- Email: [email protected]
Linear polarization-dependent core-level photoemission spectroscopy in Yb-based valence fluctuating system
Journal of Electron Spectroscopy and Related Phenomena xxx (xxxx) xxxx
Contents lists available at ScienceDirect
Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
Linear polarization-dependent core-level photoemission spectroscopy in Ybbased valence fluctuating system ⁎
Kentaro Kugaa, , Yuina Kanaia,b, Hidenori Fujiwaraa,b, Kohei Yamagamia,b, Satoru Hamamotoa,b, Yuichi Aoyamaa,b, Akira Sekiyamaa,b, Atsushi Higashiyaa,c, Toshiharu Kadonoa,d, Shin Imadaa,d, Atsushi Yamasakia,e, Kenji Tamasakua, Makina Yabashia, Tetsuya Ishikawaa, Satoru Nakatsujif,g, Takayuki Kissa,b a
RIKEN SPring-8 Center, Sayo, Hyogo 679-5148, Japan Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan Faculty of Science and Engineering, Setsunan University, Neyagawa, Osaka 572-8508, Japan d College of Science and Engineering, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan e Faculty of Science and Engineering, Konan University, Kobe, Hyogo 658-8501, Japan f The Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan g CREST, Japan Science and Technology Agency (JST), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan b c
A R T I C LE I N FO
A B S T R A C T
MSC: 00-01 99-00
In this paper, we show the linearly polarized hard X-ray core-level photoemission spectroscopy of valence fluctuating system β-YbAlB4. Interestingly, we observed subtle but distinct linear dichroisms in Yb2+ 3d5/2 corelevel spectra at several angles of β-YbAlB4. Basically linear dichroism in Yb2+ 3d5/2 core-level spectrum is not expected in the ionic picture because Yb2+ 4f orbital is fully occupied. These contradiction indicates the breakdown of ionic picture in β-YbAlB4.
Keywords: Core-level photoemission spectroscopy Linear dichroism c-f hybridisation
Δl = ± 1,
1. Introduction Linearly polarized X-ray is a powerful tool to probe the property of electron orbit in material. When electrons in material are excited by Xray and photoelectrons go outside the material, the Fermi's golden rule regulates the probability of this photoexcitation. Theories have formalized and calculated the angle-resolved and polarization-dependent photoemission [1,2], and have established the photoionization crosssection and asymmetry parameters for core-level photoemission of the ions with spherical charge distribution including polarization-dependence [3–6]. For example, the electric-dipole transitions mainly determine the angle dependence of photoemission probability. If the electric field component is linearly polarized along z axis of the material, the selection rules restrict the change of orbital quantum number (Δl) and magnetic quantum number (Δm) of the final state:
Δl = ± 1,
Δm = 0
In the case of linearly polarized perpendicular to z axis:
⁎
(1)
Δm = ± 1
(2)
The most striking example of the selection rule is an photoexcitation of the s orbital electron [7]. In s-polarization geometry, the electric-dipole transition forbids to photoexcite the s orbital electron toward photoelectron analyzer. By using the selection rules, recently, polarization-dependent angle resolved core-level photoemission spectroscopy has probed crystalline electric field ground states in Lanthanide based materials such as YbRh2Si2, YbCu2Si2, CeCu2Ge2, PrB6 and ErCo2 [8–11]. For example in Yb-based material, Yb3+ 3d core-level photoemission shows multiplet structure which originates from orbital and spin angular momentumdependent Coulomb interaction between the 4f and created 3d core holes [12]. This orbital and spin angular momentum dependent multiplet structure is significantly affected by the selection rules of electricdipole transitions, arising the linear dichroism which reflect the crystalline-electric-field wave function of 4f hole in the initial state. On the other hand, Yb2+ 3d core-level photoemission shows no multiplet structure and no linear dichroism is expected because Yb 4f orbitals in
Corresponding author. E-mail address: [email protected] (K. Kuga).
https://doi.org/10.1016/j.elspec.2019.08.004 Received 15 December 2018; Received in revised form 19 August 2019; Accepted 19 August 2019 0368-2048/ © 2019 Published by Elsevier B.V.
Please cite this article as: Kentaro Kuga, et al., Journal of Electron Spectroscopy and Related Phenomena, https://doi.org/10.1016/j.elspec.2019.08.004
Journal of Electron Spectroscopy and Related Phenomena xxx (xxxx) xxxx
K. Kuga, et al.
Yb2+ ion are fully occupied and orbital spin angular momentum dependent Coulomb interaction with created 3d core-hole is canceled out. These discussions above are based on the ionic model, in which only rare-earth ion under the crystalline electric field is taken into account. In real materials, some materials show valence fluctuation such as Yb3+ (4f13) ↔ Yb2+ (4 f 14 L ) due to c-f hybridization. Here, L denotes the conduction band with one hole. 4f electron hybridizes with conduction band and will have complicated state [13,14]. This situation is understood by single-impurity Anderson model and the core-level multiplet structure is reproduced by this model [15,16]. About the linear dichroism, for example, strongly valence fluctuating systems of heavy Fermi liquid material α-YbAlB4 [17] and of quantum critical material β-YbAlB4 [18] show strange angle dependent linear dichroisms of Yb3+ 3d core-level photoemission [19]. The careful measurements of the angle dependence of linear dichroism in Yb3+ 3d core-level photoemission determined that the crystalline electric field ground state in β-YbAlB4 is |J = 7/2, Jz = ± 5/2〉 with the principle axis along c-axis. However, the angle dependences of the amplitude of linear dichroism are much different from calculation based on the ionic model and single-impurity Anderson model assuming isotropic c-f hybridization. These differences between experiments and calculations are understood by strong anisotropic c-f hybridization effects on the crystalline electric field. How about the case of Yb2+ 3d core-level photoemission? To investigate this question, we measured Yb2+ 3d core-level photoemission in β-YbAlB4.
