# Fileset

[PrCdNi4_ver18_Supplement_20250324.pdf](https://mdr.nims.go.jp/filesets/98f61a93-8378-415c-982b-f06aef1d76a5/download)

## Creator

Yuka Kusanose, Yasuyuki Shimura, Kazunori Umeo, Naomi Kawata, Toshiro Takabatake, [Taichi Terashima](https://orcid.org/0000-0001-9239-0621), [Naoki Kikugawa](https://orcid.org/0000-0003-3975-4478), [Takako Konoike](https://orcid.org/0000-0002-6037-5782), [Yuya Hattori](https://orcid.org/0000-0002-3805-4659), Kazuhiro Nawa, Hung-Cheng Wu, Taku J. Sato, Takahiro Onimaru

## Rights

©2025 American Physical Society[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Multipolar Phase Transition in a 4f 2 fcc Lattice Compound PrCdNi4](https://mdr.nims.go.jp/datasets/9323d987-de8b-4169-adbf-4923d8b830c9)

## Fulltext

Supplemental Materials for‘Multipolar Phase Transition in a 4 f 2 fcc Lattice Compound PrCdNi4’Yuka Kusanose,1, 2, ∗ Yasuyuki Shimura,1 Kazunori Umeo,3 Naomi Kawata,3 Toshiro Takabatake,1 Taichi Terashima,4 NaokiKikugawa,5 Takako Konoike,4 Yuya Hattori,5 Kazuhiro Nawa,6 Hung-Cheng Wu,6, † Taku J. Sato,6 and Takahiro Onimaru11Department of Quantum Matter, Graduate School of Advanced Science and Engineering,Hiroshima University, Higashi-Hiroshima 739-8530, Japan2Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan3Natural Science Center for Basic Research and Development (N-BARD),Hiroshima University, Higashi-Hiroshima 739-8526, Japan4Research Center for Materials Nanoarchitectonics (MANA),National Institute for Materials Science (NIMS), Tsukuba 305-0003, Japan5Center for Basic Research on Materials (CBRM), National Institute for Materials Science (NIMS), Tsukuba 305-0003, Japan6Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan(Dated: March 24, 2025)I. SAMPLE CHARACTERIZATIONBackscattered electron images and powder x-ray diffraction patterns for samples A and B of polycrystalline PrCdNi4 areshown in Figs. S1 and S2, respectively. It is noted that a polycrystalline sample from batch A was selected because it containsmultiple phases. This sample includes not only PrCdNi4 but also impurity phases such as PrNi2Cd20 and PrNi5, which isconsistent with the emergence of additional peaks measured by the powder x-ray diffraction shown in Fig. S2. The atomicecomposition of the PrCdNi4 phase was determined by electron-probe microanalysis (EPMA) to be Pr0.99(1)Cd1.01(1)Ni3.87(3). Onthe other hand, another sample from batch B is nearly single-phase, but it contains small amounts of PrNi5 and Cd impurities. Asshown in Fig. S2, there are some peaks from PrNi5 in the powder x-ray diffraction pattern, although the peaks from PrNi2Cd20are less pronounced. The composition for the PrCdNi4 phase of sample B was determined to be Pr0.97(1)Cd1.03(1)Ni3.84(6) byEPMA. The compositions of samples A and B are similar to Pr1.00(1)Cd1.00(1)Ni3.89(4) of the sample batch for measurements, andthey are close to the stoichiometric ratio compared with Pr0.94(1)Mg1.06(1)Ni3.86(2) in Ref. [1], which shows no phase transition.FIG. S1. Backscattered electron images of the samples A and B of PrCdNi4. Sample A contains PrCdNi4 along with impurityphases, such as PrNi2Cd20 and PrNi5, whereas sample B is nearly a single phase.∗ kusanose.yuka.p7@f.mail.nagoya-u.ac.jp† Present address: National Sun Yat-sen University2 !"!#$%&$'(%)*+ !"*,-./*0$(%/1 2! !!3!4!5!2!2 !+6&718-96:(5*;   2!!22!222<  5!!<< 52!522"  55!552"< 42!"<<422=  45!452""<<<<=< 555"" 8-96:(5*>,?>/  8-:("* 8-:(2962!8-96:(5*@FIG. S2. Powder X-ray diffraction patterns of PrCdNi4 (A) and (B). The lower is the simulated pattern with the cubic MgSnCu4-type structure. Both samples can be indicated by cubic MgSnCu4-type structure, whire additional peaks due to impurity phasesshown with triangle.The impurity phase of PrNi5 was also observed in the powder neutron diffraction pattern at T = 2.0 K, as indicated by a star inFig. S3. We conducted the Rietveld analysis considering the two phases, PrCdNi4 and PrNi5, and determined their molar ratioto be PrCdNi4:PrNi5 = 98.1(1) : 1.9(1). It is noted that the peaks around 2θ = 64 and 75 deg. were excluded from the analysisbecause they were due to aluminum from the sample container. Since neutrons can penetrate the samples, this result provides areasonable stoichiometric ratio for the bulk samples in the macroscopic measurements. !!!"!!!#!!!$!!!%!!!!&!'!(! !"!#!$!%!!)*+,-." ./0/%#1'/2345%%%$$!#%%$$$)*+,-.")*-.  !/0/$1!/6/+7891!""