Superconductivity in a Misfit Phase That Combines the Topological CrystallineInsulator Pb1−xSnxSe with the CDW-Bearing Transition Metal Dichalcogenide TiSe2

Huixia Luo1+, Kai Yan2, Ivo’s Pletikosic3,4, Weiwei Xie1,Brendan F. Phelan1, Tonica Valla3, and Robert J. Cava1†

1Department of Chemistry, Princeton University, Princeton, NJ 08544, U.S.A.2School of Engineering, Brown University, Providence, RI 02912, U.S.A.

3Condensed Matter Physics and Materials Science Department, Brookhaven National Lab,Upton, NY 11973, U.S.A.

4Department of Physics, Princeton University, Princeton, NJ 08544, U.S.A.

(Received March 19, 2016; accepted April 15, 2016; published online May 13, 2016)

We report the characterization of the misfit compound (Pb1−xSnxSe2)1.16(TiSe2)2 for 0 ≤ x ≤ 0.6, in which a [100]rocksalt-structure bilayer of Pb1−xSnxSe, which is a topological crystalline insulator in bulk form, alternates with adouble layer of the normally non-superconducting transition metal dichalcogenide TiSe2. The x dependence of Tcdisplays a weak dome-like shape with a maximum Tc of 4.5K at x = 0.2; there is only a subtle change in Tc at thecomposition where the trivial to topological transition occurs in bulk Pb1−xSnxSe. We present the characterization of thesuperconductor at x = 0.4, for which the bulk Pb1−xSnxSe phase is in the topological crystalline insulator regime. For thismaterial, the Sommerfeld parameter γ = 11.06mJmol−1 K−2, the Debye temperature ΘD = 161K, the normalizedspecific heat jump value ΔC=γTc = 1.38 and the electron–phonon constant value λep = 0.72, suggesting that (Pb0.6-Sn0.4Se)1.16(TiSe2)2 is a BCS-type weak coupling superconductor. This material may be of interest for probing theinteraction of superconductivity with the surface states of a topological crystalline insulator.

1. Introduction

A broad family of layered ternary chalcogenides, the so-called misfit compounds, has recently been reported. Theyare generally described as [(MX)1þx]m(TX2)n, where M ¼ Sn,Pb, Sb, Bi, or Ln (lanthanide); T ¼ Ti, V, Cr, Nb, Mo, Ta, orW; X ¼ S, Se, or Te; 0:08 < x < 0:28; and m and n areintegers indicative of the number of MX rocksalt doublelayers stacked in an alternating fashion with TX2 dichalco-genide layers (n and m ¼ 1; 2; 3; 4).1–8) The MX and TX2layers have different symmetry and periodicity, matchingin size in one crystallographic in-plane direction but notmatching (i.e., misfitting) in the second in-plane direction,yielding the oddly non-stoichiometric formulas. The misfitis accommodated at the interface between close packedchalcogen layers in the TX2 part and the polarizable MXlayers. The individual rocksalt and dichalcogenide layers inthe misfit compounds are somewhat distorted from those ofthe constituent simple MX and TX2 materials,8) meaning thatthe electronic structures of the constituent layers are likelysimilar but not identical to those of the individual bulk MXand TX2 compounds. Our angle resolved photoemissionspectroscopy (ARPES) data, described below, shows forexample that charge is transferred from the MX layers to theTX2 layers in the current case.

The wide variations in M, T, X, m, and n allowed in thefamily lead to many different physical properties.5,9–16) Thecurrent case involves a misfit phase based on the stacking of[100] PbSe double layers and [001] TiSe2 layers. PbSe isa trivial semiconductor (i.e., the sequence of the electronicbands near the Fermi energy is as expected in a simpleelectronic picture) and has a direct band gap of 0.27 eV atroom temperature.17,18) Recently it has been shown, however,that the bulk Pb1�xSnxSe rocksalt compound undergoes aninversion of the electronic band energy sequence at x ¼ 0:23and becomes a topological crystalline insulator, with, corre-spondingly, protected topological surface states.18) When