photoelectron analyzer was equipped in the horizontal plane with an angle about incident X-ray of 60° as shown in the upper right of Fig. 1, horizontally polarized and vertically polarized X-rays correspond to sand p-polarization geometry, respectively. To prevent the counting loss effect for the analysis of linear dichroism, we always checked the intensity of photoelectron and reduced the X-ray flux during p-polarization geometry measurements to get the comparable photoelectron intensity for the case of s-polarization geometry measurements. Energy resolution of this measurement system was set to ∼400 meV. The acceptance angle of the photoelectron analyzer was ± 7°. The single crystal β-YbAlB4 was grown by aluminum self-flux method [23]. Clean sample surface along ab-plane was obtained in situ by cleaving under the pressure of 1 × 10−7 Pa. We have confirmed no impurities including oxygen and carbon by scanning core-level spectra. The sample temperature was set to 25 K, which is sufficiently lower than the Kondo temperature of ∼200 K where 4f electron start hybridizing with conduction band [24].
3. Results and discussion We show the polarization-dependent wide scan of Yb 3d3/2 and 3d5/ core-level spectra including Al 1s core-level excitation with the main peak binding energy between those of the Yb 3d3/2 and 3d5/2 levels in Fig. 1. Clear separation of Yb2+ spectral weight and Yb3+ multiplet spectra are observed. Bulk plasmon satellites are found with the energy loss of ∼20 eV from the main peak. Al 1s spectrum at the binding energy of 1560 eV is strongly suppressed in the s-polarization geometry and the integrated intensity normalized by photon flux and the measuring time is about 7% of that in p-polarization geometry. Electricdipole transition should completely restrict photoelectron of 1s orbital in s-polarization geometry. However, 7% cannot be explained by the experimental factors of inclusion of horizontally polarized X-ray (ppolarization geometry) of 4% and the counting loss of the photoelectron analyzer. Because the X-ray flux was reduced during p-polarization measurement, the counting loss effect is negligibly small. Taking account of the experimental factors, Al 1s spectral weight is suppressed to 2
2. Experimental We performed polarization-dependent Yb 3d core-level hard X-ray photoemission spectroscopy with a MBS A1-HE hemispherical photoelectron spectrometer at BL19LXU of SPring-8 [20,21]. Horizontally polarized X-ray radiation produced by an undulator was selected to be 7.9 keV by a Si (111) double-crystal and and further monochromatized by a Si (620) channel-cut crystal. To produce vertically polarized X-ray, we used two diamond (100) single crystals as a phase retarder, and vertically polarized component of the X-ray was 96% [22]. Since the
Fig. 1. Yb 3d3/2, 3d5/2, Al 1s core-level photoelectron spectra of β-YbAlB4 with the p-polarization (blue thick line) and s-polarization (red thin line) geometries. The spectra are normalized by the background intensity at the binding energies of 1515 eV and 1535 eV. Plasmon satellite of each core-level spectrum is indicated by an arrow. A schematic top-view geometry of incident X-ray, sample and photoelectron analyzer is shown in the upper right side. The blue (horizontal) and red (vertical) arrows correspond to the electric field components of the polarized X-rays. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 2
Journal of Electron Spectroscopy and Related Phenomena xxx (xxxx) xxxx
K. Kuga, et al.
Fig. 2. (a) Schematic top-view geometry of sample with the rotation θ. (b) Yb2+ and Yb3+ 3d5/2 core-level photoelectron spectra of β-YbAlB4 with the p-polarization (blue thick line) and s-polarization (red thin line) geometries at θ = 0°, 45° and 60° and the linear dichroism (green closed circle at 0°, light green closed square at 45° and brown open circle at 60°). The spectra are normalized by the spectral weight of Yb3+ 3d5/2 plus Yb2+ 3d5/2 after subtracting Shirley-type backgrounds [25,26]. Linear dichroism is defined by the subtraction of the intensity between s-polarization and p-polarization. The dotted line represents zero line of the linear dichroism. The inset is the 20 times enlarged figure of the linear dichroisms in the region surrounded by the black rectangle. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the angle-dependent linear dichroism of Yb3+ 3d5/2 multiplet spectra [19]. In the single-impurity Anderson model, the off-diagonal term between the Yb2+ and Yb3+ configurations V representing the c-f hybridizations is taken into account in both initial and final states. Of course the initial ground state is represented by the mixture of the Yb2+ and Yb3+ configurations due to the c-f hybridization effects. In the final states, such off-diagonal terms are finite although the final-state energy levels are mutually much different by the 3d-4f attractive Coulomb interactions Ucd ≫ V. Therefore, both “Yb2+” and “Yb3+” final states should be rigorously expressed as the linear combinations of both configurations even if one configuration is much predominant than the other after the diagonalization of the Hamiltonian. In this sense, the linear dichroism in the “Yb2+” component is not forbidden in the frame of the single-impurity Anderson model in which the c-f hybridization effects are explicitly taken into account. However, the origin of the positive sign of the linear dichroism and the angle dependence is unclear at present. Further theoretical study is required to understand the underlying physics in addition to the relation between photoemission spectrum and c-f hybridization.
