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, 011101 (2020)
https://doi.org/10.7566/JPSCP.30.011101

Ground State Local 4 f Symmetry of CeAgSb2
Probed by Linearly Polarized Hard X-ray Photoemission
H. Fujiwara1,2 , Y. Kondo1,2 , S. Hamamoto1,2 , Y. Kanai-Nakata1,2 ∗ , K. Kuga2 † ,A. Yamasaki2,3 , A. Higashiya2,4 , T. Kadono2,5 , S. Imada2,5 , T. Kiss1,2 , A. Tanaka6 ,K. Tamasaku2 , M. Yabashi2 , T. Ishikawa2 , T. Ebihara7 , and A. Sekiyama1,2
1

Graduate School of Engineering Science, Osaka University, Osaka 560-8531, JapanRIKEN SPring-8 Center, Hyogo 679-5148, Japan
3
Faculty of Science and Engineering, Konan University, Kobe 658-8501, Japan
4
Faculty of Science and Engineering, Setsunan University, Osaka 572-8508, Japan
5
Department of Physical Sciences, Ritsumeikan University, Shiga 525-8577, Japan
6
Department of Quantum Matter, ADSM, Hiroshima University, Hiroshima 739-8530, Japan
7
Department of Physics, Shizuoka University, Shizuoka 422-8529, Japan
2E-mail: fujiwara@mp.es.osaka-u.ac.jp(Received September 17, 2019)
We have performed a linearly polarized hard X-ray photoemission (HAXPES) for CeAgSb2 in theparamagnetic phase. The Ce 3d5/2 core-level HAXPES spectra show the linear dichroism, reflecting
the orbital anisotropy of the 4 f states. The ground state symmetry of the local 4 f electronic states is
successfully determined as Γ6 by using the atomic multiplet calculation based on an ionic model.
KEYWORDS: magnetism, quantum criticality, hard X-ray photoemission, linear dichroism

1.

Introduction

The series of tetragonal Ce systems shows the interesting low temperature properties such as
exotic superconductivity accompanying with mass enhancement in CeCu2 Si2 [1]. These phenomena
have often been explained by the competition of the interactions between local-moment ordering
due to the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the singlet formation between
the 4 f and conduction electrons. CeAgSb2 is a ferromagnet below a Curie temperature of T C of 9.7
K at ambient pressure with the crystal structure of tetragonal ZrCuSi2 -type [2, 3]. The Sommerfeld
coeﬃcient of γ is 46 mJ/(mol·K2 ), which gives the moderate mass enhancement factor of 21 for
LaAgSb2 [4]. The soft X-ray angle resolved photoemission experiments reported that the Ce 4 f states
were almost localized and the experimental band structures are well explained by the band structure
calculation for LaAgSb2 [5], suggesting that the electronic structure is basically described as Ce3+
ionic picture.
The low temperature properties of Ce compounds are determined by the ground state (GS)symmetry of the 4 f states in Ce3+ ions with J = 5/2 in the tetragonal crystalline electric field(CEF). The GS in the tetragonal CEF√ is described as one of√the three Kramers doublets equatedto |Γ6 ⟩ = |Jz = ± 21 ⟩, |Γ17 ⟩ = α |± 52 ⟩ − 1 − α2 |∓ 23 ⟩, and |Γ27 ⟩ = 1 − α2 |± 25 ⟩ + α |∓ 23 ⟩. The anisotropy
parameter α2 along the c-axis of the Γ7 states can be determined by linearly polarized X-ray absorption spectroscopy (XAS) [5–8]. However, it is insensitive for the in-plane rotational symmetry, which∗†

Present address: Department of Physical Sciences, Ritsumeikan University, Shiga 525-8577, Japan
Present address: Toyota Technological Institute, Nagoya 468-8511, Japan1■■■011101-1©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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011101-2

JPS Conf. Proc. 30, 011101 (2020)

is described by the ± sign of the linear combination of the |± 25 ⟩ and |± 32 ⟩ states, due to the fundamental limitation of the dipole selection rule in the tetragonal systems. This problem has been overcomeby the linearly polarized angle-resolved hard X-ray photoemission (HAXPES) with an additional parameter of the detection direction of the photoelectrons [9–14]. This technique works to determine
the GS symmetry of tetragonal CeCu2 Ge2 , which shows an antiferromagnetic√√ order below a Néeltemperature (T N ) of 4.15 K at ambient pressure [15], as |Γ17 ⟩ = 0.45 |± 25 ⟩ − 0.55 |∓ 32 ⟩ [16]. This
motivates us to probe the ground state 4 f symmetry of CeAgSb2 by HAXPES, whose ground states
were reported as the Γ6 symmetry [5]. In this study, we have performed linearly polarized HAXPES
for CeAgSb2 in the paramagnetic phase to establish the HAXPES as a probe of the GS symmetry of
the tetragonal Ce systems.

2.

ExperimentSingle-crystalline CeAgSb2 samples were grown by the Sb-self-flux method. The HAXPES experiments were performed at BL19LXU of SPring-8, where a MBS A1-HE hemispherical electronanalyzer was installed [11]. The energy resolution was set to 400 meV, and the measurement temperature was set to 15 K (above T C ), which was suﬃciently lower than the excited states at 150 K
obtained from the inelastic neutron scattering [3]. The samples were cleaved to expose clean (001)surfaces, and the base pressure was 1.8 × 10−7 Pa. The photoelectron detection direction was set in the[001] direction as shown in Fig. 1(a). The linear polarization of the X-ray was transformed from horizontal to vertical polarization by means of the transmission-type diamond phase retarder with p- ands-polarization configurations, respectively [11]. The degree of linear polarization of the polarizationswitched X-ray was estimated as −0.96, corresponding to the vertically linear polarization componentof 98%.

