Photon Factory Activity Report 2017 #35 (2018)

BL-4C, BL-8A, BL-8B, BL-11B/2012S2-005, 2015G549, 2016P006

Evidence for chiral crystal structure of RE3Tr4Sn13 (RE = La and Ce, Tr = Co and Rh)
Kazuaki Iwasa1,*, Yuka Otomo2, Kazuya Suyama2, Keisuke Tomiyasu2,
Hajime Sagayama3, Ryoko Sagayama3, Hironori Nakao3,
Reiji Kumai3, Yoshinori Kitajima3, and Youichi Murakami3
1
Frontier Research Center for Applied Atomic Sciences & Institute of Quantum Beam Science,
Ibaraki University, 162-1 Shirakata, Tokai, Ibaraki, 319-1106, Japan2
Department of Physics, Tohoku University, 6-3 Aramaki-aza-Aoba, Sendai, 980-8578, Japan
3
Condensed Matter Research Center and Photon Factory, Institute of Materials Structure Science,High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, 305-0801, Japan
1 Introduction
Electronic states in chiral and noncentrosymmetricstructures are recent attractive issues of condensed-matterphysics. For example, magnetic skyrmion [1] andsuperconductivity associated with the Rashba-type spinorbit interaction [2] have been investigated extensively.
We have studied the 3–4–13 class of materials
crystallizing into the Yb3Rh4Sn13-type structure, which
are categorized under the cubic space group Pm-3n (No.
223). (CaxSr1-x)3Ir4Sn13 and (CaxSr1-x)3Rh4Sn13 exhibit
superconductivity below approximately Tc = 5 K, whichis enhanced by the Ca substitution suppressing structuralphase transition at higher temperatures (~100 K) [3, 4].
The Ce-based compounds are also interesting because ofelectronic hybridization effect as well as structural
instability. Ce3Co4Sn13 is hypothesized to be a heavy
fermion system. The specific heat divided by temperaturereaches approximately 4 J/(K2 mol-Ce) at approximately
1 K [5-8]. The electrical resistivity exhibits a slight kinkat TD ≃ 160 K. This behavior at TD was suggested to be asignature of charge density wave (CDW) formation [9].
Below TD, the electrical resistivity is insensitive totemperature, and it increases below 15 K. This feature isin marked contrast to metallic La3Co4Sn13, whichbecomes a superconductor below 2.85 K [6]. Specificheat data of Ce3Co4Sn13 shows a broad peak at 0.7 K, andno magnetic ordering has been identified down to 0.4 K[9, 10]. Ce3Rh4Sn13 and La3Rh4Sn13 also exhibit similar
behaviors as those of Ce3Co4Sn13 and La3Co4Sn13,
respectively. The electrical resistivity of Ce3Rh4Sn13 ismuch higher than that of La3Rh4Sn13 undergoing a
superconducting phase transition at 2-3 K [11, 12]. The
specific-heat data of Ce3Rh4Sn13 show a peak at 1.2 K and
2 K, which had been considered to indicate magnetic
ordering phase transitions [11, 13, 14]. On the other hand,from the specific heat divided by temperature, theSommerfeld coefficient was estimated to be 0.4 J/(K2mol-Ce) at 0.1 K. Crystal structure of Ce3Rh4Sn13 andLa3Rh4Sn13 have not fully solved, despite that x-ray
diffraction spots characterized by the wave vector q =(1/2, 1/2, 0) were suggested to appear even at room
temperature [15-17].
In order to clarify the structural and electronic
properties of RE3Tr4Sn13 (RE = La and Ce, Tr = Co andRh), we conducted x-ray scattering measurements using

the Photon Factory (PF) instruments. The results were
published in several papers [18, 19]. The phase transition
from the high-temperature Pm-3n structure (phase I) to
the low-temperature I213 (phase I’) was evidenced forthese 3-4-13 compounds. Complementary x-ray
absorption spectra (XAS) and neutron scattering studies
were also performed, and the results will also bepresented later.
2 ExperimentSingle-crystalline samples (dimensions of 7 mm orless) of RE3Tr4Sn13 (RE = La and Ce, Tr = Co and Rh)
were synthesized by the molten Sn-flux method [6].
Starting materials were rare earth elements (3N), Co andRh (4N), and Sn (5N).
For indentifying the structural transformation, x-ray
diffraction experiments were performed using a fourcircle single-crystal diffractometer with a rotating anodesource of Mo Kα radiation, which are installed in theuniversity laboratories. A helium gas closed-cycle
refrigerator was used to cool down the samples. Precise
structural determination was performed using theimaging-plate x-ray diffractometer installed at BL-8A and
8B of PF, KEK. Incident x-ray energies of 18.0 keV wereselected, and a helium-gas-flow cryostat was used tocontrol the sample temperatures. Structural analysis was
carried out using softwares: Rigaku Rapid for evaluating
the structure factors, Sir2004 for a direct method, and
SHELX for refinement analysis in WinGX suite [20].
Measurements of x-ray absorption spectra (XAS) as afunction of incident light energy were performed by using
the instruments at BL-4C and BL-11B. We adopted a
setup of x-ray emission from the 110 surface of thesingle-crystalline sample. Magnetic susceptibity wasmeasured using a SQUID magnetometer at the
Department of Physics, Tohoku University.
3 Results
Figure 1 shows temperature dependencies ofsuperlattice reflections at the scattering vector Q = (6.5,
6.5, 0) from the single-crystal samples of La3Co4Sn13 andCe3Co4Sn13. Below TD = 160 K, both compounds
transform into a superlattice structure characterized by q
= (1/2, 1/2, 0), indicating doubling of the unit cell above
TD. Such second-order phase transition was also observed

Photon Factory Activity Report 2017 #35 (2018)

for La3Rh4Sn13 and Ce3Rh4Sn13, the transition temperatureof which is 350 K. The common TD for the La- and Cebased compounds indicates that the structural instability
is associated with electronic states originating from the Tr
and Sn atoms. According to the band calculation studies,
covalent bonding between the neighboring Tr and Sn
carries relatively large charge density, which might berearranged across the structural transitions [21]. We alsomeasured magnetic susceptibilities. Even in the lessmagnetic La-based compounds, the susceptibility
increases with decreasing temperature across TD. This fact
supports that the scenario of covalent bonding instability
is much favorable than the CDW formation.