3%, which is of the same order of magnitude as the previous study for Au 4s (7%) and 5s (10%) [7]. As Yb2+ and Yb3+ 3d3/2 core-level spectra are strongly affected by a so called Shirley-type background [25,26] and plasmon satellite of large Al 1s core-level spectrum, we focus on the Yb2+ and Yb3+ 3d5/2 core-level spectra. The Yb2+ and Yb3+ 3d5/2 core-level spectra at θ = 0°, 45° and 60° are shown in Fig. 2(b), where the Shirley-type background is already subtracted from the raw data. θ is defined as the angle between the direction of photoelectron analyzer and the c-axis of the sample as shown in Fig. 2(a). The comparison of integrated intensity between the Yb2+ and Yb3+ components leads the valences of Yb ion are 2.78 estimated by p-polarization measurement and 2.77 estimated by s-polarization measurement at θ = 0°. The small difference of the estimated valence value is due to the linear dichroism of Yb2+ 3d5/2 core-level spectrum as discussed later. However, these values are almost consistent with previous study [27] and large deviation from integer values in valence suggests the strong valence fluctuation and c-f hybridization. Clear linear dichroisms at θ = 0°, 45° and 60° were observed in Yb3+ 3d5/2 core-level multiplet structures which are reflected by pure |J = 7/ 2, Jz = ± 5/2〉 crystalline electric field ground state and anisotropic c-f hybridization [19]. We also observed a subtle but finite dichroisms in the Yb2+ 3d5/2 spectra, where the intensities at the s-polarization geometry are stronger than that at the p-polarization geometry. The inset of Fig. 2(b) shows the enlarged linear dichroisms which have angle-dependent peaks at 1520 eV, indicating the distinct dichroisms in Yb2+ 3d5/2 spectra. For example, at θ = 0°, the magnitude of the linear dichroism is 27 times smaller than Yb2+ 3d5/2 spectrum. These results cannot be explained by ionic picture because 4f orbital is fully occupied in Yb2+ ion and have no orbital spin angular momentum dependent Coulomb interaction with created 3d core-hole. Given the large suppression of the linear dichroism of Yb3+ 3d5/2 multiplet spectrum by the c-f hybridization [19], the distinct linear dichroisms in Yb2+ 3d5/2 core-level spectra possibly reflect Yb3+ 4f hole via the strong c-f hybridization. It should be noted that the so-called asymmetry parameters obtained for atoms with the isotropic charge distributions [4–6] do not affect the shape of linear dichroism reflecting the anisotropic charge distributions. The angle-dependent linear dichroism shown in the inset of Fig. 2(b) also reminds us the anisotropic c-f hybridization probed by
4. Conclusion We have performed core-level photoemission spectroscopy of strongly valence fluctuating system β-YbAlB4 by using horizontally and vertically polarized hard X-ray. The finite suppression of Al 1s corelevel spectrum down to 3% was observed, which is comparable to the previous report of Au 4s and 5s. We discovered a small but angle-dependent linear dichroism in Yb2+ 3d5/2 core-level spectrum which indicates the breakdown of ionic model and is possibly due to the strong and anisotropic c-f hybridization. Acknowledgments We thank S. Fujioka, H. Aratani, T. Hattori, H. Yomosa, S. Takano, T. Kashiuchi, K. Nakagawa, K. Sakamoto and Y. Kobayashi for support in experiments. Sample preparation was carried out under the Visiting Researcher's Program of the Institute for Solid State Physics, the University of Tokyo. HAXPES experiments were performed at BL19LXU 3
Journal of Electron Spectroscopy and Related Phenomena xxx (xxxx) xxxx
K. Kuga, et al.
in SPring-8 with the approval of RIKEN (proposal nos. 20170043, 20170081, 20180026 and 20180076). This work is supported by a Grant-in-Aid for Scientific Research (JP16H04014, JP16H04015, JP18K03512), and a Grant-in-Aid for Innovative Areas (JP16H01074, JP18H04317) from MEXT and JSPS, Japan. This work is partially supported by CREST (JPMJCR15Q5, JPMJCR18T3), Japan Science and Technology Agency, by Grants-in-Aid for Scientific Research (JP16H02209), and by Grants-in-Aids for Scientific Research on Innovative Areas (JP15H05882, JP15H05883) from MEXT. Y.Kanai was supported by the JSPS Research Fellowships for Young Scientists.
