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Fe substitution and pressure effects on superconductor Re6Hf
Solid State Communications 272 (2018) 12–16
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Solid State Communications journal homepage: w w w . e l s e v i e r . c o m / l o c a t e / s s c
Communication
Fe substitution and pressure effects on superconductor Re6 Hf Jinhu Yang, Yang Guo, Hangdong Wang, Bin Chen * Department of Physics, Hangzhou Normal University, Hangzhou, 310036, China
A R T I C L E
I N F O
Keywords: Noncentrosymmetric superconductor (Re1−x Fex )6 Hf Upper critical field Pressure
A B S T R A C T
Polycrystalline samples of (Re1−x Fex )6 Hf were synthesized by arc-melting method and the phase purity of the samples was confirmed by powder X-ray diffraction method. In this paper, we report the Fe substitution and pressure effect on non-centrosymmetric superconductor Re6 Hf. The superconducting transition temperature, TC , is confirmed by the measurements of magnetic susceptibility, electrical resistivity for x ≤ 0.22 samples with the temperature down to 2 K. We find that the TC is suppressed with the increase of Fe content. The upper critical field Hc 2 is larger than the value predicted by the WHH theory and shows a linear temperature dependence down to 2 K. When upon the application of external pressure up to 2.5 GPa, the TC decreases monotonically at a rate dlnTC /dP of 0.01 GPa−1 .
1. Introduction In noncentrosymmetric superconductors, a strong asymmetric spinorbit coupling (ASOC) can split the Fermi surface and remove the spin degeneracy of electrons in theory, leading to a mixing of spin-singlet and spin-triplet states in the superconducting condensate [1]. The typical example is Li2 Pd3−x Ptx B system, in which ASOC is enhanced with increasing contents of Pt, and leading to unconventional superconductivity in Li2 Pt3 B [2–8]. Recently, superconductivity was reported in Re6 Zr, which has a noncentrosymmetric 𝛼-Mn crystal structure with the space group I43m. Magnetization, heat capacity, and resistivity measurements suggest that Re6 Zr is a BCS type superconductor with enhanced electron phonon coupling [9,10]. Furthermore, 185/187 Re Nuclear Quadrupole Resonance (NQR) measurements suggest that it is a weak-coupling, conventional s-wave superconductor with a fully gap [11]. However, muon spin relaxation measurements found a small internal magnetic field below superconducting transition temperature TC , indicating unconventional superconductivity in Re6 Zr [12]. The theoretical calculation indicates that the density of states near the Fermi level is almost entirely composed of the d bands of Re and Zr. Because of the ratio of Re to Zr is 6:1, Re-d bands comprise the majority of the states [9]. The chemical substitution at Re sites will be useful to modify the electronic states at the Fermi level and in consequence the superconducting properties in this system. In our previous work, we found the analogous compound Re6 Hf is
a superconductor with TC ∼ 6.3 K [13]. The results of the specific heat indicate that Re6 Hf is possible a BCS - type superconductor. However, the very recent muSR measurement suggest unconventional superconductivity in Re6 Hf [14], as similar case in Re6 Zr. In this paper, we report the effects of partial substitution of Re with Fe on Re6 Hf, that is (Re1−x Fex )6 Hf, with x = 0.0, 0.05, 0.1, 0.15 and 0.20 samples. We found that TC is suppressed continuously by the Fe substitution. Generally, magnetic doping will destroy the BCS - type superconductivity quickly. It is interesting that the sample shows superconductivity even up to the doping level as 20%. When under pressure up to 2.5 GPa, TC shifts from 6.25 K to 6.1 K. The upper critical field Hc2 (T) shows a linear behavior and were enhanced at low temperatures, deviating from the Werthamer - Helfand - Hohenberg (WHH) theory. 2. Experimental details Polycrystalline samples of (Re1−x Fex )6 Hf were prepared by the standard arc-melting method (Re (99.9%), Hf (99.9%) and Fe (99.95%)) with a nominal molar ratio 6-6x: 6x: 1 (x = 0, 0.05, 0.1, 0.15, 0.20, 0.22, 0.25, 0.30) in an ultra-purity argon gas atmosphere on a watercooled copper hearth with a tungsten electrode. Ti button was used as an oxygen getter. The sample buttons were melted at least six times to improve the homogeneity. After that, the arc melted buttons were annealed at 1123 K for one week in an evacuated quartz tube. No obvious weight loss was observed during the above processes.
* Corresponding author. E-mail addresses: [email protected] (J. Yang), [email protected] (Y. Guo), [email protected] (H. Wang), [email protected] (B. Chen). https://doi.org/10.1016/j.ssc.2018.01.001 Received 3 November 2017; Received in revised form 26 December 2017; Accepted 2 January 2018 Available online 3 January 2018 0038-1098/© 2018 Elsevier Ltd. All rights reserved.
