Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019)
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Proc. Int. Conf. Strongly Correlated Electron Systems (SCES2019)
JPS Conf. Proc. 30, 011113 (2020)
https://doi.org/10.7566/JPSCP.30.011113

Local 4 f Electronic Structure in PrAg2In Studied by
Polarized X-Ray Absorption and Photoemission
Spectroscopy
Satoru Hamamoto1,2 , Shuhei Fujioka1,2 , Yuina Kanai-Nakata1,2 ∗ , Kohei Yamagami1,2 † ,Kentaro Kuga2 ‡ , Hidenori Fujiwara1,2 , Takayuki Kiss1,2 , Hiroyuki S. Suzuki3,4 ,Atsushi Higashiya2,5 , Atsushi Yamasaki2,6 , Shin Imada2,7 , Arata Tanaka8 ,Yukiharu Takeda9 , Yuji Saitoh9 , Kenji Tamasaku2 , Makina Yabashi2 ,Tetsuya Ishikawa2 , and Akira Sekiyama1,2
1

Graduate School of Engineering Science, Osaka University, Osaka 560-8531, JapanRIKEN SPring-8 Center (RSC), Hyogo 679-5148, Japan
3
National Institute for Materials Science (NIMS), Tsukuba 305-0047, Japan
4
Institute for Solid State Physics (ISSP), The University of Tokyo, Kashiwa 277-8581, Japan
5
Faculty of Science and Engineering, Setsunan University, Osaka 572-8508, Japan
6
Faculty of Science and Engineering, Konan University, Kobe 658-8501, Japan
7
College of Science and Engineering, Ritsumeikan University, Shiga 525-8577, Japan
8AdSM, Hiroshima University, Hiroshima 739-8530, Japan
9Materials Sciences Research Center, Japan Atomic Energy Agency (JAEA), Hyogo 679-5148,
Japan
2E-mail: shamamoto@decima.mp.es.osaka-u.ac.jp(Received September 17, 2019)
The electronic structure of PrAg2 In has been investigated by soft X-ray absorption spectroscopy(XAS) and linearly polarized hard X-ray photoemission spectroscopy (HAXPES). The Pr M4,5 XAS
shows that the Pr valence of PrAg2 In is fully trivalent. The experimental linear dichroism in Pr 3d5/2
core-level HAXPES of PrAg2 In along the [100] direction is well reproduced by spectral simulations
for the Γ3 doublet ground state.
KEYWORDS: PrAg2 In, 4 f orbital symmetry, x-ray absorption spectroscopy, photoemission
spectroscopy, linear dichroism

1.

Introduction

In 4 f electron systems, cubic Pr compounds have been studied widely because of various physical properties at low temperatures, such as the heavy fermion superconductivity [1], the multipole
ordering [2–4], and the quadrupole Kondo eﬀect [5–7]. Among the Pr systems, PrAg2 In with acubic Heusler-type crystal structure shows heavy-fermion behavior with the extremely large electronic specific heat coeﬃcient of γ ∼ 6.5 J/(mol·K2 ) [8]. When the site symmetry of the trivalent
Pr ion is a cubic symmetry, the ninefold J = 4 ground multiplet generally split into a singlet Γ1 ,a doublet Γ3 , a triplet Γ4 , and a triplet Γ5 by the cubic crystalline-electric-field (CEF) eﬀect. The
previous neutron studies have proposed that the PrAg2 In has the non-Kramers doublet Γ3 groundstate [9, 10], while there is no phase transition down to 50 mK [8]. The electrical resistivity shows∗

Present address: College of Science and Engineering, Ritsumeikan University, Shiga 525-8577, Japan
Present address: ISSP, The University of Tokyo, Kashiwa 277-8581, Japan‡
Present address: Toyota Technological Institute, Nagoya 468-8511, Japan†1■■■011113-1©2020 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
must maintain attribution to the author(s) and the title of the article, journal citation, and DOI.

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019)
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011113-2

JPS Conf. Proc. 30, 011113 (2020)+ log T -dependence above 100 mK and T 1/2 -dependence below 100 mK, which deviate from theFermi-liquid theory [11, 12]. The origin of the heavy-fermion behavior with the quite large γ is discussed as a quadrupole Kondo eﬀect for a non-Kramers doublet [5].
The 4 f CEF ground state is basic information on the strongly correlated electron systems. Experimentally, it is diﬃcult to detect the anisotropic 4 f charge distributions in cubic symmetry. Recently,
the linear dichroism (LD) in hard X-ray photoemission spectroscopy (HAXPES) has been reported asa powerful method revealing 4 f orbital symmetries of such systems [13–17]. In order to investigate
the Pr valence and the CEF ground state of PrAg2 In, we have performed Pr M4,5 X-ray absorption
spectroscopy (XAS) and linearly polarized HAXPES.

2.

Experiments

PrAg2 In single crystalline samples were grown by the Bridgman method. The XAS measurements were performed at the twin-helical undulator beamline BL23SU of SPring-8 [18]. The XAS
spectra were obtained in the total-electron-yield mode with an energy resolution better than 0.1 eV at50 K, and the base pressure was about 1.1 × 10−8 Pa. The HAXPES measurements were performedat BL19LXU of SPring-8 [19] using an MBS A1-HE hemispherical photoelectron spectrometer andtransmission-type phase retarders [20]. The PL (degree of linear polarization) of the polarizationswitched X-ray after the phase retarders was estimated as −0.90, corresponding to the vertically linear
polarization component of 95%. The photon energy and energy resolution were set to 7.9 keV and400 meV, respectively. The base pressure was about 1.0 × 10−7 Pa. We have performed ionic model
calculations including the full multiplet theory [21] and the local CEF splitting using the XTLS 9.0
program [22] in order to investigate the Pr valence and the CEF ground state. The atomic parameters,such as the 3d-4 f Coulomb and exchange interactions (Slater integrals) and the 3d and 4 f spinorbit couplings, have been obtained using Cowan’s code [23] based on the Hartree-Fock method. The
4 f -4 f Slater integrals have been obtained using Cowan’s code and their relations [24]. The 3d-4 f
and 4 f -4 f Slater integrals (3d and 4 f spin-orbit couplings) are reduced to 80% and 60% (99% and100%) to reproduce the Pr3+ 3d core-level photoemission spectra with final-state multiplet structuresincluding Pr3+ 3d3/2 spectra, respectively.

