crystalstructure is given in (b), where large, middle, and smallballs indicate Yb, In, and Cu atoms, respectively. At aglance, only the first-neighboring Yb atoms are observed.Figure 2(c) shows 3D images measured at 7 K withthe same E value, where both the Yb and Yb ions are excited. As clearly seen in the figure, only theYb ions are observed due probably to the large electronnumbers of Yb rather than other elements, and here-after only the Yb ions will be discussed. Interestingly,second- and third-neighboring Yb atoms become clearwith decreasing temperature, while the first-neighboringYb images are hardly seen. Such a feature was frequentlyseen in XFH results of impurity doping [22, 23], whichoriginates from positional fluctuations caused by unusualatoms such as impurities or Yb atoms.Figure 2(c) shows 3D images measured at 7 K with E = 8 . keV, where only the Yb ions are ex-cited. To observe the positional distortions in detail,the threshold is lowered at 10%. The first-neighboringYb atoms are again invisible due probably to large posi-tional fluctuations. In contrast to (c), the second- andthird-neighboring Yb atoms are highly deformed, andtheir enlarged figures are given in (e) and (f), respec-tively. As clearly seen in (d)–(f), both the second- andthird-neighboring atomic images have tails in the x , y ,and z directions, and they are they are stronger in thedistant directions with respect to the central Yb atom.To observe the atomic images further and quantita-tively, Fig. 3 shows those on the (001) plane at z = 0 ,where mostly the Yb ions are located in the C15bstructure. The image intensities are indicated by thecolor bar besides the figures. Figure 3(a) corresponds toFig. 2(a) measured at 300 K with E = 8 . keV. Asmentioned above, the stronger images of about 0.4 arelocated at the first-neighboring positions although un-physical artifacts are seen around the first-neighboringatoms. In addition, weak atomic images of about 0.1 aredetected at the second- and third-neighboring positions.Figure 3(b) corresponds to Fig. 2(c) measured at 7 Kwith E = 8 . keV, indicating atomic images aroundthe Yb and Yb ions. Mostly f cc sublattice is seen inthe images besides weak images of about 0.2 at the first-neighboring positions. Figure 3(c) corresponds to Fig.2(d) measured at 7 K with E = 8 . keV, indicatingatomic images around only the Yb ions. The imagesof second- and third-neighboring Yb ions are distortedalong the cross directions of h i and h i .Since the ratio of the Yb was determined by variousmethods to be 0.15–0.26 [10–12], atomic arrangementsaround the pure Yb ions can be estimated by assumingthat 20% of (b) is contributed by (c), and the obtainedpure Yb atomic images are shown in Fig. 3(d). Sincethe fraction of the Yb is not large, (d) is very similarto (b), and the error in the Yb fraction affect the es-timated result very slightly. Thus, it is concluded that (a) 300 K 8947 eV(c) 7K 8947 eV (d) 7K 8939 eV (e) 2nd(f) 3rd(b) Crystal structure YbCuIn
FIG. 2. 3D atomic images measured at (a) 300 and (c) 7 K with E = 8 . keV, and (d) those at 7 K at E = 8 . keV. Forthe clarity for (d), 2nd and 3rd neighboring Yb atoms are enlarged in (e) and (f), respectively. (b) Crystal structure [5] for thereference. <100> (nm) < > ( n m ) (b)(c) –0.9–0.6–0.30.00.30.60.9 < > ( n m ) <100> (nm) <100> (nm) < > ( n m ) (a) 0.0–0.3–0.6–0.9 0.3 0.90.6–0.9–0.6–0.30.00.30.60.9 <100> (nm) < > ( n m ) (d) Yb Yb Yb /Yb FIG. 3. 