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Solid State Communications 272 (2018) 12–16
Fig. 2. Temperature dependence of the normalized electrical resistivity of (Re1−x Fex )6 Hf (x = 0–0.22) at zero magnetic field. The inset shows the Fe content x dependence of superconducting transition temperature TC for (Re1−x Fex )6 Hf (x = 0–0.22). The inset shows the x dependence of the 10%, 50% and 90% drops of the normal-state resistivity just above TC and the onset of the superconducting transition obtained from the electrical resistivity and magnetic susceptibility measurements, respectively.
cal resistivity. The magnetic susceptibility measurements were carried out by a commercial magnetic property measurement system (MPMS7T). The electrical resistivity was measured using a standard four-probe technique in zero magnetic field and under applied magnetic field up to 9 T. The measurements were performed on a Quantum Design Physical Property Measurement System (PPMS-9T). Measurement of transition temperature under applied hydrostatic pressure was carried out in a commercial BeCu cylindrical pressure cell (Quantum Design) within PPMS. Daphne 7373 oil was used as the pressure-transmitting medium. 3. Results and discussion Fig. 1(a) shows the XRD pattern for Re6 Hf fitted by Rietield method. All the peaks could be indexed and fitted very well based on 𝛼-Mn crystal structure with the I43m space group. The refinement reveals the single phase nature of the sample. The obtained lattice parameters are of a = 9.6833 Å (wRp = 9.64%, Rp = 7.24% and 𝜒 2 = 1.21), which is consistent with the reported data [9,13]. Fig. 1(b) shows the obtained XRD patterns for (Re1−x Fex )6 Hf (x = 0–0.22) samples. There is no obvious impurity phase was observed with the increase of the amount of Fe up to x = 0.22. The estimated lattice constants a are shown in the inset of Fig. 1(b), which show a slight increase with the increasing of x. Fig. 2 shows the temperature dependence of electrical resistivity 𝜌(T) for (Re1−x Fex )6 Hf with 0 ≤ x ≤ 0.22 at zero magnetic field. A pronounced superconducting transition is observed for each sample. For x = 0, 0.05, 0.10, 0.15 samples, clear superconducting transitions
Fig. 1. (a) Powder X-ray diffraction pattern for Re6 Hf together with the result of a Rietveld refinement. Red circle denote the observed intensities; Blue and gray lines give the calculated and difference intensities, respectively. (b) Powder X-ray diffraction patterns for (Re1−x Fex )6 Hf (x = 0–0.22). The inset of Fig. (b) shows the x dependence of lattice constant a. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
The crystal structure and phase purity of the powdered samples were characterized by use of a Rigaku Geigerflex powder X-ray diffractometer (XRD) with Cu K𝛼 radiation (𝜆 = 1.54056 Å) at room temperature. Rietveld refinements of the data were carried out using the GSAS package [15,16]. The superconducting properties of the samples were characterized by the measurements of magnetization and electri-
Table 1 Some parameters of (Re1−x Fex )6 Hf. Details can be found in the text. x
TC (10%) (K)
TC (50%) (K)
TC (90%) (K)
d(Hc2 ∕dT)TC
linear fit (T)
WHH Hc2 (0) (T)
GL Hc2 (0) (T)
Pauli Hc2 (0) (T)
0 0.05 0.10 0.15 0.20
6.44 5.89 5.32 4.25 3.13
6.32 5.81 5.12 3.81 2.43
6.17 5.62 4.85 3.40 –
−2.10 −2.15 −2.07 −1.93 −2.02
13.23 12.55 10.69 7.36 6.32
9.20 8.66 7.34 5.10 3.40
10.92 10.35 8.82 6.24 5.52
11.63 10.69 9.42 7.01 4.47
13
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Solid State Communications 272 (2018) 12–16
to zero resistance were observed other than x = 0.20 and 0.22 samples because of the measurement temperature is only down to 2 K. Here the superconducting transition temperature TC are determined from the 10%, 50% and 90% drops of the normal-state resistivity just above TC . Details can be found in Table 1. With the increase of x, the value of TC decrease continuously as shown in the inset of Fig. 2. For x = 0 sample, the superconducting transition temperature width is about 0.2 K, which is relatively sharp. However, the superconducting transition is broadened upon increasing Fe content x, which is likely attributed to the enhanced sample inhomogeneity. The temperature dependence of dc magnetic susceptibility for (Re1−x Fex )6 Hf with 0 ≤ x ≤ 0.20 are shown in Fig. 3. The data were measured via the zero-field-cooling (ZFC) and field-cooling (FC) mode under the field of 10 Oe. A clear diamagnetic signal appears at TC indicating the occurrence of superconductivity. Here, TC was defined as the onset of the diamagnetic signal in the temperature dependence of magnetic susceptibility. The Fe content x dependence of superconducting transition temperature TC (x) is also presented in the inset of Fig. 2. Usually, the magnetic impurities were thought to have a strong effect in TC (x) for a conventional superconductor. However, in
Fig. 3. Temperature dependence of the dc magnetic susceptibility for (Re1−x Fex )6 Hf with x = 0–0.20. The data were measured via the zero-field-cooling (ZFC) and field-cooling (FC) mode under the field of 10 Oe.
