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Yuto Watanabe, Hiroto Arima, Saori Kawaguchi‐Imada, Hirokazu Kadobayashi, Kenta Oka, Hidetomo Usui, [Ryo Matsumoto](https://orcid.org/0000-0001-6294-5403), [Yoshihiko Takano](https://orcid.org/0000-0002-1541-6928), Takeshi Kawahata, Chizuru Kawashima, Hiroki Takahashi, Aichi Yamashita, [Yoshikazu Mizuguchi](https://orcid.org/0000-0002-4771-7805)

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[Pressure‐Induced Volumetric Negative Thermal Expansion in CoZr<sub>2</sub> Superconductor](https://mdr.nims.go.jp/datasets/1cc12260-e87e-4428-9e64-c23ab0083b7c)

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Pressure‐Induced Volumetric Negative Thermal Expansion in CoZr2 SuperconductorRESEARCH ARTICLEwww.advelectronicmat.dePressure-Induced Volumetric Negative Thermal Expansionin CoZr2 SuperconductorYuto Watanabe, Hiroto Arima, Saori Kawaguchi-Imada, Hirokazu Kadobayashi,Kenta Oka, Hidetomo Usui, Ryo Matsumoto, Yoshihiko Takano, Takeshi Kawahata,Chizuru Kawashima, Hiroki Takahashi, Aichi Yamashita, and Yoshikazu Mizuguchi*The study investigates the thermal expansion and superconducting propertiesof a CuAl2-type (tetragonal) superconductor CoZr2 under high pressures.High-pressure synchrotron X-ray diffraction is performed in a pressure rangeof 2.9 GPa < P < 10.4 GPa, and it is discovered that CoZr2 exhibits volumetricnegative thermal expansion (NTE) under high pressures. Although uniaxialpositive thermal expansion (PTE) along the a-axis is observed under ambientpressure, it is suppressed by pressure, whereas a large uniaxial NTE along thec-axis is maintained under the pressure regime. Because of the combinationof the suppressed uniaxial PTE along the a-axis and uniaxial NTE along thec-axis, volumetric NTE is achieved under high pressure in CoZr2. Thevolumetric NTE mechanism is based on the flexible crystal structure causedby the soft Co–Co bond, as observed in the isostructural compound FeZr2,which exhibits a uniaxial NTE along the c-axis. High-pressure electricalresistance measurements of CoZr2 are performed and confirmsuperconductivity at 0.03 GPa < P < 41.9 GPa. Because of the coexistence ofthe two phenomena, volumetric NTE and superconductivity, in CoZr2 underhigh pressure, coexistence can be achieved under ambient pressure by tuningthe chemical composition after the present observation.1. IntroductionThermal expansion is a phenomenon related to the propertiesof electrons and phonons. In most cases, materials expand uponY. Watanabe, H. Arima, A. Yamashita, Y. MizuguchiDepartment of PhysicsTokyo Metropolitan University1-1, Minami–Osawa, Hachioji 192-0397, JapanE-mail: mizugu@tmu.ac.jpS. Kawaguchi-Imada, H. Kadobayashi, K. OkaJapan Synchrotron Radiation Research Institute (JASRI)1-1-1 Koto, Sayo-cho, Sayo-gun, Hyogo 679-5198, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/aelm.202300896© 2024 The Authors. Advanced Electronic Materials published byWiley-VCH GmbH. This is an open access article under the terms of theCreative Commons Attribution License, which permits use, distributionand reproduction in any medium, provided the original work is properlycited.DOI: 10.1002/aelm.202300896heating; this conventional property isknown as positive thermal expansion(PTE). In contrast, negative thermal ex-pansion (NTE) is defined as contractionupon heating, and has been observedin various materials.[1–4] The mecha-nisms of NTE are diverse and correlatedwith the flexible crystal structure,[5,6]phase transition,[7] and magnetic order-to-disorder transition.[8] NTE has beenused to achieve zero thermal expan-sion in practical devices by fabricatingcomposites of PTE and NTE. In su-perconducting devices, the heat cyclebetween the working temperature be-low the superconducting transition tem-perature and room temperature whenthe device is turned off is a criti-cal issue because the heat cycle de-grades the surface and junction betweenmaterials with different coefficients ofthermal expansion. If a superconduc-tor with an NTE or zero-thermal expan-sion (ZTE) exists in a wide temperaturerange below the room temperature, the heat-cycle problemwill improve. Isotropic and uniaxial NTE has been reportedin various superconducting materials, such as single elementsNb[9,10] and Ta,[10] layered materials MgB2,[9,11] YBa2Cu3O7-𝛿 ,[12]H. UsuiDepartment of Applied PhysicsShimane UniversityMatsue, Shimane 690-8504, JapanR. Matsumoto, Y. TakanoInternational Center for Materials Nanoarchitectonics (MANA)National Institute for Materials ScienceTsukuba, Ibaraki 305-0047, JapanT. Kawahata, C. Kawashima, H. TakahashiDepartment of PhysicsCollege of Humanities and SciencesNihon UniversitySetagaya, Tokyo 1568550, JapanAdv. Electron. Mater. 