2D atomic images on the (001) plane at z = 0 measured at (a) 300 and (b) 7 K with E = 8 . keV. (c) Those at 7K at E = 8 . keV. (d) Estimated pure Yb contributions obtained from the contrast between (b) and (c). Yb Yb /Yb FIG. 4. A reasonable model around the Yb ions obtainedfrom the present XFH results. valence-selective XFH experiment provides a clear differ-ence in local atomic arrangements, i.e., the reconstructedimages around Yb show a clear f cc structure as ob-served by diffraction experiments, whereas those aroundYb have curious cross features.Based on the experimental results, a structural modelis proposed around the Yb ions as shown in Fig. 4.Since the ionic radius of Yb is larger than that of Yb by about 17% [14] while the increase in the lattice con-stant is only about 0.15% [6], the Yb ions may hardlystay at the lattice positions. The shifts cause by avoid-ing the first-neighboring Tb atoms, i.e., h i , h i , or h i direction, as shown in the shifted balls of the fig-ure, which causes curious hexagonal-cross atomic imagesfor the second- and third-neighboring Yb atoms. Bymoving the central Yb ion, this atom pushes the first-neighboring atoms towards the same directions to avoidthe second- and third-neighboring atoms as indicated bythe arrows in the figure. Therefore, the positional fluc-tuations of the first-neighboring atoms are very large.In summary, a valence-selective XFH experiment wasapplied to a YbInCu valence transition material to in-vestigate the local atomic arrangements around the Yb and Yb ions in this material. A large difference wasobserved, indicating an excellent feasibility for obtainingthe valence-selective structural information, which is not easy by usual diffraction and XAFS measurements.The authors thank Professor Ichiro Akai and Profes-sor Masato Okada for useful information on the sparsemodeling. The XFH experiments were performed at thebeamline BL39XU in the SPring-8 with the approvalof the Japan Synchrotron Radiation Research Institute(JASRI) (Proposal No. 2015A1005 and 2018A1214).This works was supported by JSPS Grant-in-Aid for Sci-entific Research (B) (No. 17H02814), those on Innova-tive Areas "3D Active-Site Science" (Nos. 26105006 and26105013) and "Sparse Modeling" (No. 16H01553), andby JST CREST (No. JPMJCR1861). JRS gratefully ac-knowledges a financial support as Overseas Researcherunder a JSPS fellowship (No. P16796). ∗ Corresponding Author: [email protected] † Present address: Deutsches Elektronen-Synchrotron(DESY), 22603 Hamburg, Germany[1] I. Felner and I. Nowik, Phys. Rev. B , 617 (1986).[2] I. Felner et al., Phys. Rev. B , 6956 (1987).[3] I. Felner and I. Nowik, J. Mag. Mag. Mater. , 615(1987).[4] I. Nowik et al., Phys. Rev. B , 5633 (1988).[5] K. Kojima et al., J. Mag. Mag. Mater. , 267 (1989).[6] K. Kojima et al., J. Phys. Soc. Jpn. , 792 (1990).[7] B. Kindler et al., Phys. Rev. B , 704 (1994).[8] J. M. Lawrence et al., Phys. Rev. B , 6011 (1996).[9] C. Moriyoshi et al., J. Mag. Mag. Mater. , 206 (2003).[10] T. Zhuang et al., JPS Conf. Proc. , 011069 (2014).[11] H. Sato et al., Phys. Rev. Lett. , 246404 (2004).[12] H. Yamaoka et al., Phys. Rev. B , 045127 (2008).[13] Y. Utsumi et al., Phys. Rev. B , 115143 (2011).[14] R. D. Shannon, Acta Cryst. A , 751 (1976).[15] Y. Utsumi et al., Jpn. J. Appl. Phys. , 05FC10 (2011).[16] S. Tsutsui et al., J. Phys. Soc. Jpn. , 063602 (2016).[17] J. R. Stellhorn et al., J. Appl. Crystallogr. , 1583(2017).[18] A. K. R. Ang et al., Phys. Status Solidi B 255, 1800100(2018).[19] M. Tegze and G. Faigel, Europhys. Lett. , 41 (1991).[20] K. Hayashi et al., J. Phys.: Condens. Matter , 093201(2012).[21] T. Matsushita, e-J. Surf. Sci. Nanotech. , 158 (2016).[22] S. Hosokawa et al., Phys. Rev. B , 094104 (2013).[23] S. Hosokawa, N. Happo, and K. Hayashi, Phys. Rev. B80