Fig. 4. Temperature dependence of the electrical resistivity for (Re1−x Fex )6 Hf system with x = 0.05, 0.10, 0.15 and 0.20 samples under various constant magnetic fields.
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(Re1−x Fex )6 Hf, we found that superconductivity still alive even the Fe substitution level up to 20%. Similar case were also discovered in Li2 Pd3 B system [17]. When the nonmagnetic element substitution of Pd with Cu or Pt produces a strong decrease of TC than the magnetic element substitution of Pd with Ni [17]. To determine the Hc2 , we measured the electrical resistivity as a function of magnetic field 𝜌(T) (x = 0, 0.05, 0.10, 0.15, 0.20) with the temperature down to 2 K. Obviously, the TC is shifted to lower temperatures upon increasing magnetic field as shown in Fig. 4 for x = 0.05, 0.10, 0.15, 0.20 samples. The superconducting transition of x = 0, 0.05, 0.10 remains fairly sharp in a magnetic field, but it is broadened in other samples with larger x = 0.15, 0.20. The temperature dependence of Hc2 was extracted from the curves in Fig. 4 by use of the midpoint (50% drops) TC . As shown in Fig. 5(a), the Hc2 - TC shows nearly linear behavior for all samples. The linear extrapolation at T = 0 K gives values of Hc2 (0) as 13.23 T, 12.55 T, 10.69 T, 7.36 T and 6.32 T for x = 0, 0.05, 0.10, 0.15 and 0.20 samples, respectively. The slope of the Hc2 (T) - TC figure (dHc 2 /dT) near TC is shown in Table 1. Such values of Hc2 (0) largely exceed the corre-
sponding orbital limiting field, and are close to or even larger than the Pauli limiting field. In Fig. 5(b), we show the normalized upper critical field h = Hc2 ∕[TC (dHc2 ∕dT)TC ] versus t = T∕TC for various Fe contents. For comparison, we include the fits of the upper critical fields by the WHH method in the dirty limit (dotted line) as well as the Ginzburg-Landau (GL) formula (solid line). One can see that the WHH method fails to describe the experimental data over a wide temperature region. The GL formula can give a much better illustration of the experimental data. Of course, the low temperature data are greatly desired here. This phenomenon had been observed in some noncentrosymmetric superconductors, such as, Li2 Pd3−x Cux B [17], Nbx Re1−x [18] system. According to Ginzburg-Landau theory, the upper critical field Hc2 evolves with temperature following the formula: GL Hc2 (T) = Hc2 (0)(1 − t 2 )∕(1 + t 2 ),
(1)
where t is the renormalized temperature T∕TC . The upper critical GL estimated for each sample are summarized in Table 1. With field Hc2 GL the increase of Fe amount, the Hc2 is suppressed from 10.92 T for x = 0–5.52 T for x = 0.20 sample. On the other hand, according to the WHH theory, the upper critical field originated from the orbital mechanism can be estimated from TC and the initial slope of the Hc2 (T) - T plot by use of the formula: ) ( dHc2 WHH (0) = −0.693 × × TC . (2) Hc2 dT TC WHH (0) = 9.20 T, 8.66 T, 7.34 T, The above formula gives Hc2 5.10 T and 3.40 T for x = 0, 0.05, 0.10, 0.15 and 0.20, respectively. Furthermore, superconductivity can be destroyed by the Pauli paramagnetic effect in a magnetic field as a result of the Zeeman effect. For a conventional BCS superconductor the Pauli paramagnetic limit can be simplified as Pauli Hc2 = 1.84TC .