PbSe is stacked in a misfit compound with NbSe2, theintrinsic Tc of NbSe2 (7K) is degraded and superconductivityresults for (PbSe)1.14(NbSe2)n for n ¼ 2 and 3 at 3.4 and4.8K respectively, with no reported superconductivity forn ¼ 1 down to 2K.19) When stacked with non-superconduct-ing 1T-TiSe2,20–23) on the other hand, the resulting misfitcompound (PbSe)1.16(TiSe2)2 is reported to be a super-conductor with Tc ¼ 2:3K.24) Motivated by these observa-tions, here we report the superconductivity that results whenSn partially substitutes for Pb in the (Pb1�xSnxSe)1.16(TiSe2)2misfit compound solid solution, in order to determinewhether the superconductivity is still present at thecomposition in the MX layers where bulk Pb1�xSnxSe is atopological crystalline insulator. It is superconductor, andwe observe only a subtle change in Tc vs x at the compo-sition where the trivial to topological crossover is found inPb1�xSnxSe.

2. Experimental

(Pb1�xSnxSe2)1.16(TiSe2)2 single crystals and polycrystalswere grown in three steps. First, mixtures of high-purityfine powders of Pb (99.9%), Sn (99.5%), Ti (99.9%), and Se(99.999%) in the appropriate stoichiometric ratios weremixed and heated in sealed evacuated silica tubes at a rateof 1 °C=min to 700 °C and held there for 48 h. Subsequently,the as-prepared powders were reground and heated at a rateof 3 °C=min to 900 °C and held there for 16 h. Finally, largerand smaller crystals from the as-prepared powders weregrown in the third step by the chemical vapor transport(CVT) method, using SeCl4 as a transport agent. 50mg of theas-prepared powders of (Pb1�xSnxSe2)1.16(TiSe2)2 were mixedwith 35mg SeCl4, sealed in evacuated silica tubes and heatedfor one week in a two-zone furnace, where the temperature ofsource and growth zones were fixed at 750 and 680 °C,respectively. After one week, polycrystalline samples andsome shiny, plate-like grey single crystals of (Pb1�xSnx-Se2)1.16(TiSe2)2 were found at the cold end. Property meas-

Journal of the Physical Society of Japan 85, 064705 (2016)http://doi.org/10.7566/JPSJ.85.064705

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urements were performed on the crystals and polycrystals(collections of small single crystals) from the cold end. Thissynthetic method differs from the one reported previously24)

but is suitable for uniformly preparing the samples in thesolid solution series studied here.

The identity and phase purity of the materials studied weredetermined by powder X-ray diffraction (PXRD) on poly-crystals and crystal plates using a Bruker D8 ECOdiffractometer with Cu Kα radiation and a Lynxeye detector.To determine the phase purity, LeBail fits were performed onthe powder diffraction data through the use of the FULLPROFdiffraction suite using Thompson–Cox–Hastings pseudo-Voigt peak shapes.25) Single crystals selected from partiallycrushed crystalline samples were studied on a Bruker D8ECO single crystal diffractometer with Cu Kα radiation tofully verify that the materials matched the misfit structurepreviously reported for the Pb-containing end member. Thecompositions of the materials were determined by employingEnergy dispersive X-ray fluorescence spectroscopy (EDX)on the crystals using a Quanta 200 FEG ESEM electronmicroscope operated at 20 kV; PbSe, SnSe, and TiSe2crystals were employed as standards. Measurements of thetemperature dependence of the electrical resistivity andspecific heat were performed in a Quantum Design physicalproperty measurement system (PPMS). Zero-field cooled(ZFC) and field cooled (FC) magnetic susceptibilities weremeasured in a field of 10Oe using a Quantum Designsuperconducting quantum interference device (SQUID)magnetometer.