#$%&FIG. S3. Powder neutron diffraction patterns of PrCdNi4 at T = 2.0 K. The black line represents the fits to the data with theRietveld analysis. The blue line shows the difference between the data and calculation. The brown and green bars indicate thescattering angles for the nuclear Bragg peaks of PrCdNi4 and PrNi5.3In Table S1, the structural parameters of PrCdNi4 obtained from the Rietveld profile fitting analysis of neutron powder diffrac-tion patterns for T = 2.0 and 0.32 K, shown with the black solid lines in Fig. 7 of the main text, are presented, along with thereliable factors for the fitting. The lattice parameter at 0.32 K decreases by 0.23% compared with the value at 273 K determinedby the single-crystal X-ray analysis described in the next section.Table S1: Structural parameters of PrCdNi4 refined by the Rietveld profile fitting analysis of neutron powder diffraction patterns.The space group is F4̄3m (#216), where the Pr atoms occupy the 4a site at (0, 0, 0), the Cd atoms the 4c site at (1/4, 1/4, 1/4),and the Ni atoms 16e site at (xNi, xNi, xNi) with Z = 4.0.32 K 2.0 KLattice parametersa (Å) 7.1112(3) 7.1114(1)V (Å3) 359.61(3) 359.644(9)xNi 0.6278(4) 0.625(2)Reliable factorRp 4.74 5.20Rwp 6.24 6.75Re 5.40 5.36S 1.15 1.264II. SINGLE-CRYSTAL X-RAY STRUCTURAL ANALYSISTo identify the crystal structure, the single-crystal x-ray structural analysis was performed at 273 K with Mo Kα radiation,λ = 0.071073 nm, monochromated by a multilayered confocal mirror using a Bruker APEX-II ULTRA CCD area-detectordiffractometer at N-BARD, Hiroshima University. Crystallographic parameters and details for the measurement, data collection,and refinement of the single-crystal X-ray diffraction experiment are described in Tables S2 and S3.Table S2: Information of the measurement, data collection, and refinement of the single-crystal x-ray diffraction experiment forPrCdNi4.Crystal system Cubic MgSnCu4Space group F4̄3m (#216)a (Å) 7.12758(4)V (Å3) 362.098(3)Z 4Dimensions (mm3) 0.21 × 0.14 × 0.08Temperature (K) 293Radiation, λ (nm) Mo-Kα, 0.0710732θ range (◦) 9.908 – 89.674µ (mm−1) 39.061Data collectionMeasured reflections 15017Unique reflections 186h −14 ≤ h ≤ 14k −14 ≤ k ≤ 14l −14 ≤ l ≤ 14Refinement∆ρmax/∆ρmin (eA−3) 1.50/−1.62GoF 1.257Reflections/parameters 186/7R1 0.0157wR2 0.0412Table S3: Crystallographic parameters for PrCdNi4 determined at 273 K. Ueq is the isotropic displacement parameter defined as1/3 of the trace of the orthogonalized Ui j tensor.Cubic MgSnCu4-typeSpace group: F4̄3m (#216)a = 7.12758(4) Å, V = 362.098(3) Å3, Z = 4Atom Site x y z Occ. Ueq (Å2)Pr 4a 0 0 0 1 0.0071(2)Cd 4c 0.25 0.25 0.25 1 0.0041(2)Ni 16e 0.62376(5) 0.62376(5) 0.62376(5) 1 0.0052(2)5III. PHONON CONTRIBUTION TO THE SPECIFIC HEATFigure S3 shows the temperature dependence of the specific heat C(T ) of PrCdNi4 from 2 K to 300 K. The C(T ) data increasewith elevating temperatures and approach the Dulong-Petit value of 3nR = 149.7 J/K mol, where n = 6 is the number of atoms performula unit and R the gas constant. The inset displays the C/T 3 plots with the logarithmical scale. The C/T 3 data increase oncooling. The (red) solid curve is a fit to the C/T 3 data between 50 and 300 K by adopting the Debye model for acoustic phononmodes [2] with the Debye temperatures of θD = 270.7(6) K. Since the acoustic phonon contribution to C(T ) is proportional to T 3at lower temperatures, the calculated C/T 3 curve approaches a constant on cooling below 20 K. Thereby, the difference betweenthe data and the calculated curve for T < 50 K is ascribed to the electronic and magnetic contributions due to, respectively, theconduction electrons and the 4 f 2 electrons of the Pr ion. The value of θD = 270.7(6) K is lower than that of θD = 300.3(6)K for an isostructural LaMgNi4 [1]. This is reasonable because the molecular weight of PrCdNi4 is much heavier than that ofLaMgNi4. !" ""!"" ##$%&'#()*+,""-"" """!#$'+./01234#5,67*)89:;<=3=./01234- " "#"!$" $ ":,%&'4# ()*+ "  "" ,""%6#>##-?"@?$A+#'FIG. S4. Temperature variation of the specific heat of PrCdNi4. The inset shows the C/T 3 plot with respect to the logarithmictemperature scale. The (red) solid lines are simulated by adopting the Debye model with a Debye temperature of θD = 270.7(6)K.[1] Y. Kusanose, T. Onimaru, G.B. Park, Y. Yamane, K. Umeo, T. Takabatake, N. Kawata, and T. Mizuta Jpn. J. Phys. Soc. Jpn. 88, 083703(2019).[2] C. Kittel, Introduction to Solid State Physics, 8th ed..,, John wiley & Sons,, 2005, p.112, Chap. 5.