(3)
The Pauli limiting fields are, therefore, estimated to be 11.63 T, 10.69 T, 9.42 T, 7.01 T and 4.47 T for x = 0, 0.05, 0.10, 0.15 and 0.20, respectively. All the results are summarized in Table 1. We can find an enhancement of the Hc2 (T) which deviates from the WHH theory at low temperatures. Usually, this enhancement can be ascribed to different causes, such as the strong electron-phonon coupling [19], anisotropic Fermi surface [20], granularity [21] and local-
Fig. 5. (a) The upper critical field Hc 2 as a function of temperature for (Re1−x Fex )6 Hf system determined from the electrical resistivity data. The lines are a linear fit of the data near to TC . (b) Normalized upper critical field h(= Hc2 ∕[TC (dHc2 ∕dT)TC ]) as a function of normalized temperature t(=T/TC ). The solid and dashed lines represent fits of the GL and WHH methods, respectively.
Fig. 6. Temperature dependence of electrical resistivity under various pressures from 0 to 2.5 GPa for Re6 Hf sample from 2 K to 20 K. The inset shown the pressure dependence of TC for Re6 Zr and Re6 Hf. The solid lines represent the linear fit for the data. 15
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Solid State Communications 272 (2018) 12–16
Acknowledgements
ization effects in highly disordered superconductors [22]. Our previous study indicates that the electron-phonon coupling constant 𝜆ep is about 0.67 and ΔC∕𝛾n Tc ∼ 1.63 for Re6 Hf, which is slightly larger than 1.43 predicted by BCS theory [13]. These values indicate that electronphonon coupling is moderately strong in Re6 Hf and can be regarded as an intermediate coupling superconductor. Then the Hc2 (T) enhancement may not be this characteristic. However, as it had been pointed out by D. A. Mayoh et.al. [10] that the polycrystalline sample of Re6 Zr will contain grain boundaries. The upper critical field will be increased above the bulk value once the grain size becomes smaller than the coherence length [21]. This is possibly one reason for the enhancement Hc2 (T) in Re6 Hf system. Pressure is considered as a clean method for tuning the electronic states in a material. Here, we present the electrical resistivity as a function of pressure in the range 0–2.5 GPa. The temperature dependence of the resistance in the vicinity of superconducting transition at various external pressure were performed on the compound Re6 Hf as shown in Fig. 6. There is a clear systematic shift of the onset TC towards lower temperature with increasing pressure. It can be seen that TC decreases from the value of 6.25 K at ambient pressure to 6.1 K at 2.5 GPa. For comparison, the pressure effect data for Re6 Zr [9] system are also shown in Fig. 6. We found that the pressure only had a small effect on the transition temperature up to 2.5 GPa, just like that of Re6 Zr system. The rate of decrease of TC per unit pressure dTC /dP is found to be 0.07 K/GPa and dlnTC /dP = [(1/TC )(dTC /dP)] is about 0.01 GPa−1 , which is satisfy with the value predicted for a conventional superconductor [23].
This research is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY14A040007, LY16A040012). References [1] F. Kneidinger, E. Bauer, I. Zeiringer, P. Rogl, C. Blaas-Schenner, D. Reith, R. Podloucky, Phys. Can. 514 (2015) 388–398. [2] K. Togano, P. Badica, Y. Nakamori, S. Orimo, H. Takeya, K. Hirata, Phys. Rev. Lett. 93 (2004) 247004. [3] P. Badica, T. Kondo, T. Kudo, Y. Nakamori, S. Orimo, K. Togano, Appl. Phys. Lett. 85 (2004) 4433. [4] S. Harada, J.J. Zhou, Y.G. Yao, Y. Inada, Guo-qing Zheng, Phys. Rev. B 86 (2012) 220502. [5] P. Badica, T. Kondo, K. Togano, J. Phys. Soc. Jpn. 74 (2005) 