2024, 2300896 2300896 (1 of 9) © 2024 The Authors. Advanced Electronic Materials published by Wiley-VCH GmbHhttp://www.advelectronicmat.demailto:mizugu@tmu.ac.jphttps://doi.org/10.1002/aelm.202300896http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Faelm.202300896&domain=pdf&date_stamp=2024-03-14www.advancedsciencenews.com www.advelectronicmat.deFigure 1. Schematic images of thermal expansion of a) NiZr2, b) CoZr2, and c) CoZr2 under high pressures.Bi2Sr2CaCu2O8+x,[13] PrFeAsO,[14] and Ba(Fe1−xCox)2As2 (x =0.16, 0.23).[15] Those NTEs were observed over a limited temper-ature range, and volumetric NTE over a wide temperature rangehave not been achieved in bulk superconducting materials.Recently, we observed a uniaxial NTE along the c-axis over awide temperature range in the CuAl2-type (tetragonal) supercon-ductors TrZr2 and TrZr3 (Tr: transition metal).[16–18] In the TrZr2system, we revealed that the uniaxial NTE along the c-axis can becontrolled by the lattice constant ratio c/a, through chemical ele-ment substitution.[19,20] The sign of the linear coefficient of ther-mal expansion along the c-axis changes from positive to negativeupon the substitution of Ni with Co at ambient pressure.[20] Theanomalous bonding states related to the uniaxial NTE along thec-axis in TrZr2 have also been observed using X-ray absorptionspectroscopy.[21] Moreover, Xu et al. revealed that FeZr2 exhibitsa giant uniaxial NTE along the c-axis and proposed that the softFe–Fe bond and flexible structure caused by optical phonons playan important role in the origin of the uniaxial NTE along the c-axis.[22] The absence of NTE along the c-axis for NiZr2 is related tothe stiff bonds between the Ni atoms derived from antibondinginteractions. Therefore, crystal structure modification is criticalfor the NTE phenomenon in TrZr2.Herein, we report the observation of volumetric NTE in CoZr2under high pressure. At ambient pressure, CoZr2 exhibits super-conductivity at Tc = 5.8 K (Tc: superconducting transition tem-perature), uniaxial PTE along the a-axis, and uniaxial NTE alongthe c-axis. The uniaxial PTE along the a-axis was suppressed bypressure, whereas the uniaxial NTE along the c-axis was not sup-pressed by pressure. As a consequence of the competition be-tween uniaxial PTE and NTE along the a- and c-axes, the volu-metric NTE was realized under pressure because of 𝛽 = 2𝛼a + 𝛼c,as expressed in Equation (1). Because the coexistence of super-conductivity and volumetric NTE over a wide temperature rangeis rare, we confirmed the presence of superconductivity in CoZr2under high pressure using electrical resistance measurements.2. Results and Discussion2.1. Thermal Expansion under High PressureWe show the schematic images of the thermal expansions of thestructural analogs NiZr2 and CoZr2 (under ambient and highpressures) in Figure 1. These compounds have tetragonal CuAl2-type crystal structures (space group: I4/mcm). NiZr2 exhibits PTEboth along the a- and c-axes, and thus, the coefficient of volu-metric thermal expansion 𝛽 is positive (Figure 1a).[19,20] In thetetragonal crystal structure, 𝛽 can be calculated according to thefollowing equation:𝛽 = 2𝛼a + 𝛼c (1)where 𝛼a and 𝛼c denote the coefficients of linear thermal expan-sion along the a- and c-axes, respectively. In contrast to NiZr2,CoZr2 exhibited a uniaxial NTE along the c-axis (Figure 1b).