3.

Results and Discussion

Figure 1(b) displays the overview of the Ce 3d, Sb 3p and Sb 3s core-level spectra obtainedby the s and p configurations, which are normalized by the photon flux. The peak intensities of theSb 3s and Sb 3p states are drastically suppressed in the s-polarization configuration in contrast to
those of the Ce 3d states. This is due to the anisotropic photoionization cross section (PICS) forthe linearly polarized X-ray [17–19]. However, the Ce 3d5/2 spectra shows the noticeable diﬀerencein shape around the peak top by changing the polarization in Fig. 2(a). This is not possible to beexplained by the intensity diﬀerence due to the asymmetry factor of the PICS. By subtracting thebackground (dashed line) and normalizing the spectral weight in the area ranging from 873 to 890
eV, the linear polarization dependence in the Ce 3d5/2 spectra is clearly observed in Fig. 2(b). The
intensity obtained with the s- and p-polarized configurations labeled as I s and I p shows the diﬀerenceat around 884.5 and 882.5 eV indicated by the vertical bars. Moreover, the polarization dependenceof the Ce 3d spectral shape of CeAgSb2 diﬀers from that of CeCu2 Ge2 around 884.5 eV. This ishighlighted in the comparison of the linear dichroism (LD) spectrum, which is defined as I s -I p . Notethat the LD is due to the anisotropic Coulomb and exchange interactions between the 3d hole and 4 felectrons, reflecting the anisotropic charge distribution of the Ce 4 f states deviated from the sphericalsymmetry. The dichroic signal of CeAgSb2 at 885 eV show the positive peak, while the negative peakshows up at 883 eV. This trend is opposite for the LD spectrum of CeCu2 Ge2 with the Γ7 symmetry,suggesting that the local 4 f states of CeAgSb2 is in the Γ6 symmetry.
Figure 2(c) shows the spectral simulation using full multiplet calculations for Ce3+ 3d10 4 f 1 →3d9 4 f 1 +−e electric-dipole transitions, respectively, implemented by the XTLS 9.0 program [20]. The atomic
parameters of the 3d-4 f Coulomb interactions, the 3d and 4 f spin-orbit couplings, were obtained
from the Hartree-Fock values for Ce3+ [21] by taking into account for a reduction factor of 76%2■■■

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019)
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JPS Conf. Proc. 30, 011101 (2020)(a) Experimental geometry(b)sample
[110]
[001]

60

e-s-pol.
p-pol.
hνFig. 1. (a) Schematic view of the experimental geometry (b) The overview of the core level spectra for Ce
3d, Sb 3p and Sb 3s states in CeAgSb2 . The spectra are normalized by the photon flux for s- and p-polarized
configurations.

(a)

(c)

~

Intensity (a.u.)

890

885

880

875
(b)

~

890

885

880

875
888
Binding Energy (eV)884880876

Fig. 2. (a) The Ce 3d5/2 core level spectra of CeAgSb2 . The dashed lines denote the background signals. (b)The linear polarization dependence of the Ce 3d5/2 spectra obtained at the s- and p-polarized configurations andthe linear dichroism for CeAgSb2 and CeCu2 Ge2 . The vertical bars are guide to the eye. (c) Spectral simulations
based on the Ce3+ ionic model assuming the Γ6 symmetry and the Γ7 symmetry with α2 = 0.45 [16].

(99%) for the 3d-4 f interactions (3d spin-orbit coupling). The simulation based on the ionic model
assuming the Γ6 symmetry captures the linear polarization dependence of the experimental spectrain fig.2(c) (top). Moreover, the experimental LD spectrum (bottom) is properly explained by the Γ6symmetry. On the other hand, the simulated spectrum assuming the Γ7 symmetry shows the opposite
sign to the experimental LD spectrum of CeAgSb2 . Since this feature is irrespective to the α2 values3■■■Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019)
Downloaded from journals.jps.jp by 157.1.136.5 on 10/06/24011101-4

JPS Conf. Proc. 30, 011101 (2020)(not shown here), the possibility of the Γ7 symmetry is clearly excluded. The CEF-split GS symmetryof CeAgSb2 is thus successfully determined as Γ6 by using HAXPES-LD, which is consistent withthe results obtained by XAS-LD [5]. These results show that the HAXPES-LD is capable for probing
all possible symmetry of the CEF-split GS of local 4 f states in the tetragonal Ce systems not only forc-axis anisotropy but also in-plane symmetry, giving the strong impact for the orbital physics in thestrongly correlated Ce systems.

4.

Summary

We have performed the HAXPES-LD for CeAgSb2 in the paramagnetic phase. The Ce 3d5/2 corelevel spectra show the LD for the multiplet structures, reflecting the orbital anisotropy of the 4 f states,
The experimental LD spectrum is well reproduced by the atomic multiplet calculation based on theionic model assuming the Γ6 symmetry. These results show that the HAXPES-LD is a powerful tool
to precisely determine the local 4 f symmetry in the CEF-split GS tetragonal Ce systems.

5.

Acknowredgement

We thank S. Takano, T. Kashiuchi, M. Kawada, and K. Nakagawa for supporting the experiments. S. H. and Y. K.-N. were supported by the JSPS Research Fellowships for Young Scientists.
HAXPES experiments were performed at BL19LXU in SPring-8 with the approval of RIKEN (Proposals No. 20180026 and 20180076). This work is supported by a Grant-in-Aid for Scientific Research (16H04014, 18K03512), and a Grant-in-Aid for Innovative Areas (16H01074, 18H04317)
from MEXT and JSPS, Japan.
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