1014. [6] M. Nishiyama, Y. Inada, G.Q. Zheng, Phys. Rev. Lett. 98 (2007) 47002. [7] H.Q. Yuan, D.F. Agterberg, N. Hayashi, P. Badica, D. Vandervelde, K. Togano, M. Sigeist, M.B. Salamon, Phys. Rev. Lett. 97 (2006) 17006. [8] Lingwei Li, Katsuhiko Nishimura, Jyungo Ishiyama, Katsunori Mori, Phys. Can. 468 (2008) 244–248. [9] Mojammel A. Khan, A.B. Karki, T. Samanta, D. Browne, S. Stadler, I. Vekhter, Abhishek Pandey, P.W. Adams, D.P. Young, S. Teknowijoyo, K. Cho, R. Prozorov, D.E. Graf, Phys. Rev. B 94 (2016) 144515. [10] D.A. Mayoh, J.A.T. Barker, R.P. Singh, G. Balakrishnan, D. McK. Paul, M.R. Lees, Phys. Rev. B 96 (2017) 064521. [11] K. Matano, R. Yatagai, S. Maeda, Guo-qing Zheng, Phys. Rev. B 94 (2016) 214513. [12] R.P. Singh, A.D. Hillier, B. Mazidian, J. Quintanilla, J.F. Annett, D. McK. Paul, G. Balakrishnan, M.R. Lees, Phys. Rev. Lett. 112 (2014) 107002. [13] Bin Chen, Yang Guo, Hangdong Wang, Qiping Su, Qianhui Mao, Jianhua Du, Yuxing Zhou, Jinhu Yang, Minghu Fang, Phys. Rev. B 94 (2016) 024518. [14] D. Singh, J. A. T. Barker, A. Thamizhavel, D. McK. Paul, A. D. Hillier, R. P. Singh, arXiv:1710.08598v1. [15] A.C. Larson, R.B. Von Dreele, Los Alamos National Laboratory Report LAUR 86 (2000) 748. [16] B.H. Toby, EXPGUI, a graphical user interface for GSAS, J. Appl. Cryst 34 (2001) 210. [17] A.A. Castro, O. Olicn, R. Escamilla, F. Morales, Solid State Commun. 255–256 (2017) 11–14. [18] J. Chen, L. Jiao, J.L. Zhang, Y. Chen, L. Yang, M. Nicklas, F. Steglich, H.Q. Yuan, Phys. Rev. B 88 (2013) 14. [19] L.N. Bulaevskii, O.V. Dolgov, M.O. Ptitsyn, Phys. Rev. B 38 (1988) 11290–11295. [20] T. Kita, M. Arai, Phys. Rev. B 70 (2004) 224522. [21] P. deGennes, M. Tinkham, Physics 1 (1964) 107. [22] L. Coffey, K. Levin, K.A. Muttalib, Phys. Rev. B 32 (1985) 4382–4391. [23] H.D. Yang, S. Mollah, W.L. Huang, P.L. Ho, H.L. Huang, C.-J. Liu, J.-Y. Lin, Y.-L. Zhang, R.-C. Yu, C.-Q. Jin, Phys. Rev. B 68 (2003) 092507.
4. Conclusion In summary, we prepared polycrystalline samples of (Re1−x Fex )6 Hf for x ≤ 0.22 by arc-melting method successfully. We measured resistivity and magnetic susceptibility for each sample and found that TC is suppressed with the increase of Fe content. A linear behavior was observed in Hc2 (T), deviating from the prediction of the WHH theory. The TC was suppressed a bit under the external pressure up to 2.5 GPa, with a rate dlnTC /dP of 0.01 GPa−1 .
16
Contents lists available at ScienceDirect
Solid State Communications journal homepage: w w w . e l s e v i e r . c o m / l o c a t e / s s c
Communication
Fe substitution and pressure effects on superconductor Re6 Hf Jinhu Yang, Yang Guo, Hangdong Wang, Bin Chen * Department of Physics, Hangzhou Normal University, Hangzhou, 310036, China
A R T I C L E
I N F O
Keywords: Noncentrosymmetric superconductor (Re1−x Fex )6 Hf Upper critical field Pressure
A B S T R A C T
Polycrystalline samples of (Re1−x Fex )6 Hf were synthesized by arc-melting method and the phase purity of the samples was confirmed by powder X-ray diffraction method. In this paper, we report the Fe substitution and pressure effect on non-centrosymmetric superconductor Re6 Hf. The superconducting transition temperature, TC , is confirmed by the measurements of magnetic susceptibility, electrical resistivity for x ≤ 0.22 samples with the temperature down to 2 K. We find that the TC is suppressed with the increase of Fe content. The upper critical field Hc 2 is larger than the value predicted by the WHH theory and shows a linear temperature dependence down to 2 K. When upon the application of external pressure up to 2.5 GPa, the TC decreases monotonically at a rate dlnTC /dP of 0.01 GPa−1 .