[11]
[12] [13] [14] [15] [16] [17]
References
[18]
[1] J.W. Gadzuk, Phys. Rev. B 12 (1975) 5608. [2] S. Goldberg, C. Fadley, S. Kono, J. Electron Spectrosc. Relat. Phenom. 21 (1981) 285. [3] J.J. Yeh, I. Lindau, At. Data Nucl. Data Tables 32 (1985) 1. [4] M.B. Trzhaskovskaya, V.I. Nefedov, V.G. Yarzhemsky, At. Data Nucl. Data Tables 77 (2001) 97. [5] M.B. Trzhaskovskaya, V.I. Nefedov, V.G. Yarzhemsky, At. Data Nucl. Data Tables 82 (2002) 257. [6] M.B. Trzhaskovskaya, V.K. Nikulin, V.I. Nefedov, V.G. Yarzhemsky, At. Data Nucl. Data Tables 92 (2006) 245. [7] A. Sekiyama, J. Yamaguchi, A. Higashiya, M. Obara, H. Sugiyama, M.Y. Kimura, S. Suga, S. Imada, I.A. Nekrasov, M. Yabashi, K. Tamasaku, T. Ishikawa, New J. Phys. 12 (2010) 043045. [8] T. Mori, S. Kitayama, Y. Kanai, S. Naimen, H. Fujiwara, A. Higashiya, K. Tamasaku, A. Tanaka, K. Terashima, S. Imada, A. Yasui, Y. Saitoh, K. Yamagami, K. Yano, T. Matsumoto, T. Kiss, M. Yabashi, T. Ishikawa, S. Suga, Y. Ōnuki, T. Ebihara, A. Sekiyama, J. Phys. Soc. Jpn. 83 (2014) 123702. [9] H. Aratani, Y. Nakatani, H. Fujiwara, M. Kawada, Y. Kanai, K. Yamagami, S. Fujioka, S. Hamamoto, K. Kuga, T. Kiss, A. Yamasaki, A. Higashiya, T. Kadono, S. Imada, A. Tanaka, K. Tamasaku, M. Yabashi, T. Ishikawa, A. Yasui, Y. Saitoh, Y. Narumi, K. Kindo, T. Ebihara, A. Sekiyama, Phys. Rev. B 98 (2018) 121113(R). [10] S. Hamamoto, S. Fujioka, Y. Kanai, K. Yamagami, Y. Nakatani, K. Nakagawa,
[19]
[20]
[21] [22]
[23] [24] [25] [26] [27]
4
H. Fujiwara, T. Kiss, A. Higashiya, A. Yamasaki, T. Kadono, S. Imada, A. Tanaka, K. Tamasaku, M. Yabashi, T. Ishikawa, K.T. Matsumoto, T. Onimaru, T. Takabatake, A. Sekiyama, J. Phys. Soc. Jpn. 86 (2017) 123703. A.A. Abozeed, T. Kadono, A. Sekiyama, H. Fujiwara, A. Higashiya, A. Yamasaki, Y. Kanai, K. Yamagami, K. Tamasaku, M. Yabashi, T. Ishikawa, A.V. Andreev, H. Wada, S. Imada, J. Phys. Soc. Jpn. 87 (2018) 033710. B.T. Thole, G. van der Laan, J.C. Fuggle, G.A. Sawatzky, R.C. Karnatak, J.-M. Esteva, Phys. Rev. B 32 (1985) 5107. S. Imada, T. Jo, J. Phys. Soc. Jpn. 58 (1989) 2665. S. Imada, T. Jo, J. Phys. Soc. Jpn. 58 (1989) 402. O. Gunnarsson, K. Schönhammer, Phys. Rev. B 28 (1983) 4315. J.-M. Imer, E. Wuilloud, Zeitsch. Phys. B: Condens. Matter 66 (1987) 153. Y. Matsumoto, K. Kuga, T. Tomita, Y. Karaki, S. Nakatsuji, Phys. Rev. B 84 (2011) 125126. S. Nakatsuji, K. Kuga, Y. Machida, T. Tayama, T. Sakakibara, Y. Karaki, H. Ishimoto, S. Yonezawa, Y. Maeno, E. Pearson, G.G. Lonzarich, L. Balicas, H. Lee, Z. Fisk, Nat. Phys. 4 (2008) 603–607. K. Kuga, Y. Kanai, H. Fujiwara, K. Yamagami, S. Hamamoto, Y. Aoyama, A. Sekiyama, A. Higashiya, T. Kadono, S. Imada, A. Yamasaki, A. Tanaka, K. Tamasaku, M. Yabashi, T. Ishikawa, S. Nakatsuji, T. Kiss, Phys. Rev. Lett. 123 (2019) 036404. M. Yabashi, T. Mochizuki, H. Yamazaki, S. Goto, H. Ohashi, K. Takeshita, T. Ohata, T. Matsushita, K. Tamasaku, Y. Tanaka, T. Ishikawa, Nucl. Instrum. Methods Phys. Res. A 467-L 468 (2001) 678–681. M. Yabashi, K. Tamasaku, T. Ishikawa, Phys. Rev. Lett. 87 (2001) 140801. H. Fujiwara, S. Naimen, A. Higashiya, Y. Kanai, H. Yomosa, K. Yamagami, T. Kiss, T. Kadono, S. Imada, A. Yamasaki, K. Takase, S. Otsuka, T. Shimizu, S. Shingubara, S. Suga, M. Yabashi, K. Tamasaku, T. Ishikawa, A. Sekiyama, J. Synchrotron. Radiat. 23 (2016) 735–742. R.T. Macaluso, S. Nakatsuji, K. Kuga, E.L. Thomas, Y. Machida, Y. Maeno, Z. Fisk, J.Y. Chan, Chem. Mater. 19 (2007) 1918–1922. Y. Matsumoto, S. Nakatsuji, K. Kuga, Y. Karaki, N. Horie, Y. Shimura, T. Sakakibara, A. Nevidomskyy, P. Coleman, Science 331 (2011) 316. D.A. Shirley, Phys. Rev. B 5 (1972) 4709–4714. A. Proctor, P.M.A. Sherwood, Anal. Chem. 54 (1982) 13–19. M. Okawa, M. Matsunami, K. Ishizaka, R. Eguchi, M. Taguchi, A. Chainani, Y. Takata, M. Yabashi, K. Tamasaku, Y. Nishino, T. Ishikawa, K. Kuga, N. Horie, S. Nakatsuji, S. Shin, Phys. Rev. Lett. 104 (2010) 247201.