The electronic band spectra were obtained from ARPESmeasurements along highsymmetry direction Gamma-M atbeamline 10 of the Advanced Light Source, Berkeley, using aScienta R4000 analyzer at photon energies of 78 eV (1Tcrystals) and 47 eV (misfit compounds). Sample cleaving anddata collection were performed in an ultrahigh vacuum of5 � 10�9 Pa at T ¼ 15K.3. Results and Discussion

Figure 1 shows the comparison of the Pb=Ti and Sn=Tiratios obtained from the EDX measurements compared to thestarting material compositions. The Pb=Ti and Sn=Ti ratiosobtained from the EDX results were found to be withinexperimental error of the ratios present in the startingmaterials, indicating that the compositions of the (Pb1�x-SnxSe)1.16(TiSe2)2 crystals and polycrystals grown betweenx ¼ 0 and 0.6 for the synthetic method described are withinerror of the nominal compositions. Single phase crystalsof the (Pb1�xSnxSe)1.16(TiSe2)2 misfit phase could only beobtained by our method up to x ¼ 0:6. For higher x, the((Pb,Sn)Se)1.16(TiSe2)2 misfit crystals were multiple-phase.Pure crystals of (SnSe)1.16(TiSe2)2 were also obtained, butthey were not superconducting above 1.8K, and are not thesubject of this study.

A representative room temperature X-ray diffractionpattern (PXRD), obtained from a crystal plate of (Pb0.6-Sn0.4Se)1.16(TiSe2)2 (example shown in the inset), looking atdiffraction from the (00l) planes, is shown in Fig. 2. Thepattern is very similar to that reported previously for theknown TiSe2 double layer misfit (PbSe)1.16(TiSe2)224) andother misfit phases.8) The structure of (PbSe)1.16(TiSe2)2 haspreviously been described24) and is not re-determined here.

Figures 3(a) and 3(b) show schematics of the misfit crystalstructure of the (Pb1�xSnxSe)1.16(TiSe2)2, (using the exampleof x ¼ 0:4) viewed in different directions. The figureshighlight the basic structure as an alternating stacking of(Pb1�xSnx)Se rocksalt-type bi-layers with two 1T-like TiSe2layers, and also the incommensurate nature of their in-planematching.

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.4

0.8

1.2

expected Pb/TiEDX Pb/Tiexpected Sn/TiEDX Sn/Ti

Ratio

s

x in (Pb1-xSnxSe)1.16(TiSe2)2

Fig. 1. (Color online) Comparison of the starting material Pb=Ti and Sn=Ti ratios with the EDX analysis of the single crystals grown of the misfitphase (Pb1�xSnxSe)1.16(TiSe2)2 (0 � x � 0:6).

1 cm

Fig. 2. (Color online) XRD pattern showing the (00L) reflections for aselected single crystal of (Pb0.6Sn0.4Se)1.16(TiSe2)2. Inset, an example of acrystal plate of (Pb0.6Sn0.4Se)1.16(TiSe2)2.

TiSe2

TiSe2

Pb0.6Sn0.4Se

TiSe2

Pb0.6Sn0.4Se

TiSe2

TiSe2

TiSe2

Pb0.6Sn0.4Se

TiSe2

Pb0.6Sn0.4Se

TiSe2

(Pb0.6Sn0.4Se)1.16(TiSe2)2

Pb/Sn

Ti

Se

(a) (b)

Fig. 3. (Color online) Schematic of the crystal structure of (Pb1�xSnx-Se)1.16(TiSe2)2 (x ¼ 0:4), (a) along the b-direction; and (b) along thea-direction. The figures highlight the rocksalt double layers and the two 1T-like TiSe2 layers whose interlayering generates the crystal structure of themisfit phase, while also showing that the in-plane matching of the layers inthese directions is incommensurate.