Fig. 2: X-ray diffraction spots on the imaging plates from
Ce3Co4Sn13 at 200 K (top panel) and at 30 K (bottom
panel with superlattice reflections).

Fig. 1: Temperature dependencies of integrated counts ofthe superlattice reflections at Q = (6.5, 6.5, 0) of
Ce3Co4Sn13 and La 3Co4Sn13.
We measured x-ray diffraction intensities using
imaging plates installed at BL-8A and 8B. The data of
Ce3Co4Sn13 measured at 200 and 30 K are shown in top
and bottom panels of Fig. 2, respectively. The lowtemperature data clearly show superlattice peaks. As
mentioned above, the structural refinement procedures
based on the WinGX suite were carried out for these data.
The high-temperature phase-I data are reproduced by the
Pm-3n structure, as proposed in previous studies. The
low-temperature phase-I’ data do not show any clear peak
splitting. Thus, we examined structural models forvarious cubic space groups that are subgroups of Pm-3n,
which are allowed for the second-order transition. We
concluded that all of the phase-I’ structure of RE3Tr4Sn13(RE = La and Ce, Tr = Co and Rh) are well reproduced by
the I213 space group. Schematic view of the determined
crystal structures in phases I’ is shown in Fig. 3.
XAS spectra were measured using BL-4C and BL-11B
in order to investigate electronic states relevant to thestructural phase transition. The Co K edge spectrum in
Ce3Co4Sn13 and the Rh L edge spectra in Ce3Rh4Sn13
depend on temperature, while the Ce L3 edge does notshow clear temperature dependence. These experimental
results are consistent with the charge rearrangement
scenario for the structural transformation.

We also performed neutron diffraction measurement of
Ce3Rh4Sn13 down to 50 mK, in order to reveal whether
the magnetic ordering occurs or not [19]. No clear
magnetic long-range order was detected. Therefore,
Ce3Co4Sn13 and Ce3Rh4Sn13 are considered to beparamagnetic semimetal systems in phase I’. In addition,
inelastic neutron scattering measurements revealed that
two inequivalent crystal-electric-field (CEF) level
schemes of the Ce 4f1 electron appear in Ce3Co4Sn13,
which are consntent with the inequivalent atomic sites of
the Ce ions, Ce1 and Ce2, as shown in Fig. 3 [22]. The
CEF ground state doublet mediates spin fluctuation withcharacteristic energy of 0.5 meV, which emerges with theelectrical-resistivity enhancement below 15 K [6].

Fig. 3: One of enantiomers of chiral crystal structure of
Ce3Co4Sn13 in phase I’ below TD = 160 K [18]. The same
crystal-structure symmetry also appears in phase I’ of
La3Co4Sn13 below TD = 160 K [18] and RE3Rh4Sn13 (RE :La and Ce) below TD = 350 K [19].

Photon Factory Activity Report 2017 #35 (2018)

4 Discussion
The low-temperature phase I’ of RE3Tr4Sn13 (RE = La
and Ce, Tr = Co and Rh) is characterized by the chiralstructure. It is noteworthy that the chiral symmetry is
proposed to protect topologically the Weyl fermion state[23]. Because of a crossing of linear electron band of the
Weyl fermion at particular momentum points, a threedimensional semimetal state can be realized if the Fermi
energy is close to the crossing point. Therefore, theparamagnetic semimetal state in the Ce-based compounds
is expected to be the Weyl semimetal in which the large
band gap is formed by the c-f hybridization (Kondo
semiconductor), and the topologically protected linear
band mediates the semimetal conductivity. In addition,
the superconductivity in the La-based compounds occurs
in the chiral lattice, which means noncentrosymmetricsuperconductivity as in the CePt3Si [2]. Therefore, we
conclude that new strongly correlated electron systems
are found in the 3-4-13 series.
5 Summary
The present quantum-beam-scattering study including
the synchrotron radiations evidences the chiral symmetry
phase in RE3Tr4Sn13 (RE = La and Ce, Tr = Co and Rh). It
is a further issue to search for topological features ofelectronic state in these materials.
Acknowledgement
We thank M. Onodera, K. Kaneko, S. K. Goh, D. T.
Adroja, and Z. Fisk for collaborations and fruitful
discussions. The neutron scattering studies wereconducted under collaboration with J.-M. Mignot, A
Gukasov, B. Gillon, and F. Damay at the Laboratoire
Léon Brillouin, CEA-Saclay, France, and S. OhiraKawamura and K. Nakajima at the Materials and Life
Science Experimental Facility, J-PARC. This study is
supported in part by JSPS KAKENHI [Scientific
Research (S) (No. 21224008), Scientific Research (A)(No. 23244068), Exploratory Research (No. 24654080)],
Scientific Research on Innovative Areas “3D Active-Site
Science" (JP17H05209), Scientific Research on
Innovative Areas “J-Physics"(JP15H05885)], and the
JSPS FIRST program “Quantum Science on Strong
Correlation.” Experiments at PF were based on theapproved proposals 2012S2-005, 2015G549, and2016P006.
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* kazuaki.iwasa.ifrc@vc.ibaraki.ac.jp