Contents lists available at ScienceDirect
Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
Linear polarization-dependent core-level photoemission spectroscopy in Ybbased valence fluctuating system ⁎
Kentaro Kugaa, , Yuina Kanaia,b, Hidenori Fujiwaraa,b, Kohei Yamagamia,b, Satoru Hamamotoa,b, Yuichi Aoyamaa,b, Akira Sekiyamaa,b, Atsushi Higashiyaa,c, Toshiharu Kadonoa,d, Shin Imadaa,d, Atsushi Yamasakia,e, Kenji Tamasakua, Makina Yabashia, Tetsuya Ishikawaa, Satoru Nakatsujif,g, Takayuki Kissa,b a
RIKEN SPring-8 Center, Sayo, Hyogo 679-5148, Japan Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan Faculty of Science and Engineering, Setsunan University, Neyagawa, Osaka 572-8508, Japan d College of Science and Engineering, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan e Faculty of Science and Engineering, Konan University, Kobe, Hyogo 658-8501, Japan f The Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan g CREST, Japan Science and Technology Agency (JST), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan b c
A R T I C LE I N FO
A B S T R A C T
MSC: 00-01 99-00
In this paper, we show the linearly polarized hard X-ray core-level photoemission spectroscopy of valence fluctuating system β-YbAlB4. Interestingly, we observed subtle but distinct linear dichroisms in Yb2+ 3d5/2 corelevel spectra at several angles of β-YbAlB4. Basically linear dichroism in Yb2+ 3d5/2 core-level spectrum is not expected in the ionic picture because Yb2+ 4f orbital is fully occupied. These contradiction indicates the breakdown of ionic picture in β-YbAlB4.
Keywords: Core-level photoemission spectroscopy Linear dichroism c-f hybridisation
Δl = ± 1,
1. Introduction Linearly polarized X-ray is a powerful tool to probe the property of electron orbit in material. When electrons in material are excited by Xray and photoelectrons go outside the material, the Fermi's golden rule regulates the probability of this photoexcitation. Theories have formalized and calculated the angle-resolved and polarization-dependent photoemission [1,2], and have established the photoionization crosssection and asymmetry parameters for core-level photoemission of the ions with spherical charge distribution including polarization-dependence [3–6]. For example, the electric-dipole transitions mainly determine the angle dependence of photoemission probability. If the electric field component is linearly polarized along z axis of the material, the selection rules restrict the change of orbital quantum number (Δl) and magnetic quantum number (Δm) of the final state:
Δl = ± 1,
Δm = 0
In the case of linearly polarized perpendicular to z axis:
⁎
(1)
Δm = ± 1
(2)
The most striking example of the selection rule is an photoexcitation of the s orbital electron [7]. In s-polarization geometry, the electric-dipole transition forbids to photoexcite the s orbital electron toward photoelectron analyzer. By using the selection rules, recently, polarization-dependent angle resolved core-level photoemission spectroscopy has probed crystalline electric field ground states in Lanthanide based materials such as YbRh2Si2, YbCu2Si2, CeCu2Ge2, PrB6 and ErCo2 [8–11]. For example in Yb-based material, Yb3+ 3d core-level photoemission shows multiplet structure which originates from orbital and spin angular momentumdependent Coulomb interaction between the 4f and created 3d core holes [12]. This orbital and spin angular momentum dependent multiplet structure is significantly affected by the selection rules of electricdipole transitions, arising the linear dichroism which reflect the crystalline-electric-field wave function of 4f hole in the initial state. On the other hand, Yb2+ 3d core-level photoemission shows no multiplet structure and no linear dichroism is expected because Yb 4f orbitals in
Corresponding author. E-mail address: [email protected] (K. Kuga).
https://doi.org/10.1016/j.elspec.2019.08.004 Received 15 December 2018; Received in revised form 19 August 2019; Accepted 19 August 2019 0368-2048/ © 2019 Published by Elsevier B.V.
Please cite this article as: Kentaro Kuga, et al., Journal of Electron Spectroscopy and Related Phenomena, https://doi.org/10.1016/j.elspec.2019.08.004
Journal of Electron Spectroscopy and Related Phenomena xxx (xxxx) xxxx
K. Kuga, et al.
Yb2+ ion are fully occupied and orbital spin angular momentum dependent Coulomb interaction with created 3d core-hole is canceled out. These discussions above are based on the ionic model, in which only rare-earth ion under the crystalline electric field is taken into account. In real materials, some materials show valence fluctuation such as Yb3+ (4f13) ↔ Yb2+ (4 f 14 L ) due to c-f hybridization. Here, L denotes the conduction band with one hole. 4f electron hybridizes with conduction band and will have complicated state [13,14]. This situation is understood by single-impurity Anderson model and the core-level multiplet structure is reproduced by this model [15,16]. About the linear dichroism, for example, strongly valence fluctuating systems of heavy Fermi liquid material α-YbAlB4 [17] and of quantum critical material β-YbAlB4 [18] show strange angle dependent linear dichroisms of Yb3+ 3d core-level photoemission [19]. The careful measurements of the angle dependence of linear dichroism in Yb3+ 3d core-level photoemission determined that the crystalline electric field ground state in β-YbAlB4 is |J = 7/2, Jz = ± 5/2〉 with the principle axis along c-axis. However, the angle dependences of the amplitude of linear dichroism are much different from calculation based on the ionic model and single-impurity Anderson model assuming isotropic c-f hybridization. These differences between experiments and calculations are understood by strong anisotropic c-f hybridization effects on the crystalline electric field. How about the case of Yb2+ 3d core-level photoemission? To investigate this question, we measured Yb2+ 3d core-level photoemission in β-YbAlB4.
