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[High-pressure effects on crystal structure and critical temperature in superconducting NbB2 and stabilized MoB2.pdf](https://mdr.nims.go.jp/filesets/ec0fbd6b-87c0-4aca-9058-371fbd2d5849/download)

## Creator

[Kazuki Yamane](https://orcid.org/0000-0002-0162-5411), [Ryo Matsumoto](https://orcid.org/0000-0001-6294-5403), Takafumi D Yamamoto, [Kensei Terashima](https://orcid.org/0000-0003-0375-3043), Shintaro Adachi, [Hiroyuki Takeya](https://orcid.org/0000-0001-9445-4705), Mitsuharu Nagasawa, [Yoshihiko Takano](https://orcid.org/0000-0002-1541-6928)

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This is the Accepted Manuscript version of an article accepted for publication in Superconductor Science and Technology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.  The Version of Record is available online at https://dx.doi.org/10.1088/1361-6668/adb6f8.[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

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[High-pressure effects on the crystal structure and critical temperature in superconducting NbB<sub>2</sub> and stabilized MoB<sub>2</sub>](https://mdr.nims.go.jp/datasets/622cf2f7-f210-4cd1-b268-78cd08ab945c)

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1  1 High-pressure effects on crystal structure and critical 2 temperature in superconducting NbB2 and stabilized MoB2  3  4 Kazuki Yamane1,2, *Ryo Matsumoto1, Takafumi D. Yamamoto3, Kensei Terashima1,  5 Shintaro Adachi4, Hiroyuki Takeya5, Mitsuharu Nagasawa6, Yoshihiko Takano1,2 6  7 1 Research Center for Materials Nanoarchitectonics (MANA), 8 National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan 9 2Graduate School of Pure and Applied Sciences, University of Tsukuba, 10 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan 11 3 Department of Material Science and Technology, Tokyo University of Science, 12 Tokyo 125-8585, Japan 13 4Department of Mechanical and Electrical Systems Engineering, Faculty of Engineering, Kyoto 14 University of Advanced Science (KUAS), Kyoto, 615-8577, Japan 15 5 Research Center for Energy and Environmental Materials (GREEN) 16 National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan 17 6 Department of Natural Sciences, Tokyo Denki University, Adachi, Tokyo 120-8551, Japan  18  19 *Corresponding author; Email: MATSUMOTO.Ryo@nims.go.jp 20  21  22 Abstract 23 Exploration for superconducting metal diborides with a high critical temperature (Tc) has 24 attracted much attention since the discovery of MgB2. Recently reported high Tc in compressed MoB2 25 has motivated us to investigate the electrical transport property under high pressure in other metal 26 diborides. We focused on the relationship between Tc and a stretched c-lattice parameter (c/a), known 27 as an important parameter for superconductivity in MgB2, which shows the main contribution of p 28 electron to electronic structure. In this study, the correlation of Tc and c/a is investigated in NbB2 and 29 MoB2-based superconducting diborides, which have totally different electronic structures mainly 30 composed of d electron from transition metal. Our high-pressure electrical transport measurements 31 and structural analysis reveal that the common positive correlation between Tc and c/a is observed in 32 NbB2, Zr-stabilized MoB2, and these defected systems. Our insight opens further issues for the 33 development of superconducting metal diborides. 34  35  36  37  2  38 I. INTRODUCTION 39 Exploration of superconductors attracts significant attention in materials composed of light 40 elements with high Debye frequency, which is a constant of proportionality for superconducting 41 critical temperature (Tc) within Bardeen-Cooper-Schrieffer (BCS) theory [1]. Among the explorations, 42 high-Tc above 39 K have been discovered in MgB2 crystallizing in AlB2-type hexagonal structure 43 (P6/mmm) about two decades ago [2]. Exploration of superconductivity in diborides with another 44 transition metal (TM) except for MgB2 is also continued to realize higher Tc [3–5]. However, all the 45 examined TMB2s exhibit drastically lower Tc than that of MgB2. In a recent report, MoB2 with CaSi2-46 type rhombohedral structure (R-3m) shows a structural phase transition to the AlB2-type at high 47 pressure of 70 GPa and the second highest Tc of 32.4 K among superconducting TMB2s is observed 48 at 110 GPa [6]. The Tc monotonically increases with pressure above 100 GPa at a rate of 0.1 K/GPa 49 and still does not show the trend of saturation. After the discovery, pressure-induced superconductivity 50 in WB2 with Tc of 17 K at 90 GPa has been immediately reported [7]. Also, the application of pressure 51 suppresses antiferromagnetic transition in CrB2 and induces superconductivity at 7 K under 110 GPa 52 [8]. The high-pressure research opens a novel strategy to create high-Tc superconducting TMB2s in 53 the past few years. 