[16]For CoZr2, 𝛼a and 𝛼c at ambient pressure are 21.5± 0.6 and−17.8± 0.5 μK−1, respectively. Therefore, we obtain 𝛽 = 25 ± 1 μK−1(see Figure S1, Supporting Information). As discussed later, un-der high pressures, we find that the uniaxial PTE along the a-axis is suppressed, but uniaxial NTE along the c-axis is not sup-pressed. Consequently, 𝛽 could be a negative value, implying thatvolumetric NTE is realized in CoZr2 under pressure (Figure 1c).To investigate the thermal expansion properties at high pres-sure, high-pressure synchrotron X-ray diffraction (HP-SXRD)was performed using a diamond anvil cell (DAC). Figure 2ashows the HP-SXRD patterns obtained at T = 303 K at P = 2.9,5.0, 6.7, 7.4, and 10.4 GPa. The crystal structure remains tetrag-onal CuAl2-type up to P = 10.4 GPa. We observed a shift in the002 and 220 peaks toward higher angles upon applying pressure,as shown in Figure 2b,c. The shifts in the peaks resulted in de-creasing lattice constants a and c. Figure 2d shows the pressuredependence of the lattice constants. The lattice constants normal-ized by the values at ambient pressure (a0 and c0) are shown inFigure 2e. The a-axis is stiffer than the c-axis under high pres-sure. This implies that the crystal structure of CoZr2 along thec-axis is more flexible under pressure. The same trend of a andc against pressure was also observed in laboratory experiments,which were conducted using another DAC with a Mo–K𝛼 radia-tion (see Figure S2, Supporting information). As mentioned inthe Introduction section, FeZr2, which is an isostructural com-pound of CoZr2 and NiZr2, exhibits a large uniaxial NTE alongthe c-axis.[22] They revealed that the strong Fe3dz2–Fe3dz2 inter-action can play an important role in stabilizing the large c/a inthe CuAl2-type crystal structure and contributes to the soft Fe–Febond, which provides a large contraction space along the c-axis.Adv. Electron. Mater. 2024, 2300896 2300896 (2 of 9) © 2024 The Authors. Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aelm.202300896 by Cochrane Japan, Wiley Online Library on [11/04/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.deFigure 2. a) HP-SXRD patterns at T = 303 K for CoZr2. b,c) Shift of 002 and 220 peaks owing to pressure. Pressure dependence of d) lattice constantsa and c and e) a and c normalized by a value at ambient pressure. f) Lattice volume V. The solid line is fit to the third-order Birch–Murnaghan formula.Furthermore, optical phonons with a phonon energy of severalmillielectronvolts create a flexible structure in FeZr2, resultingin a giant uniaxial NTE along the c-axis. These flexible character-istics of the crystal structure are common to CoZr2 because theyhave the same crystal structure with a similar c/a ratio to that ofFeZr2 and exhibit a large uniaxial NTE along the c-axis. Figure 2fshows the pressure dependence of lattice volume V of CoZr2. Thesolid line represents the fit to the third-order Birch–Murnaghanformula, expressed by the following equation:[23]P = 32B0{(V0V) 73−(V0V) 53}{1 + 34(B′0 − 4)[(V0V) 23− 1]}(2)where V0, B0, and B′0 denote the volumes at ambient pressure,bulk modulus, and the first-order pressure derivative of B0, re-spectively. As the fitting result, we obtain B0 = 102 ± 3 GPa andB′0= 6.1 ± 0.8. The obtained B0 value was close to the compu-tational results of B0 = 134.81[24] and 129 GPa.[25] Notably, thethird-order Birch–Murnaghan formula assumes a cubic struc-ture; thus, the obtained B0 values can deviate from the actual val-ues.Next, we show the results of the thermal expansion of CoZr2at P = 2.9 GPa as an example of a high-pressure dataset. For allexperiments under pressure, we evaluated the fluctuation in theapplied pressures because thermal expansion is easily affected bypressure changes. The data presented in this study were carefullyobtained in this manner. Figure 3a shows the HP-SXRD patternsat P = 2.9 GPa at temperatures ranging from T = 303 to 453 Kin increments of 10 K. There was no crystal structural transitionin the temperature region (P = 2.9 GPa, which was commonlyconfirmed at all other applied pressures (see Figure S3, Support-ing Information). The absence of a crystal structural transition atambient pressure was confirmed over a wide temperature range(7 K < T < 572 K) in ref. [16]. As the temperature increased, aclear shift in the 002 peak toward higher angles was observed, asshown in Figure 3b. However, the position of the 220 peak wasalmost the same as that of the pressure, as shown in Figure 3c.The robustness of the a-axis to pressure observed from the 220peak results in a small value of 𝛼a = 9 ± 1 μK−1, which is clearlysmaller than that at ambient pressure (see Figure