1. Introduction In noncentrosymmetric superconductors, a strong asymmetric spinorbit coupling (ASOC) can split the Fermi surface and remove the spin degeneracy of electrons in theory, leading to a mixing of spin-singlet and spin-triplet states in the superconducting condensate [1]. The typical example is Li2 Pd3−x Ptx B system, in which ASOC is enhanced with increasing contents of Pt, and leading to unconventional superconductivity in Li2 Pt3 B [2–8]. Recently, superconductivity was reported in Re6 Zr, which has a noncentrosymmetric 𝛼-Mn crystal structure with the space group I43m. Magnetization, heat capacity, and resistivity measurements suggest that Re6 Zr is a BCS type superconductor with enhanced electron phonon coupling [9,10]. Furthermore, 185/187 Re Nuclear Quadrupole Resonance (NQR) measurements suggest that it is a weak-coupling, conventional s-wave superconductor with a fully gap [11]. However, muon spin relaxation measurements found a small internal magnetic field below superconducting transition temperature TC , indicating unconventional superconductivity in Re6 Zr [12]. The theoretical calculation indicates that the density of states near the Fermi level is almost entirely composed of the d bands of Re and Zr. Because of the ratio of Re to Zr is 6:1, Re-d bands comprise the majority of the states [9]. The chemical substitution at Re sites will be useful to modify the electronic states at the Fermi level and in consequence the superconducting properties in this system. In our previous work, we found the analogous compound Re6 Hf is
a superconductor with TC ∼ 6.3 K [13]. The results of the specific heat indicate that Re6 Hf is possible a BCS - type superconductor. However, the very recent muSR measurement suggest unconventional superconductivity in Re6 Hf [14], as similar case in Re6 Zr. In this paper, we report the effects of partial substitution of Re with Fe on Re6 Hf, that is (Re1−x Fex )6 Hf, with x = 0.0, 0.05, 0.1, 0.15 and 0.20 samples. We found that TC is suppressed continuously by the Fe substitution. Generally, magnetic doping will destroy the BCS - type superconductivity quickly. It is interesting that the sample shows superconductivity even up to the doping level as 20%. When under pressure up to 2.5 GPa, TC shifts from 6.25 K to 6.1 K. The upper critical field Hc2 (T) shows a linear behavior and were enhanced at low temperatures, deviating from the Werthamer - Helfand - Hohenberg (WHH) theory. 2. Experimental details Polycrystalline samples of (Re1−x Fex )6 Hf were prepared by the standard arc-melting method (Re (99.9%), Hf (99.9%) and Fe (99.95%)) with a nominal molar ratio 6-6x: 6x: 1 (x = 0, 0.05, 0.1, 0.15, 0.20, 0.22, 0.25, 0.30) in an ultra-purity argon gas atmosphere on a watercooled copper hearth with a tungsten electrode. Ti button was used as an oxygen getter. The sample buttons were melted at least six times to improve the homogeneity. After that, the arc melted buttons were annealed at 1123 K for one week in an evacuated quartz tube. No obvious weight loss was observed during the above processes.
* Corresponding author. E-mail addresses: [email protected] (J. Yang), [email protected] (Y. Guo), [email protected] (H. Wang), [email protected] (B. Chen). https://doi.org/10.1016/j.ssc.2018.01.001 Received 3 November 2017; Received in revised form 26 December 2017; Accepted 2 January 2018 Available online 3 January 2018 0038-1098/© 2018 Elsevier Ltd. All rights reserved.
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Solid State Communications 272 (2018) 12–16
Fig. 2. Temperature dependence of the normalized electrical resistivity of (Re1−x Fex )6 Hf (x = 0–0.22) at zero magnetic field. The inset shows the Fe content x dependence of superconducting transition temperature TC for (Re1−x Fex )6 Hf (x = 0–0.22). The inset shows the x dependence of the 10%, 50% and 90% drops of the normal-state resistivity just above TC and the onset of the superconducting transition obtained from the electrical resistivity and magnetic susceptibility measurements, respectively.
cal resistivity. The magnetic susceptibility measurements were carried out by a commercial magnetic property measurement system (MPMS7T). The electrical resistivity was measured using a standard four-probe technique in zero magnetic field and under applied magnetic field up to 9 T. The measurements were performed on a Quantum Design Physical Property Measurement System (PPMS-9T). Measurement of transition temperature under applied hydrostatic pressure was carried out in a commercial BeCu cylindrical pressure cell (Quantum Design) within PPMS. Daphne 7373 oil was used as the pressure-transmitting medium. 