54 The high Tc in MgB2 originates from the strong coupling between σ-bands and E2g phonon modes, 55 which are related to the in-plane B–B bond. Based on the strong anisotropic feature, the c/a, known 56 as a stretched c-lattice parameter, is an important character in superconducting metal borides. The 57 relatively high c/a of 1.14 in MgB2 contributes to the realization of high-Tc with a two-dimensional 58 character [9,10]. In contrast, double sharp peaks of electronic density of state (DOS) at Fermi energy 59 (EF) in pressure-stabilized MoB2, which are mainly composed of Mo dz2 orbital, provide high Tc above 60 30 K by coupling with out-of-plane vibrations in Mo [11]. In such the d electron system among TMB2, 61 the relationship between Tc and c/a is still uninvestigated issue for further exploration of high-Tc 62 superconductors.  63 In this study, we investigate the relationship between Tc and c/a in superconducting TMB2s via a 64 high-pressure application, which is an effective way to manipulate the crystal structure without 65 chemical modification. We select NbB2, Mo1−xZrxB2, and these defected system Nb1−xB2 and 66 (Mo1−xZrx)1−yB2 as the candidates of examined AlB2-type TMB2s because these exhibit 67 superconductivity at ambient pressure with d electron character [12,13]. The electrical transport 68 properties and crystal structures in these materials under high pressure are measured to reveal the 69 relationship between Tc and c/a. The Tc of NbB2 is increased from 1.3 K to 9.2 K by introducing Nb 70 deficiency [14]. Although the high-pressure study on superconductivity has been reported in the 71 Nb1−xB2, the applied pressure is less than 6 GPa [15]. Also, a slight substitution of Zr in the Mo site 72 stabilizes the metastable AlB2-type structure in MoB2 even at ambient pressure [13]. The Mo1−xZrxB2 73 and defected (Mo1−xZrx)1−yB2 show superconductivity at 5.9 and 8.2 K, respectively [13]. Considering 74 the drastic enhancement of Tc against pressure in the pressure-induced superconducting phase of 75 pristine MoB2, high-pressure behavior in the Zr-stabilized MoB2 is also worth investigating. Our high-76 pressure electrical measurements and structural analysis suggest a positive relationship between Tc 77 and c/a for all the examined TMB2. The serial investigation of high-pressure behavior in TMB2 is 78  3 helpful for further research on the exploration of superconductors in this system. 79  80 II. EXPERIMENTAL PROCEDURES 81 Polycrystalline samples of NbB2, Mo1−xZrxB2, and (Mo1−xZrx)1−yB2 were synthesized via argon 82 arc-melting process. The starting materials with a stoichiometric composition (x = 0.04, y = 0.15) were 83 placed on a water-cooled copper hearth in the furnace under an Ar atmosphere and melted several 84 times to obtain a homogeneous sample. Defected Nb1−xB2 was synthesized by a solid-state reaction 85 using a high-temperature and high-pressure method in a Kawai-type multi-anvil apparatus. A mixture 86 of starting materials with a composition of Nb : B = 0.8 : 2 was filled into a sintered hexagonal BN 87 tube. The prepared tube was compressed under 5 GPa and heated at 1200 ℃ for 0.5 h and quenched 88 to room temperature. The details of sample preparation in the defected Nb1−xB2 are described in 89 another paper [14].  