photoelectron analyzer was equipped in the horizontal plane with an angle about incident X-ray of 60° as shown in the upper right of Fig. 1, horizontally polarized and vertically polarized X-rays correspond to sand p-polarization geometry, respectively. To prevent the counting loss effect for the analysis of linear dichroism, we always checked the intensity of photoelectron and reduced the X-ray flux during p-polarization geometry measurements to get the comparable photoelectron intensity for the case of s-polarization geometry measurements. Energy resolution of this measurement system was set to ∼400 meV. The acceptance angle of the photoelectron analyzer was ± 7°. The single crystal β-YbAlB4 was grown by aluminum self-flux method [23]. Clean sample surface along ab-plane was obtained in situ by cleaving under the pressure of 1 × 10−7 Pa. We have confirmed no impurities including oxygen and carbon by scanning core-level spectra. The sample temperature was set to 25 K, which is sufficiently lower than the Kondo temperature of ∼200 K where 4f electron start hybridizing with conduction band [24].
3. Results and discussion We show the polarization-dependent wide scan of Yb 3d3/2 and 3d5/ core-level spectra including Al 1s core-level excitation with the main peak binding energy between those of the Yb 3d3/2 and 3d5/2 levels in Fig. 1. Clear separation of Yb2+ spectral weight and Yb3+ multiplet spectra are observed. Bulk plasmon satellites are found with the energy loss of ∼20 eV from the main peak. Al 1s spectrum at the binding energy of 1560 eV is strongly suppressed in the s-polarization geometry and the integrated intensity normalized by photon flux and the measuring time is about 7% of that in p-polarization geometry. Electricdipole transition should completely restrict photoelectron of 1s orbital in s-polarization geometry. However, 7% cannot be explained by the experimental factors of inclusion of horizontally polarized X-ray (ppolarization geometry) of 4% and the counting loss of the photoelectron analyzer. Because the X-ray flux was reduced during p-polarization measurement, the counting loss effect is negligibly small. Taking account of the experimental factors, Al 1s spectral weight is suppressed to 2
2. Experimental We performed polarization-dependent Yb 3d core-level hard X-ray photoemission spectroscopy with a MBS A1-HE hemispherical photoelectron spectrometer at BL19LXU of SPring-8 [20,21]. Horizontally polarized X-ray radiation produced by an undulator was selected to be 7.9 keV by a Si (111) double-crystal and and further monochromatized by a Si (620) channel-cut crystal. To produce vertically polarized X-ray, we used two diamond (100) single crystals as a phase retarder, and vertically polarized component of the X-ray was 96% [22]. Since the
Fig. 1. Yb 3d3/2, 3d5/2, Al 1s core-level photoelectron spectra of β-YbAlB4 with the p-polarization (blue thick line) and s-polarization (red thin line) geometries. The spectra are normalized by the background intensity at the binding energies of 1515 eV and 1535 eV. Plasmon satellite of each core-level spectrum is indicated by an arrow. A schematic top-view geometry of incident X-ray, sample and photoelectron analyzer is shown in the upper right side. The blue (horizontal) and red (vertical) arrows correspond to the electric field components of the polarized X-rays. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 2
Journal of Electron Spectroscopy and Related Phenomena xxx (xxxx) xxxx
K. Kuga, et al.
Fig. 2. (a) Schematic top-view geometry of sample with the rotation θ. (b) Yb2+ and Yb3+ 3d5/2 core-level photoelectron spectra of β-YbAlB4 with the p-polarization (blue thick line) and s-polarization (red thin line) geometries at θ = 0°, 45° and 60° and the linear dichroism (green closed circle at 0°, light green closed square at 45° and brown open circle at 60°). The spectra are normalized by the spectral weight of Yb3+ 3d5/2 plus Yb2+ 3d5/2 after subtracting Shirley-type backgrounds [25,26]. Linear dichroism is defined by the subtraction of the intensity between s-polarization and p-polarization. The dotted line represents zero line of the linear dichroism. The inset is the 20 times enlarged figure of the linear dichroisms in the region surrounded by the black rectangle. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the angle-dependent linear dichroism of Yb3+ 3d5/2 multiplet spectra [19]. In the single-impurity Anderson model, the off-diagonal term between the Yb2+ and Yb3+ configurations V representing the c-f hybridizations is taken into account in both initial and final states. Of course the initial ground state is represented by the mixture of the Yb2+ and Yb3+ configurations due to the c-f hybridization effects. In the final states, such off-diagonal terms are finite although the final-state energy levels are mutually much different by the 3d-4f attractive Coulomb interactions Ucd ≫ V. Therefore, both “Yb2+” and “Yb3+” final states should be rigorously expressed as the linear combinations of both configurations even if one configuration is much predominant than the other after the diagonalization of the Hamiltonian. In this sense, the linear dichroism in the “Yb2+” component is not forbidden in the frame of the single-impurity Anderson model in which the c-f hybridization effects are explicitly taken into account. However, the origin of the positive sign of the linear dichroism and the angle dependence is unclear at present. Further theoretical study is required to understand the underlying physics in addition to the relation between photoemission spectrum and c-f hybridization.