J. Phys. Soc. Jpn. 85, 064705 (2016) H. Luo et al.

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Figure 4 shows the systematic change in the transportproperties of (Pb1�xSnxSe)1.16(TiSe2)2 on increasing x.Figure 4(a) shows the temperature dependence of theresistivity ratio (�=�300K) for polycrystalline (Pb1�xSnx-Se2)1.16(TiSe2)2 (0:0 � x � 0:6). The inset to the figureenlarges the resistivity behavior in the low temperatureregion (2–5.5K); showing the superconducting transition.Figure 4(b) shows the d�=dT for (Pb1�xSnxSe)1.16(TiSe2)2(0:0 � x � 0:6) in the low temperature region (2–5.5K),further showing the superconducting transition. At lowtemperatures, a clear, sharp (�Tc < 0:5K) drop of �ðTÞ isobserved, signifying the onset of superconductivity. The Tcchanges just slightly with the increase of doped Sn content x,displaying a very weak dome-shaped peak at intermediatecompositions. We note that the Tc observed here for x ¼ 0 ishigher than the one previously reported for that material.24)

The reason for the improved Tc is not currently known butdifferences in the synthetic method may be behind thedifference: there may be defects in the rocksalt layers thatimpact the amount of charge donated to the TiSe2 layers.

The characterization of the superconducting propertiesof single crystal (Pb0.6Sn0.4Se)1.16(TiSe2)2 by specific heatis shown in Fig. 5. Figure 5(a) shows the temperaturedependence of the specific heat (Cp=T versus T2) underzero-field and under a 5 T field for (Pb0.6Sn0.4Se)1.16(TiSe2)2.

The normal state specific heat at low temperatures (but aboveTc) obeys the relation of Cp ¼ �T þ �T3, where γ and βcharacterize the electronic and phonon contributions, res-pectively, the latter of which is a measure of the Debyetemperature (�D). By fitting the data in the temperature rangeof 2–5K, we obtain the electronic specific heat coefficient� ¼ 11:06mJ·mol−1·K−2 for (Pb0.6Sn0.4Se)1.16(TiSe2)2. PerTiSe2 layer, this number (11:06=2 � 5:5mJ·mol−1·K−2) islarger than that found for other superconductors basedon TiSe2 (i.e., 4.3mJ·mol−1·K−2 for Cu0.08TiSe226) and2mJ·mol−1·K−2 for Ti0.8Ta0.2Se227)).

The superconducting transition temperature observed inthe specific heat measurements for (Pb0.6Sn0.4Se)1.16(TiSe2)2is in excellent agreement with the Tc determined in the�ðTÞ measurements. From the inset in Fig. 5, using theequal area construction method, we obtain �C=Tc ¼ 11:28mJ·mol−1·K−2 for (Pb0.6Sn0.4Se)1.16(TiSe2)2. The normalizedspecific heat jump value �C=�Tc is thus found to be 1.38 for(Pb0.6Sn0.4Se)1.16(TiSe2)2, which confirms the bulk super-conductivity. This value is slightly smaller than that of theBardeen–Cooper–Schrieffer (BCS) weak-coupling limit val-ue (1.43), but is in a range typically observed in complexmaterials. Using the Debye temperature (�D), the criticaltemperature Tc, and assuming that the electron–phononcoupling constant (�ep) can be calculated from the invertedMcMillan formula:28)

�ep ¼1:04 þ �� ln

��D

1:45Tc

�

ð1 � 0:62��Þ ln�

�D

1:45Tc

�� 1:04

;

the value of �ep obtained is 0.72 for (Pb0.6Sn0.4Se2)1.16-(TiSe2)2. This suggests weak coupling superconductivity.The density of states at the Fermi level [NðEFÞ] can becalculated from the following equation:

NðEFÞ ¼ 3�2k2Bð1 þ �epÞ

�;

0 50 100 150 200 250 300

0.0

0.2

0.4

0.6

0.8

1.0

x=0x=0.1x=0.2x=0.3x=0.4x=0.6

(Pb1-xSnxSe)1.16(TiSe2)2ρ⁄ρ

300Κ

T (K)

2 3 4 5 60.00

0.05

0.10

0.15

ρ/ρ 3

00Κ

T (K)

(a)

(Pb1-xSnxSe)1.16(TiSe2)2

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

x=0x=0.1x=0.2x=0.3x=0.4x=0.6

dρ⁄dT

(Ohm

K-1)