3. Results and discussion Fig. 1(a) shows the XRD pattern for Re6 Hf fitted by Rietield method. All the peaks could be indexed and fitted very well based on 𝛼-Mn crystal structure with the I43m space group. The refinement reveals the single phase nature of the sample. The obtained lattice parameters are of a = 9.6833 Å (wRp = 9.64%, Rp = 7.24% and 𝜒 2 = 1.21), which is consistent with the reported data [9,13]. Fig. 1(b) shows the obtained XRD patterns for (Re1−x Fex )6 Hf (x = 0–0.22) samples. There is no obvious impurity phase was observed with the increase of the amount of Fe up to x = 0.22. The estimated lattice constants a are shown in the inset of Fig. 1(b), which show a slight increase with the increasing of x. Fig. 2 shows the temperature dependence of electrical resistivity 𝜌(T) for (Re1−x Fex )6 Hf with 0 ≤ x ≤ 0.22 at zero magnetic field. A pronounced superconducting transition is observed for each sample. For x = 0, 0.05, 0.10, 0.15 samples, clear superconducting transitions
Fig. 1. (a) Powder X-ray diffraction pattern for Re6 Hf together with the result of a Rietveld refinement. Red circle denote the observed intensities; Blue and gray lines give the calculated and difference intensities, respectively. (b) Powder X-ray diffraction patterns for (Re1−x Fex )6 Hf (x = 0–0.22). The inset of Fig. (b) shows the x dependence of lattice constant a. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
The crystal structure and phase purity of the powdered samples were characterized by use of a Rigaku Geigerflex powder X-ray diffractometer (XRD) with Cu K𝛼 radiation (𝜆 = 1.54056 Å) at room temperature. Rietveld refinements of the data were carried out using the GSAS package [15,16]. The superconducting properties of the samples were characterized by the measurements of magnetization and electri-
Table 1 Some parameters of (Re1−x Fex )6 Hf. Details can be found in the text. x
TC (10%) (K)
TC (50%) (K)
TC (90%) (K)
d(Hc2 ∕dT)TC
linear fit (T)
WHH Hc2 (0) (T)
GL Hc2 (0) (T)
Pauli Hc2 (0) (T)
0 0.05 0.10 0.15 0.20
6.44 5.89 5.32 4.25 3.13
6.32 5.81 5.12 3.81 2.43
6.17 5.62 4.85 3.40 –
−2.10 −2.15 −2.07 −1.93 −2.02
13.23 12.55 10.69 7.36 6.32
9.20 8.66 7.34 5.10 3.40
10.92 10.35 8.82 6.24 5.52
11.63 10.69 9.42 7.01 4.47
13
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to zero resistance were observed other than x = 0.20 and 0.22 samples because of the measurement temperature is only down to 2 K. Here the superconducting transition temperature TC are determined from the 10%, 50% and 90% drops of the normal-state resistivity just above TC . Details can be found in Table 1. With the increase of x, the value of TC decrease continuously as shown in the inset of Fig. 2. For x = 0 sample, the superconducting transition temperature width is about 0.2 K, which is relatively sharp. However, the superconducting transition is broadened upon increasing Fe content x, which is likely attributed to the enhanced sample inhomogeneity. The temperature dependence of dc magnetic susceptibility for (Re1−x Fex )6 Hf with 0 ≤ x ≤ 0.20 are shown in Fig. 3. The data were measured via the zero-field-cooling (ZFC) and field-cooling (FC) mode under the field of 10 Oe. A clear diamagnetic signal appears at TC indicating the occurrence of superconductivity. Here, TC was defined as the onset of the diamagnetic signal in the temperature dependence of magnetic susceptibility. The Fe content x dependence of superconducting transition temperature TC (x) is also presented in the inset of Fig. 2. Usually, the magnetic impurities were thought to have a strong effect in TC (x) for a conventional superconductor. However, in
Fig. 3. Temperature dependence of the dc magnetic susceptibility for (Re1−x Fex )6 Hf with x = 0–0.20. The data were measured via the zero-field-cooling (ZFC) and field-cooling (FC) mode under the field of 10 Oe.
Fig. 4. Temperature dependence of the electrical resistivity for (Re1−x Fex )6 Hf system with x = 0.05, 0.10, 0.15 and 0.20 samples under various constant magnetic fields.
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(Re1−x Fex )6 Hf, we found that superconductivity still alive even the Fe substitution level up to 20%. Similar case were also discovered in Li2 Pd3 B system [17]. When the nonmagnetic element substitution of Pd with Cu or Pt produces a strong decrease of TC than the magnetic element substitution of Pd with Ni [17]. To determine the Hc2 , we measured the electrical resistivity as a function of magnetic field 𝜌(T) (x = 0, 0.05, 0.10, 0.15, 0.20) with the temperature down to 2 K. Obviously, the TC is shifted to lower temperatures upon increasing magnetic field as shown in Fig. 4 for x = 0.05, 0.10, 0.15, 0.20 samples. The superconducting transition of x = 0, 0.05, 0.10 remains fairly sharp in a magnetic field, but it is broadened in other samples with larger x = 0.15, 0.20. The temperature dependence of Hc2 was extracted from the curves in Fig. 4 by use of the midpoint (50% drops) TC . As shown in Fig. 5(a), the Hc2 - TC shows nearly linear behavior for all samples. The linear extrapolation at T = 0 K gives values of Hc2 (0) as 13.23 T, 12.55 T, 10.69 T, 7.36 T and 6.32 T for x = 0, 0.05, 0.10, 0.15 and 0.20 samples, respectively. The slope of the Hc2 (T) - TC figure (dHc 2 /dT) near TC is shown in Table 1. Such values of Hc2 (0) largely exceed the corre-