90 The crystal structures of the obtained metal diborides at ambient pressure were confirmed by 91 powder X-ray diffraction (XRD) analysis using a Mini Flex 600 (Rigaku) with Cu Kα radiation (λ = 92 1.5418 Å). In-situ XRD measurements were performed to reveal the crystal structure under high 93 pressure for NbB2, Nb1−xB2, Mo1−xZrxB2, and (Mo1−xZrx)1−yB2 in diamond anvil cell (DAC) using 94 synchrotron radiation at the AR-NE1A beamline of the Photon Factory (PF) at the High Energy 95 Accelerator Research Organization (KEK). The X-ray beam was monochromatized to an energy of 30 96 keV (λ = 0.4180 Å for NbB2 and Nb1−xB2, λ = 0.4172 Å for Mo1−xZrxB2 and (Mo1−xZrx)1−yB2) and 97 introduced through a collimator with a 50 μm diameter. One-dimensional XRD patterns were obtained 98 from the collected Debye-Scherrer diffraction rings using the IPAnalyzer [16]. Re sheet with a 200 99 µm diameter hole was used as a gasket in DAC. The pulverized sample itself, or cubic BN, was filled 100 in the hole of the gasket as the pressure-transmitting medium. Here, the XRD patterns of NbB2 and 101 Nb1−xB2 at ambient pressure were measured in DAC without compression. The results of XRD analysis 102 under ambient pressure and high pressure are shown in Fig. S1 and S2. 103 The temperature dependence of the electrical resistance under high pressure in all the samples 104 was measured via a four-probe method using the DAC with boron-doped diamond electrodes [17–19]. 105 A stainless steel (SUS316) sheet with a 200 µm diameter hole was used for a gasket. Cubic BN 106 powders were filled around the gasket hole, which act as the pressure-transmitting medium and an 107 insulating layer between a gasket and the electrodes. Applied pressures in the DAC were estimated by 108 the peak shift of a ruby fluorescence from a tiny piece of ruby in a sample space [20] and a Raman 109 spectrum of diamond anvil [21] in both XRD analysis and electrical measurements. 110  111 III. RESULTS and discussion 112 The XRD analysis reveals that the synthesized samples exhibit an AlB2-type structure (hexagonal, 113 P6/mmm) at ambient pressure. The details, including the lattice constants, are shown in Fig. S1. The 114 average amount of Nb deficiency x in Nb1−xB2 is determined to be 0.07 by comparing the lattice 115 constant with that in the literature [14]. By using a similar estimation, the average amount of 116 substituted Zr (x) in Mo1−xZrxB2 is determined to be 0.04 [13]. When the Zr amount x in 117 (Mo1−xZrx)1−yB2 is assumed to be 0.04, the amount of deficiency y is determined to be 0.1 from the 118 reported relationship [13]. Hereafter, the compositions in these TMB2 are written with the 119  4 aforementioned values, although a precise analysis of the composition is needed in future 120 investigations.  121 Figure 1 (a-d) shows temperature (T) dependence of resistance (R) under various pressures at 122 around low-temperature regions in NbB2, Nb0.93B2, Mo0.96Zr0.04B2, and (Mo0.96Zr0.04)0.90B2. In the R-T 123 curve of NbB2 at the lowest pressure of 0.2 GPa, the resistance starts to decrease at 2.3 K, indicating 124 superconductivity. The Tc, defined by the onset temperature of decreasing resistance, gradually 125 decreases from 2.3 to 2.0 K with increasing pressure up to 34 GPa. The Tc near ambient pressure is 126 drastically increased by introducing Nb deficiency, as shown in the R-T properties in Nb0.93B2. The 127 Tconset of 7.7 K at 3 GPa monotonically decreases to 4.1 K at 39 GPa. The R-T curve of Mo0.96Zr0.04B2 128 near ambient pressure shows a slight increase in resistance just above Tc, which is typically observed 129 in nonhomogeneous superconductors with different transition temperatures [22]. This observation 130 indicates a distributed Zr amount in synthesized Mo0.96Zr0.04B2. The onset Tc of starting temperature 131 of the reduction in resistance, which reflects the highest Tc in the inhomogeneous superconductor, 132 decreases from 5.5K at ambient pressure to 3.7 K at 35 GPa. The Tc near ambient pressure in 133 (Mo0.96Zr0.04)0.90B2 is also enhanced by introducing the deficiency of (Mo0.96Zr0.04). The R-T behavior 134 exhibits similar inhomogeneity, and Tconset gradually decreases from 8.0 K at 0.4 GPa to 6.0 K at 40 135 GPa. The inhomogeneity of superconducting transition in Zr-stabilized MoB2 would be due to a 136 distribution of the amount of deficiency and substitution. Also, a distortion in crystal, which is 137 generally introduced during the arc-melting method, affects the sharpness of the superconducting 138 transition [23]. The distortion will be improved by a post-annealing treatment after the arc-melting 139 method [24]. Since