S1, SupportingInformation). Figure 3d,e show the temperature dependence ofa and c, respectively, at P = 2.9 GPa. Even under pressure, thelarge c-axis NTE is present with 𝛼c = −24 ± 1 μK−1, which is al-most the same as that observed under ambient pressure. FromEquation (1), we obtain 𝛽 =−6 ± 2 μK−1, suggesting the pressure-induced volumetric NTE in CoZr2. Figure 3f shows the temper-ature dependence of V at P = 2.9 GPa. The volume contractedslightly as the temperature increased. The solid line in Figure 3fis a linear fit curve against the temperature and the fitting deriveda similar value of 𝛽, which was calculated using Equation (1). Al-most all the data points were aligned in the linear fitting curvewithin the error bars.We summarize the pressure dependence of 𝛼a, 𝛼c, and 𝛽 inFigure 4. When the pressure is applied to CoZr2, the uniaxial PTEalong the a-axis is suppressed; thus, 𝛼a under high pressure islower than at ambient pressure (Figure 4a). In contrast, even un-der high-pressure conditions, the uniaxial NTE along the c-axis isnot suppressed; therefore, 𝛼c is almost independent of pressure(Figure 4b). Above the ambient pressure, the 𝛽 value can be neg-ative because the impact of uniaxial NTE along the c-axis on theAdv. Electron. Mater. 2024, 2300896 2300896 (3 of 9) © 2024 The Authors. Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aelm.202300896 by Cochrane Japan, Wiley Online Library on [11/04/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.deFigure 3. a) HP-SXRD patterns at P = 2.9 GPa for CoZr2. b,c) Shift of 002 and 220 peaks owing to heating. Temperature dependence of lattice constantsd) a and e) c. f) Temperature dependence of lattice volume V. Solid lines in insets (d–f) are fit to the linear line.volume exceeds the suppressed uniaxial PTE along the a-axis, re-sulting in volumetric NTE. Unfortunately, we could not conductpressure experiments between P = 0 and 2.9 GPa because of ex-perimental difficulties. However, we expect that the suppressionof the uniaxial PTE along the a-axis occurs in the low-pressureregion. The results of Rietveld refinement of CoZr2 underP = 2.9 GPa (303 and 453 K) and P = 10.4 GPa (303 and403 K) are shown in Figure S4 (Supporting information). Theresults of the same pressure experiment are shown in Figure S5(Supporting Information). We observe a decreasing trend in vol-ume against temperature under the applied pressures.2.2. Superconducting PropertiesWe measured the electrical resistance (R) of CoZr2 under highpressures (0.03 GPa < P < 41.9 GPa) to confirm the presenceof superconductivity. Figure 5a,b show the temperature depen-dence of R under pressures. As the temperature decreased, RFigure 4. Pressure dependence of the coefficient of linear thermal expansion along the a) a-axis 𝛼a and b) c-axis 𝛼c. c) Pressure dependence of thecoefficient of volumetric thermal expansion 𝛽. In the tetragonal crystal structure, 𝛽 can be calculated as 𝛽 = 2𝛼a + 𝛼c.Adv. Electron. Mater. 2024, 2300896 2300896 (4 of 9) © 2024 The Authors. Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aelm.202300896 by Cochrane Japan, Wiley Online Library on [11/04/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.deFigure 5. a,b) Temperature dependence of electrical resistance (R) under applied pressures. The solid lines are fit to the parallel-resistor model.c,d) Pressure dependence of superconducting transition temperature Tc and Debye temperature ΘD.decreases with a negative curvature, which is a trend commonlyobserved in d-electron superconductors.[26,27] At low tempera-tures, R drops to zero at Tc under all applied pressures. A dome-shaped pressure dependence of Tc is observed, as shown inFigure 5c. Tc obtained from the R data at ambient pressure (P= 0.03 GPa) was 5.8 K, consistent with the value obtained frommagnetic susceptibility measurements at ambient pressure (seeFigure S6, Supporting Information). As pressure increases, Tc in-creases up to P = 17.9 GPa and reaches 6.5 K, but the trend of Tcchanged at P > 17.9 GPa; Tc decreases with increasing pressure.In a study on a single crystal of CoZr2, Tc reached 9.5 K at P =8 GPa,[26] which is higher than the highest Tc obtained in thisstudy with polycrystalline CoZr2. The discrepancy in the highestTc values may be due to the difference