T (K)

(b)

Fig. 4. (Color online) Transport characterization of the normal statesand superconducting transitions. (a) The temperature dependence of theresistivity ratio (�=�300K) for polycrystalline (Pb1�xSnxSe2)1.16(TiSe2)2 (0:0 �x � 0:6), including the low temperature region (2–5.5K); (b) d�=dT for(Pb1�xSnxSe2)1.16(TiSe2)2 (0:0 � x � 0:6) in the low temperature region(2–5.5K), showing the information used to determine the superconductingtransition temperatures.

Fig. 5. (Color online) Low temperature specific heat characterization of(Pb0.6Sn0.4Se)1.16(TiSe2)2. Temperature dependence of the specific heat Cp ofa single crystal of (Pb0.6Sn0.4Se)1.16(TiSe2)2 measured under magnetic fieldsof 0 and 5T, presented in the form of Cp=T vs T2. The values of γ and β (seetext) were obtained by fitting the heat capacity data obtained in the range2–5K in the magnetic field of 5 T. The inset shows the electronic specificheat and the equal area construction employed to determine �C=�Tc.

J. Phys. Soc. Jpn. 85, 064705 (2016) H. Luo et al.

064705-3 ©2016 The Physical Society of Japan

by using the value of Sommerfeld parameter (γ) and theelectron–phonon coupling (�ep). This yields NðEFÞ ¼ 2:73states=eV f.u. for (Pb0.6Sn0.4Se2)1.16(TiSe2)2.

ARPES data comparing the electronic structures of thehost TiSe2 material and two doped superconducting materialsbased on TiSe2 is presented in Fig. 6. The TiSe2 data isequivalent with those presented in previous reports29,30) andshows the band folding that creates an echo of the valenceband at Γ to the M point that is due to the CDW in the hostmaterial. The Ti0.8Ta0.2Se2 data show the same basicelectronic structure, but now with the CDW stronglysuppressed (the echo of the valence band at Γ is muchweaker at the M point), and a significant degree of filling ofthe conduction band at the M points. The electronic bandstructure of (Pb0.6Sn0.4Se)1.16(TiSe2)2 [Fig. 6(c)] shows allthe features characteristic of bulk TiSe2 and Ti0.8Ta0.2Se2[Figs. 6(a) and 6(b)]: two (three at other kc are not shownhere) hole-like bands in the center of the Brillouin zone andelectron pockets centered at six M points of the Brillouinzone are seen. No bands that can be ascribed to the(Pb1�xSnx)Se layers are observed at the measured Fermisurface of the misfit phase: no fourfold symmetry in thelow-energy band structure is present. The cleavage of(Pb0.6Sn0.4Se)1.16(TiSe2)2 most likely results in single-layerTiSe2 termination of the cleaved crystal because thedouble TiSe2 layers are separated by a weakly bondedvan der Waals gap. Thus The complete absence of (Pb,Sn)Sestates is probably due to short probing depth at the photonenergies employed the (PbSn)Se layers are too deep to beprobed and are not exposed in the cleave. Comparing theelectron pocket in the misfit phase with that of Ta-dopedTiSe2 [Figs. 6(b) and 6(c)] shows that the conduction band isoccupied to a lesser degree in the misfit. The CDW-generatedreplica of the hole pocket is well developed at the M-point ofthe Brillouin zone in TiSe2 and is only weakly present, inboth the Ta doped and misfit phases, where it exists to nearroom temperature in the latter. The implication of the ARPESdata is that the CDW amplitude in the TiSe2 layers issubstantially suppressed, although not completely disrupted,in both doped superconducting phases.

Finally, the electronic phase diagram as a function oftemperature and doping level for the (Pb1�xSnxSe)1.16(TiSe2)2misfit phase series is summarized in Fig. 7. It can be seen thatin the (Pb1�xSnxSe)1.16(TiSe2)2 system, the x dependence ofTc displays a dome-like shape that is broad in composition.