3%, which is of the same order of magnitude as the previous study for Au 4s (7%) and 5s (10%) [7]. As Yb2+ and Yb3+ 3d3/2 core-level spectra are strongly affected by a so called Shirley-type background [25,26] and plasmon satellite of large Al 1s core-level spectrum, we focus on the Yb2+ and Yb3+ 3d5/2 core-level spectra. The Yb2+ and Yb3+ 3d5/2 core-level spectra at θ = 0°, 45° and 60° are shown in Fig. 2(b), where the Shirley-type background is already subtracted from the raw data. θ is defined as the angle between the direction of photoelectron analyzer and the c-axis of the sample as shown in Fig. 2(a). The comparison of integrated intensity between the Yb2+ and Yb3+ components leads the valences of Yb ion are 2.78 estimated by p-polarization measurement and 2.77 estimated by s-polarization measurement at θ = 0°. The small difference of the estimated valence value is due to the linear dichroism of Yb2+ 3d5/2 core-level spectrum as discussed later. However, these values are almost consistent with previous study [27] and large deviation from integer values in valence suggests the strong valence fluctuation and c-f hybridization. Clear linear dichroisms at θ = 0°, 45° and 60° were observed in Yb3+ 3d5/2 core-level multiplet structures which are reflected by pure |J = 7/ 2, Jz = ± 5/2〉 crystalline electric field ground state and anisotropic c-f hybridization [19]. We also observed a subtle but finite dichroisms in the Yb2+ 3d5/2 spectra, where the intensities at the s-polarization geometry are stronger than that at the p-polarization geometry. The inset of Fig. 2(b) shows the enlarged linear dichroisms which have angle-dependent peaks at 1520 eV, indicating the distinct dichroisms in Yb2+ 3d5/2 spectra. For example, at θ = 0°, the magnitude of the linear dichroism is 27 times smaller than Yb2+ 3d5/2 spectrum. These results cannot be explained by ionic picture because 4f orbital is fully occupied in Yb2+ ion and have no orbital spin angular momentum dependent Coulomb interaction with created 3d core-hole. Given the large suppression of the linear dichroism of Yb3+ 3d5/2 multiplet spectrum by the c-f hybridization [19], the distinct linear dichroisms in Yb2+ 3d5/2 core-level spectra possibly reflect Yb3+ 4f hole via the strong c-f hybridization. It should be noted that the so-called asymmetry parameters obtained for atoms with the isotropic charge distributions [4–6] do not affect the shape of linear dichroism reflecting the anisotropic charge distributions. The angle-dependent linear dichroism shown in the inset of Fig. 2(b) also reminds us the anisotropic c-f hybridization probed by
4. Conclusion We have performed core-level photoemission spectroscopy of strongly valence fluctuating system β-YbAlB4 by using horizontally and vertically polarized hard X-ray. The finite suppression of Al 1s corelevel spectrum down to 3% was observed, which is comparable to the previous report of Au 4s and 5s. We discovered a small but angle-dependent linear dichroism in Yb2+ 3d5/2 core-level spectrum which indicates the breakdown of ionic model and is possibly due to the strong and anisotropic c-f hybridization. Acknowledgments We thank S. Fujioka, H. Aratani, T. Hattori, H. Yomosa, S. Takano, T. Kashiuchi, K. Nakagawa, K. Sakamoto and Y. Kobayashi for support in experiments. Sample preparation was carried out under the Visiting Researcher's Program of the Institute for Solid State Physics, the University of Tokyo. HAXPES experiments were performed at BL19LXU 3
Journal of Electron Spectroscopy and Related Phenomena xxx (xxxx) xxxx
K. Kuga, et al.
in SPring-8 with the approval of RIKEN (proposal nos. 20170043, 20170081, 20180026 and 20180076). This work is supported by a Grant-in-Aid for Scientific Research (JP16H04014, JP16H04015, JP18K03512), and a Grant-in-Aid for Innovative Areas (JP16H01074, JP18H04317) from MEXT and JSPS, Japan. This work is partially supported by CREST (JPMJCR15Q5, JPMJCR18T3), Japan Science and Technology Agency, by Grants-in-Aid for Scientific Research (JP16H02209), and by Grants-in-Aids for Scientific Research on Innovative Areas (JP15H05882, JP15H05883) from MEXT. Y.Kanai was supported by the JSPS Research Fellowships for Young Scientists.