in the reactions of Tc tothe pressure generated by the experimental conditions, that is,the pressure cells and sample type (single or polycrystalline). Inthe low-temperature region where Tc < T ≪ ΘD (Debye temper-ature), R could be fitted to the power-law relation:R (T) = R0 + ATn (3)where R0 denotes the residual resistance, A denotes a numeri-cal temperature-independent coefficient, and n is a componentthat depends on the carrier scattering mechanism. We used Rat 10 K < T < 30 K under pressures in the fitting to power-lawrelation, which yielded n ≈ 3 for all applied pressures as shownin Figure S7 (Supporting information). The T 3 dependence onlow-temperature R can be explained with a phonon-assisteds–d electron scattering model.[28] R of compounds comprisingd-block elements is empirically known to fit the parallel-resistormodel[27,29] developed by Wiesmann et al.[30] In the model, R isdescribed by the following equation:R (T) =[1Rsat (T)+ 1Rideal (T)]−1(4)where Rsat denotes the saturated R at high temperatures. Fisk andWebb found that at high temperatures, R of strongly coupled su-perconducting transition metal compounds, such as Nb3Sn andNb3Sb, saturates at a certain value that corresponds to an elec-tron mean free path of the order of the interatomic spacing inthe compound.[31] Rideal comprises the residual electrical resis-tance R0 and the phonon-assisted s–d electron scattering term, asfollows:Rideal (T) = R0 + C(TΘD)3 ΘDT∫0x3(ex − 1) (1 − e−x)dx (5)where C denotes a numerical temperature-independent coeffi-cient. We used the R data at 10 K < T < 300 K for fitting to theparallel-resistor model and evaluated the ΘD values as a functionof applied pressure as shown in Figure 5d. The calculated ΘD isAdv. Electron. Mater. 2024, 2300896 2300896 (5 of 9) © 2024 The Authors. Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aelm.202300896 by Cochrane Japan, Wiley Online Library on [11/04/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.deFigure 6. a) Total Electrical DOS for CoZr2 at P = 0, 5, and 10 GPa. b,c) Partial DOS for Co-3d and Zr-4d orbitals at P = 0 and 10 GPa, respectively.d,e) Partial DOS for Co-3dxy, 3dxz + yz, 3dz2, and 3dx2-y2 orbitals at P = 0 and 10 GPa, respectively.292 K at ambient pressure (P = 0.03 GPa), which slightly deviatesfrom the value ΘD = 260 K obtained by another experimental re-sult using specific heat measurement.[32]As mentioned previously, we observed a dome-shaped pres-sure dependence of Tc (Figure 5c). In conventional weak-coupling superconductors, Tc can be expressed as follows:[33]Tc = 1.13ΘDexp{− 1N (0) U}(6)where N(0) denotes the electronic density of states (DOS) at theFermi energy and U denotes the effective Coulomb interactionconstant. According to Equation (6), Tc is mostly controlled byΘDand N(0). ΘD gradually increases upon applying pressure above6 GPa (Figure 5d), contributing to an enhancement of Tc. In con-trast, N(0) typically decreases under high-pressure conditions be-cause of the expansion of the bandwidth,[34] which contributes tothe suppression of Tc. Therefore, the competition of the contri-butions of ΘD and N(0) to pairing would cause the dome-shapedpressure dependence of Tc. The dome-shaped pressure depen-dence of Tc has been observed in other superconductors, suchas CaSb2,[35] CsV3Sb5,[36] AuTe2,[37] and Cd2Re2O7.[38] Possiblecauses of the discontinuation or dome-shaped pressure depen-dence of Tc were proposed to be crystal structural transitions orLifshitz transitions.ΘD is related to the elastic properties of the material, particu-larly the stiffness.[39] As is well known, diamond or crystals witha diamond-type structure whose large ΘD exhibit a small linearthermal expansion coefficient.[40,41] There would be similar corre-lation between 𝛼c and ΘD in CoZr2. However, to clarify the corre-lation, further experimental and theoretical studies on this phe-nomenon are needed. The pressure effect on 𝛼c would be neg-ligible because of the Co–Co soft bond similar to the Fe–Fe softbond observed in FeZr2.