However, Tc changes only slightly with the increase contentof doped Sn x, with a maximum Tc of 4.5K at x ¼ 0:2. Ifthere is any change on crossing the trivial to topologicalcomposition regime in bulk Pb1�xSnxSe at x ¼ 0:25 it is onlya subtle change in the slope of Tc vs x near the top of thedome. For x ¼ 0:4, well into the topological regime of bulkPb1�xSnxSe, the misfit material remains superconducting.Whether the band structure of (Pb,Sn)Se layers in the misfit isof the trivial or topological type remains to be seen in futurestudy. For compositions between x ¼ 0:6 and 1.0 we couldnot obtain single phase materials by our synthetic method,and thus no data is shown in Fig. 7 for higher x; singlephase misfit material was obtained at x ¼ 1 [i.e., (SnSe)1.16-(TiSe2)2], but we did not observe any superconductingtransition down to 2K.

4. Conclusion

The misfit phase (Pb1�xSnxSe)1.16(TiSe2)2 (0 � x � 0:6)series, which combines layers of the rocksalt structuretopological crystalline insulator Pb1�xSnxSe with the layersof the transition metal dichalcogenide TiSe2, is reported, andthe trends in superconductivity in the series characterized.The superconducting transition temperature shows a weakdome shape with varying x, with a maximum Tc � 4:5Kclose to the composition of the trivial to inverted transition in

(c) (Pb0.6Sn0.4Se)1.16(TiSe2)2(b) Ti0.8Ta0.2Se2(a) TiSe2

Fig. 6. Electronic band structures of (a) TiSe2, (b) Ti0.8Ta0.2Se2, and (c) (Pb0.6Sn0.4Se)1.16(TiSe2)2 as determined by ARPES, at 15K. All spectra are samplingthe electronic states around kc ¼ �=c.

Metal

SC Mixed Phase

TiSe2

TiSe2

Pb0.6Sn0.4Se

TiSe2

Pb0.6Sn0.4Se

TiSe2

(Pb0.6Sn0.4Se)1.16(TiSe2)2

Trivial Pb1-xSnxSe

TopologicalPb1-xSnxSe

Pb/Sn

Ti

Se

Fig. 7. (Color online) The Tc vs Sn content x of the superconductor in the(Pb1�xSnxSe)1.16(TiSe2)2 misfit system. The composition of the trivial totopological transition in bulk rocksalt Pb1�xSnxSe is shown by a dashed line.

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the band structure of bulk rocksalt Pb1�xSnxSe. For the misfitsuperconductor (Pb0.6Sn0.4Se)1.16(TiSe2)2, whose Pb:Sn ratiois well within the topological composition regime of thebulk rocksalt material, the Sommerfeld parameter � ¼ 11:06mJ·mol−1·K−2, the Debye temperature �D ¼ 161K, thenormalized specific heat jump value �C=�Tc ¼ 1:38 andthe electron–phonon constant value �ep ¼ 0:72, suggestingthat (Pb0.6Sn0.4Se)1.16(TiSe2)2 is a BCS-type weak couplingsuperconductor. No superconducting transition is observedfor the (SnSe)1.16(TiSe2)2 misfit above 1.8K. Why the SnSe-based misfit material is not superconducting at temperaturescomparable to those exhibited by the Pb+Sn containingmisfit phases is not currently known. Further work thatinvestigates the electronic state of the Pb1�xSnxSe layers inthe misfit phase, to see whether they indeed host topologicalstates, would be of interest. If they do, then interaction ofthose topological states with the superconductivity would beof future interest.

Acknowledgements

The materials synthesis and physical property character-ization of this superconductor were supported by theDepartment of Energy, division of basic energy sciences,Grant DE-FG02-98ER45706. The ARPES work was sup-ported by the ARO MURI on topological insulators grantW911NF-12-0461. The authors acknowledge discussionswith Ali Yazdani.

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J. Phys. Soc. Jpn. 85, 064705 (2016) H. Luo et al.

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