[11]
[12] [13] [14] [15] [16] [17]
References
[18]
[1] J.W. Gadzuk, Phys. Rev. B 12 (1975) 5608. [2] S. Goldberg, C. Fadley, S. Kono, J. Electron Spectrosc. Relat. Phenom. 21 (1981) 285. [3] J.J. Yeh, I. Lindau, At. Data Nucl. Data Tables 32 (1985) 1. [4] M.B. Trzhaskovskaya, V.I. Nefedov, V.G. Yarzhemsky, At. Data Nucl. Data Tables 77 (2001) 97. [5] M.B. Trzhaskovskaya, V.I. Nefedov, V.G. Yarzhemsky, At. Data Nucl. Data Tables 82 (2002) 257. [6] M.B. Trzhaskovskaya, V.K. Nikulin, V.I. Nefedov, V.G. Yarzhemsky, At. Data Nucl. Data Tables 92 (2006) 245. [7] A. Sekiyama, J. Yamaguchi, A. Higashiya, M. Obara, H. Sugiyama, M.Y. Kimura, S. Suga, S. Imada, I.A. Nekrasov, M. Yabashi, K. Tamasaku, T. Ishikawa, New J. Phys. 12 (2010) 043045. [8] T. Mori, S. Kitayama, Y. Kanai, S. Naimen, H. Fujiwara, A. Higashiya, K. Tamasaku, A. Tanaka, K. Terashima, S. Imada, A. Yasui, Y. Saitoh, K. Yamagami, K. Yano, T. Matsumoto, T. Kiss, M. Yabashi, T. Ishikawa, S. Suga, Y. Ōnuki, T. Ebihara, A. Sekiyama, J. Phys. Soc. Jpn. 83 (2014) 123702. [9] H. Aratani, Y. Nakatani, H. Fujiwara, M. Kawada, Y. Kanai, K. Yamagami, S. Fujioka, S. Hamamoto, K. Kuga, T. Kiss, A. Yamasaki, A. Higashiya, T. Kadono, S. Imada, A. Tanaka, K. Tamasaku, M. Yabashi, T. Ishikawa, A. Yasui, Y. Saitoh, Y. Narumi, K. Kindo, T. Ebihara, A. Sekiyama, Phys. Rev. B 98 (2018) 121113(R). [10] S. Hamamoto, S. Fujioka, Y. Kanai, K. Yamagami, Y. Nakatani, K. Nakagawa,
[19]
[20]
[21] [22]
[23] [24] [25] [26] [27]
4
H. Fujiwara, T. Kiss, A. Higashiya, A. Yamasaki, T. Kadono, S. Imada, A. Tanaka, K. Tamasaku, M. Yabashi, T. Ishikawa, K.T. Matsumoto, T. Onimaru, T. Takabatake, A. Sekiyama, J. Phys. Soc. Jpn. 86 (2017) 123703. A.A. Abozeed, T. Kadono, A. Sekiyama, H. Fujiwara, A. Higashiya, A. Yamasaki, Y. Kanai, K. Yamagami, K. Tamasaku, M. Yabashi, T. Ishikawa, A.V. Andreev, H. Wada, S. Imada, J. Phys. Soc. Jpn. 87 (2018) 033710. B.T. Thole, G. van der Laan, J.C. Fuggle, G.A. Sawatzky, R.C. Karnatak, J.-M. Esteva, Phys. Rev. B 32 (1985) 5107. S. Imada, T. Jo, J. Phys. Soc. Jpn. 58 (1989) 2665. S. Imada, T. Jo, J. Phys. Soc. Jpn. 58 (1989) 402. O. Gunnarsson, K. Schönhammer, Phys. Rev. B 28 (1983) 4315. J.-M. Imer, E. Wuilloud, Zeitsch. Phys. B: Condens. Matter 66 (1987) 153. Y. Matsumoto, K. Kuga, T. Tomita, Y. Karaki, S. Nakatsuji, Phys. Rev. B 84 (2011) 125126. S. Nakatsuji, K. Kuga, Y. Machida, T. Tayama, T. Sakakibara, Y. Karaki, H. Ishimoto, S. Yonezawa, Y. Maeno, E. Pearson, G.G. Lonzarich, L. Balicas, H. Lee, Z. Fisk, Nat. Phys. 4 (2008) 603–607. K. Kuga, Y. Kanai, H. Fujiwara, K. Yamagami, S. Hamamoto, Y. Aoyama, A. Sekiyama, A. Higashiya, T. Kadono, S. Imada, A. Yamasaki, A. Tanaka, K. Tamasaku, M. Yabashi, T. Ishikawa, S. Nakatsuji, T. Kiss, Phys. Rev. Lett. 123 (2019) 036404. M. Yabashi, T. Mochizuki, H. Yamazaki, S. Goto, H. Ohashi, K. Takeshita, T. Ohata, T. Matsushita, K. Tamasaku, Y. Tanaka, T. Ishikawa, Nucl. Instrum. Methods Phys. Res. A 467-L 468 (2001) 678–681. M. Yabashi, K. Tamasaku, T. Ishikawa, Phys. Rev. Lett. 87 (2001) 140801. H. Fujiwara, S. Naimen, A. Higashiya, Y. Kanai, H. Yomosa, K. Yamagami, T. Kiss, T. Kadono, S. Imada, A. Yamasaki, K. Takase, S. Otsuka, T. Shimizu, S. Shingubara, S. Suga, M. Yabashi, K. Tamasaku, T. Ishikawa, A. Sekiyama, J. Synchrotron. Radiat. 23 (2016) 735–742. R.T. Macaluso, S. Nakatsuji, K. Kuga, E.L. Thomas, Y. Machida, Y. Maeno, Z. Fisk, J.Y. Chan, Chem. Mater. 19 (2007) 1918–1922. Y. Matsumoto, S. Nakatsuji, K. Kuga, Y. Karaki, N. Horie, Y. Shimura, T. Sakakibara, A. Nevidomskyy, P. Coleman, Science 331 (2011) 316. D.A. Shirley, Phys. Rev. B 5 (1972) 4709–4714. A. Proctor, P.M.A. Sherwood, Anal. Chem. 54 (1982) 13–19. M. Okawa, M. Matsunami, K. Ishizaka, R. Eguchi, M. Taguchi, A. Chainani, Y. Takata, M. Yabashi, K. Tamasaku, Y. Nishino, T. Ishikawa, K. Kuga, N. Horie, S. Nakatsuji, S. Shin, Phys. Rev. Lett. 104 (2010) 247201.