the superconducting transition in all high-pressure measurements is broad due to 140 the influence of a solid pressure-transmitting medium, the Tc values are determined using various 141 criteria and exhibit a similar trend, as shown in Fig. S4. This suggests that the reduction in Tc is an 142 intrinsic property of these compounds. In particular, the determination of Tconset in Zr-stabilized MoB2 143 is presented in Fig. S5, as it is difficult to see. Also, all the samples maintain the metallic behavior 144 even under high pressure, as shown in Fig. S2. Moreover, we examined an emergence of pressure-145 induced superconductivity in other metal diborides of AlB2, TiB2, ZrB2, and VB2, as shown in Fig. S3. 146 No superconductivity is observed in these diborides at least less than 50 GPa. In this study, all the 147 evaluations for superconductivity are performed via the electrical transport measurements, which 148 reflect the local properties in the DAC with large pressure distribution. For future research, 149 temperature-dependent magnetization measurements under high pressure could reveal bulk 150 superconducting properties and provide deeper insights into the underlying physics of this system. 151  5  152 FIG. 1. Temperature dependence of resistance at around low-temperature region in all the 153 obtained samples under high pressure. (a) NbB2, (b) Nb0.93B2, (c) Mo0.96Zr0.04B2 and (d) 154 (Mo0.96Zr0.04)0.90B2. 155  156 Figure 2 (a) shows a pressure dependence of Tc in NbB2 and Nb0.93B2 up to around 40 GPa. The 157 Tcs linearly decrease as a function of the pressure with the slope of dTc/dP = −0.012 K/GPa in NbB2 158 and −0.086 K/GPa in Nb1−xB2. Compared with dTc/dP = −1.11 K/GPa in MgB2 [25], NbB2 and 159 Nb0.93B2 have blurry pressure-dependence of Tc. The high-pressure effect on Tc in MgB2 has been 160 understood within the range of a conventional BCS-type superconductor. The Tc is drastically reduced 161 by pressure due to a decrease in DOS at EF and an increase in averaged phonon frequency, reducing 162 electron-phonon coupling strength [26,27]. The negative correlations in NbB2 and Nb0.93B2 are also 163 understood to be the same as the case of MgB2. A smaller phonon frequency in NbB2 possibly 164 contributes to exhibiting the blurry change in Tc as a function of pressure [28]. Also, the amount of 165 Nb deficiency x in Nb1−xB2 is estimated to be 0.11 from the comparison between the intercept of dTc/dP 166 and the reported value [15], which is larger than that estimated by XRD analysis. Figure 2 (b) shows 167 a pressure-dependent Tc in Mo0.96Zr0.04B2 and (Mo0.96Zr0.04)0.90B2. Although a positive correlation of 168 Tc against pressure is expected as the behavior in pressure-stabilized AlB2-type MoB2 [6], the Tc in 169 both Zr-stabilized MoB2s exhibit negative slopes with dTc/dP = −0.054 K/GPa in Mo0.96Zr0.04B2 and 170 −0.045 K/GPa in (Mo0.96Zr0.04)0.90B2. Yet, the positive slope of Tc in MoB2 at high pressure deviates 171 from theoretical calculations, suggesting the negative correlation due to the reduction of DOS at EF 172 and phonon hardening [28]. Also, a steady decrease of Tc from 8 K at 0 GPa to 4 K at 50 GPa in Nb-173  6 stabilized MoB2 has recently been reported in a high-pressure experiment [29]. Our observations of Tc 174 reduction in Zr-stabilized MoB2s show a similar trend as their research. 175  176 FIG. 2. (a) Applied pressure dependence of Tc of NbB2 and Nb0.93B2, (b) Mo0.96Zr0.04B2, and 177 (Mo0.96Zr0.04)1−yB2. 178  179 To investigate the relationship between superconducting properties and crystal structure, XRD 180 patterns were measured under various pressures, as shown in Fig. 3.  The AlB2-type structures of all 181 the samples are maintained at around 30 GPa without a structural phase transition. Figure 4 (a) and 182 (b) shows the pressure dependences of lattice constants a and c in NbB2, Nb0.93B2, Mo0.96Zr0.04B2, and 183 (Mo0.96Zr0.04)0.90B2, which are determined from the peak position in XRD patterns. The lattice 184 constants of all the compounds monotonically decrease with increasing pressure. The stretched c-185 lattice parameter c/a of these compounds is plotted as a function of pressure in Fig. 4 (c). The 186 decreasing rate of c/a in Nb0.93B2 (−2.2×10−4 GPa−1) is higher than that in NbB2 (−1.2×10−4 GPa−1). A 187 similar tendency is observed in stabilized MoB2, namely, the decreasing rate of c/a in 188 (Mo0.96Zr0.04)0.90B2 is −6.4×10−4 GPa−1, which is almost twice, compared with that of −2.7×10−4 GPa−1 189 in Mo0.96Zr0.04B2. These results suggest that the defected system in TMB2 has the common feature of 190 sensitive c/a against applied pressure. Also, the pressure dependence of Tc and c/a exhibits a similar 191 trend with a negative correlation in all the examined superconducting TMB2. 