[22]2.3. Electrical StructureThe total electronic DOS and partial DOS are shown in Figure 6.The total DOS values near the Fermi energy (EF) were compara-ble at P = 0, 5, and 10 GPa (Figure 6a). Therefore, the incrementtrend of Tc below P = 17.9 GPa described in Figure 5c may beexplained by ΘD increment. We expect that the decrease in Tcabove P = 17.9 GPa is due to the reduction in N(0) because thepeak near EF gradually shifted to the low-energy side under rigidband shifting with increasing pressure. The partial DOS for theCo-3d and Zr-4d orbitals are shown in Figure 6b,c at P = 0 and10 GPa, respectively. The total DOS near EF mainly comprisesCo-3d and Zr-4d orbitals. Figure 6d,e show the details of Co-3dpartial DOS at P = 0 and 10 GPa, respectively. Most of the par-tial Co-3d DOS are located below EF at both P = 0 and 10 GPa.However, the DOS of the Co-3dz2 orbital is above EF, which is anunoccupied state. In the study of FeZr2, the bonding interactionbetween Fe3dz2 and Fe3dz2 contributes to the contraction of theFe–Fe bond. The Co3dz2 orbital below EF should be related to theCo–Co bond contract, similar to that of FeZr2.[22]Figure 7a shows the charge density isosurfaces of CoZr2 at P =0, 3, 5, and 10 GPa. As pressure was applied, the charge densityof the isosurface between Co–Co and Co–Zr bonds increased, re-sulting in a decrease in the bond lengths. The Co–Co and Co–Zrbond lengths were reversed at P = 10 GPa (Figure 7b). Figure 7cshows the pressure dependence of the bond lengths normalizedby the values at ambient pressure. The normalized Co–Co bondlength becomes shorter than the normalized Co–Zr bond lengthunder pressure, suggesting that CoZr2 flexibly contracts alongthe c-axis as compared to the a-axis, as shown in Figure 2e. A vol-umetric NTE emerging above P = 2.9 GPa would be achievedby changing the bonding state from ambient pressure to P =2.9 GPa.3. ConclusionWe measured the temperature-dependent HP-SXRD patternsand the temperature dependence of R on polycrystalline CoZr2under various pressures. From the HP-SXRD results, we foundno crystal structural transition below 10.4 GPa in the measuredtemperature ranges. The most important result of this studyis the discovery of a volumetric NTE induced by the applica-tion of high pressure in CoZr2. The uniaxial PTE along thea-axis was suppressed by pressure, whereas the uniaxial NTEalong the c-axis was not. Because of the competition betweenAdv. Electron. Mater. 2024, 2300896 2300896 (6 of 9) © 2024 The Authors. Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aelm.202300896 by Cochrane Japan, Wiley Online Library on [11/04/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.deFigure 7. a) Charge density isosurface of CoZr2 at P = 0, 3, 5, and 10 GPa. The bond length comparison between Co–Zr and Co–Co is shown at eachapplied pressure. b) Pressure dependence of Co–Co and Co–Zr bond lengths. c) Bond lengths normalized by a value at ambient pressure.uniaxial PTE and NTE, volumetric NTE was achieved under highpressures in CoZr2. The robustness of the NTE along the c-axis under pressure is related to the flexible crystal structurecaused by the soft Co–Co bond proposed in the structural ana-log FeZr2, which also exhibits a giant uniaxial NTE along the c-axis under ambient pressure. The increase inΘD against pressurecould contribute to the suppression of uniaxial PTE along the a-axis. From electronic structure calculations, we found that theCo–Co and Co–Zr bond lengths were reversed at P = 10 GPa.The change in the bonding state under pressure is related tothe emergence of a unique axis thermal expansion of CoZr2 un-der high pressures. From pressure–temperature dependencesof R, we observed the dome-shaped pressure dependence of Tcand an increase of ΘD with pressure. The dome-shaped pres-sure dependence of Tc was caused by the competition betweenthe pressure evolutions of ΘD and N(0). Further investigation ofphonon states potentially coupled with uniaxial NTE along thec-axis in CoZr2 and its pressure dependence is required to un-derstand the mechanisms of volumetric NTE in CoZr2 underhigh pressure. Through a systematic investigation of the struc-tural and physical properties of the CoZr2 superconductor, weconcluded that CoZr2 exhibits both superconductivity and vol-umetric NTE, which is possibly maintained in a temperaturerange lower than room temperature, because the NTE along thec-axis was observed over a wide temperature range in a previousstudy of CoZr2 under ambient pressure. The