Pr M4,5 XAS
4+Intensity (arb. units)

BaPrO3 : Pr

3+Pr2O3 : Pr

3+Simulation : PrPrAg2In925

930

935940945
Photon Energy (eV)950955960

Fig. 1. Pr M4,5 XAS spectra of the tetravalent compound BaPrO3 [25], trivalent compound Pr2 O3 [25], Pr3+ion model [22], and PrAg2 In.
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Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019)
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JPS Conf. Proc. 30, 011113 (2020)

3.

Results and discussion

Figure 1 shows Pr M4,5 XAS spectra of the tetravalent compound BaPrO3 [25], trivalent compound Pr2 O3 [25], Pr3+ ionic model [22], and PrAg2 In. The XAS spectrum of PrAg2 In is significantly
diﬀerent from that of BaPrO3 . On the other hand, the spectral shape of PrAg2 In can be explained by
the multiplet structure of |3d9 4 f 3 ⟩ final state, which is well reproduced by atomic multiplet calculations [21]. This result suggests that the Pr valence of PrAg2 In is fully trivalent, which is consistent
with the eﬀective moment 3.65µB [8] close to 3.58µB for a free Pr3+ ion.
Figure 2(c) shows the polarization-dependent Pr3+ 3d5/2 HAXPES spectra of PrAg2 In and theirLD (defined as the diﬀerence of the spectral weight between the s- and p-polarization configurations)along the [100] photoemission direction compared with the simulated ones for the Γ5 , Γ3 , and Γ1states. The simulated polarization-dependent Pr3+ 3d5/2 spectra are shown in Fig. 2(b). Here, the polarized HAXPES spectra have been normalized by the spectral weight from the binding energy of 929
eV to 940 eV after subtracting the Shirley-type background from the raw spectra. A weak shoulder-[100](a) sample
[010]
60°

[100] dir.
ep-pol.
s-pol.

h(b)Simulation

p-pol.
s-pol.

(c)
PrAg2InPr 3d5/2
T = 10 K[100] dir.

3+

Sim.

Sim.

13

Normalized Intensity (arb. units)

Normalized Intensity (arb. units)

Pr 3d5/2[100] dir.

p-pol.
s-pol.

Linear Dichroism (×10)
Exp.
Sim. 5Sim. 3Sim. 
10Sim.

940

935
930
Binding Energy (eV)

925

5940

935930Binding Energy (eV)925

Fig. 2. (a) Geometry of the polarization-dependent HAXPES measurements in the [100] direction forPrAg2 In. (b) Simulated polarization-dependent 3d5/2 photoemission spectra of Pr3+ ions assuming the crystalfield-split ground state in cubic symmetry in the [100] direction. (c) Polarization-dependent Pr 3d5/2 core-level
HAXPES spectra and LD of PrAg2 In compared with the simulated LDs for the Γ5 , Γ3 , and Γ1 states in the[100] direction. The experimental LD is displayed in the energy region of the normalization (929∼940 eV).
The Shirley-type background has been subtracted from the raw spectra.
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JPS Conf. Proc. 30, 011113 (2020)

like spectral weight below 929 eV is ascribed to the |3d9 4 f 3 ⟩ final states, which is out of focus when
the spectra have been analyzed by the ionic Pr3+ model (|3d9 4 f 2 ⟩ final states). As shown in Fig. 2(c),the sign of the experimental LD at ∼932 eV is positive, whereas LD in the 933-937 eV region isvery subtle (nearly zero). The sign and magnitude of LD for the Γ5 state are completely inconsistent
with our experimental result. The experimental LD is strongly suppressed in comparison with thesimulated LD of the Γ1 state, thus ruling out the possibility of the Γ1 ground state. The observed LD
is quantitatively reproduced by the spectral simulation for the Γ3 state. Therefore, we conclude that
our experimental results support the Γ3 CEF ground state for PrAg2 In, which is consistent with theprevious report [10].

4.

Conclusion

We performed Pr M4,5 XAS and Pr 3d5/2 linearly polarized HAXPES for cubic PrAg2 In. The Pr
valence in PrAg2 In is a trivalent state since the experimental XAS spectrum is consistent with thePr3+ ion model calculations. The LD in Pr3+ 3d5/2 HAXPES indicates that the Pr3+ 4 f ground statein PrAg2 In is the Γ3 state.

acknowledgment
We are grateful to Y. Nakatani, S. Naimen, K. Yano, H. Yomosa, H. Aratani, K. Nagai, Y.
Aoyama, T. Hattori, M. Murata, C. Morimoto, and K. Nakagawa for supporting the experiments. S.
Hamamoto and Y. Kanai-Nakata were supported by the JSPS Research Fellowships for Young Scientists. The measurements were performed under the approval of BL23SU (Proposal Nos. 2014B3882
and 2016A3832), and BL19LXU (Proposals Nos. 2014B1305, 2015A1533, 20160034) at SPring-8.
This work was supported by a Grant-in-Aid for Scientific Research (JP16H04014, JP18K03512), anda Grant-in-Aid for Innovative Areas (JP16H01074, JP18H04317) from MEXT and JSPS, Japan.
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