192  7  193 FIG. 3. XRD pattern under high pressure of (a) NbB2, (b) Nb1−xB2, (c) Mo1−xZrxB2, and (d) 194 (Mo1−xZrx)1−yB2.  195  196 FIG. 4. Pressure-dependent lattice constants a and c in (a) NbB2 and Nb0.93B2, (b) Mo0.96Zr0.04B2 197 and (Mo0.96Zr0.04)0.90B2, and (c) The c/a in these compounds. 198  199 Finally, the relationship between c/a and Tc in NbB2, Nb0.93B2, Mo0.96Zr0.04B2, and 200 (Mo0.96Zr0.04)0.90B2 are shown in Fig. 5. Because experimentally observed c/a and Tc are measured 201 under slightly different pressures, these values measured at nearest pressures are used for the circle 202 plots. The straight lines are determined from the slopes in the pressure dependence of c/a and Tc. 203  8 Interestingly, a positive trend between Tc and c/a is commonly observed in the examined samples. This 204 fact suggests that c/a is strongly correlated with superconductivity in NbB2 and MoB2 systems with a 205 large contribution of d electron to EF [12,13], in spite of different electronic states with MgB2, which 206 exhibit p electron feature [30]. In particular, the electronic structure in MoB2-based systems is mainly 207 composed of Mo dz2 orbital, coupled with out-of-plane vibrations in Mo. This observation highlights 208 the universal importance of two-dimensionality in the crystal structure for superconductivity in TMB2, 209 regardless of characteristics in electronic structure. A possible explanation for this correlation is the 210 contribution of B p orbitals to EF. In the NbB2 system, the in-plane dispersion of σ-bonding in B 2p 211 states contributes to EF[12], despite the dominant Nb d orbital character. Similarly, in-plane breathing-212 like vibrations of B atoms are believed to enhance superconductivity in pristine MoB2[6]. Additionally, 213 high-Tc MoB2, which exhibits the Tc of 32 K under extreme pressure, has a high c/a value of 1.09[11], 214 comparable with that in MgB2. Furthermore, the theoretically predicted AlB2-type CaB2 with the 215 estimated Tc above 50 K at 30 GPa [31] is suggested to have the highest c/a of 1.27 among 216 superconducting TMB2. Although the obvious mechanism of this correlation is still an open question, 217 the observed relationship between c/a and Tc provides valuable insights for further research on metal 218 diborides. 219  220 FIG. 5. Relationship between c/a and Tc in NbB2, Nb0.93B2, Mo0.96Zr0.04B2 and (Mo0.96Zr0.04)0.90B2. 221  222 IV. CONCLUSIONS 223 The high-pressure electrical transport measurements and structural analysis for superconducting 224 NbB2, Nb0.93B2, Mo0.96Zr0.04B2, and (Mo0.96Zr0.04)0.90B2 reveal that the relationship between the Tc and 225 a stretched c-lattice parameter (c/a), which is considered as important parameter for high-Tc 226 superconductivity in MgB2. All the examined diborides exhibit a common correlation in Tc and c/a 227 with a positive slope. The observation makes an open issue for the guideline of development in 228 superconducting diborides because the electronic state and key factor for superconductivity between 229 MgB2 and superconducting TMB2 is totally different. The c/a is expected to be a future guideline for 230 the exploration of high-Tc superconductors in metal diborides and related materials. 231  232  233  9 ACKNOWLEDGMENTS 234 This work was partly supported by JSPS KAKENHI Grant Number 23H01835, 23K13549, and 235 23KK0088. The fabrication process of diamond electrodes was partially supported by the NIMS 236 Nanofabrication Platform in the Nanotechnology Platform Project sponsored by the Ministry of 237 Education, Culture, Sports, Science and Technology (MEXT), Japan. The synchrotron X-ray 238 experiments were performed at AR-NE1A (KEK-PF) under the approval of Proposal No. 2022G049 239 with support from Dr. Y. 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