discovery presentedhere will lead to material exploration using volumetric NTEunder ambient pressure in TrZr2 and related superconductingmaterials.4. Experimental SectionSample Preparation: A polycrystalline sample of CoZr2 was preparedusing a Co rod (99.98%, Nilaco) and Zr plates (99.2%, Nilaco) via arc melt-ing. The sample chamber was filled with Ar after three gas replacements.The sample was synthesized on a water-cooled Cu stage and turned sev-eral times during each melting step for homogenization.XRD and HP-SXRD Measurements: The laboratory XRD patterns atambient pressure were measured by the 𝜃–2𝜃 method with Cu–K𝛼 radi-ation using a Miniflex-600 (RIGAKU) diffractometer equipped with a high-resolution semiconductor detector D/tex-Ultra. The BTS-500 attachmentcontrolled the temperature of the samples. HP-SXRD was measured at theBL10XU beam line of SPring-8 with a wavelength of 0.413278 Å (ProposalAdv. Electron. Mater. 2024, 2300896 2300896 (7 of 9) © 2024 The Authors. Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aelm.202300896 by Cochrane Japan, Wiley Online Library on [11/04/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.deNo.: 2023A1254). The sample was loaded into the DAC with a pressuremedium (He gas). The actual pressure was determined from the shift inthe fluorescence line of ruby R1.[42] A band heater was mounted aroundthe DAC to heat the samples. A K-type thermocouple was placed in thegasket to measure the temperature. The collected laboratory XRD and HP-SXRD patterns were refined by the Rietveld method using RIETAN-FP; siteoccupancies have been fixed as 1.[43] The images of crystal structures wereobtained using VESTA.[44]Magnetic Susceptibility Measurement: The temperature and field de-pendences of the magnetic susceptibility were measured using an MPMS3(Quantum Design), a superconducting quantum interference device mag-netometer. The temperature dependence was measured at μ0H = 1 mTafter both zero-field cooling (ZFC) and field cooling (FC) protocols. Thefield-dependence was measured at T = 1.8 K.High-Pressure Electrical Resistance Measurement: The T dependence ofR under various pressures was investigated using a DAC with boron-dopeddiamond microelectrodes[45,46] in a PPMS (Quantum design). Cubic BNpowder was filled into a hole around a metal gasket (SUS316) as a pressuremedium. The generated pressures were determined from the shift in theruby R1 fluorescence line[42] and Raman peak from the diamond on theculet surface.[47]First Principles Calculation: First-principles calculations were per-formed using the VASP software package, employing the projector-augmented wave method.[48–51] The Perdew–Burke–Ernzerhof exchange-correlation functional[52] was used. K-point meshes of 11 × 11 × 12 and22 × 24 × 24 were utilized for internal coordinate optimization and DOScalculations, respectively. Calculations were performed using experimen-tally determined lattice constants. A plane-wave cut-off energy of 350 eVwas used. Partial DOS was visualized using PyProcar software.[53]Data Presentation: Coefficients of thermal expansion values are ex-pressed as fitted value ± SD (standard deviation). The fitted value wasobtained using the Python curve-fit function. The SD values were calcu-lated according to error propagation rules using error values derived fromthe fitting.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThis work was partly supported by a Grant-in-Aid for Scientific Research(KAKENHI) (Proposal Nos. 21K18834, 23KK0088, and 23K13549), JST-ERATO (JPMJER2201), TMU Research Project for Emergent Future Society,and Tokyo Government-Advanced Research (H31-1).Conflict of InterestThe authors declare no conflict of interest.Data Availability StatementThe data that support the findings of this study are available from thecorresponding author upon reasonable request.Keywordsnegative volumetric thermal expansion, pressure, superconductorReceived: December 24, 2023Revised: February 8, 2024Published online:[1] J. P. Attfield, Front. Chem. 2018, 6, 371.[2] G. D. Barrera, J. A. O. Bruno, T. H. K. Barron, N. L. Allan, J. Phys.:Condens. Matter. 2005, 17, R217.[3] J. Chen, L. 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See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.de