sponding orbital limiting field, and are close to or even larger than the Pauli limiting field. In Fig. 5(b), we show the normalized upper critical field h = Hc2 ∕[TC (dHc2 ∕dT)TC ] versus t = T∕TC for various Fe contents. For comparison, we include the fits of the upper critical fields by the WHH method in the dirty limit (dotted line) as well as the Ginzburg-Landau (GL) formula (solid line). One can see that the WHH method fails to describe the experimental data over a wide temperature region. The GL formula can give a much better illustration of the experimental data. Of course, the low temperature data are greatly desired here. This phenomenon had been observed in some noncentrosymmetric superconductors, such as, Li2 Pd3−x Cux B [17], Nbx Re1−x [18] system. According to Ginzburg-Landau theory, the upper critical field Hc2 evolves with temperature following the formula: GL Hc2 (T) = Hc2 (0)(1 − t 2 )∕(1 + t 2 ),
(1)
where t is the renormalized temperature T∕TC . The upper critical GL estimated for each sample are summarized in Table 1. With field Hc2 GL the increase of Fe amount, the Hc2 is suppressed from 10.92 T for x = 0–5.52 T for x = 0.20 sample. On the other hand, according to the WHH theory, the upper critical field originated from the orbital mechanism can be estimated from TC and the initial slope of the Hc2 (T) - T plot by use of the formula: ) ( dHc2 WHH (0) = −0.693 × × TC . (2) Hc2 dT TC WHH (0) = 9.20 T, 8.66 T, 7.34 T, The above formula gives Hc2 5.10 T and 3.40 T for x = 0, 0.05, 0.10, 0.15 and 0.20, respectively. Furthermore, superconductivity can be destroyed by the Pauli paramagnetic effect in a magnetic field as a result of the Zeeman effect. For a conventional BCS superconductor the Pauli paramagnetic limit can be simplified as Pauli Hc2 = 1.84TC .
(3)
The Pauli limiting fields are, therefore, estimated to be 11.63 T, 10.69 T, 9.42 T, 7.01 T and 4.47 T for x = 0, 0.05, 0.10, 0.15 and 0.20, respectively. All the results are summarized in Table 1. We can find an enhancement of the Hc2 (T) which deviates from the WHH theory at low temperatures. Usually, this enhancement can be ascribed to different causes, such as the strong electron-phonon coupling [19], anisotropic Fermi surface [20], granularity [21] and local-
Fig. 5. (a) The upper critical field Hc 2 as a function of temperature for (Re1−x Fex )6 Hf system determined from the electrical resistivity data. The lines are a linear fit of the data near to TC . (b) Normalized upper critical field h(= Hc2 ∕[TC (dHc2 ∕dT)TC ]) as a function of normalized temperature t(=T/TC ). The solid and dashed lines represent fits of the GL and WHH methods, respectively.
Fig. 6. Temperature dependence of electrical resistivity under various pressures from 0 to 2.5 GPa for Re6 Hf sample from 2 K to 20 K. The inset shown the pressure dependence of TC for Re6 Zr and Re6 Hf. The solid lines represent the linear fit for the data. 15
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Acknowledgements
ization effects in highly disordered superconductors [22]. Our previous study indicates that the electron-phonon coupling constant 𝜆ep is about 0.67 and ΔC∕𝛾n Tc ∼ 1.63 for Re6 Hf, which is slightly larger than 1.43 predicted by BCS theory [13]. These values indicate that electronphonon coupling is moderately strong in Re6 Hf and can be regarded as an intermediate coupling superconductor. Then the Hc2 (T) enhancement may not be this characteristic. However, as it had been pointed out by D. A. Mayoh et.al. [10] that the polycrystalline sample of Re6 Zr will contain grain boundaries. The upper critical field will be increased above the bulk value once the grain size becomes smaller than the coherence length [21]. This is possibly one reason for the enhancement Hc2 (T) in Re6 Hf system. Pressure is considered as a clean method for tuning the electronic states in a material. Here, we present the electrical resistivity as a function of pressure in the range 0–2.5 GPa. The temperature dependence of the resistance in the vicinity of superconducting transition at various external pressure were performed on the compound Re6 Hf as shown in Fig. 6. There is a clear systematic shift of the onset TC towards lower temperature with increasing pressure. It can be seen that TC decreases from the value of 6.25 K at ambient pressure to 6.1 K at 2.5 GPa. For comparison, the pressure effect data for Re6 Zr [9] system are also shown in Fig. 6. We found that the pressure only had a small effect on the transition temperature up to 2.5 GPa, just like that of Re6 Zr system. The rate of decrease of TC per unit pressure dTC /dP is found to be 0.07 K/GPa and dlnTC /dP = [(1/TC )(dTC /dP)] is about 0.01 GPa−1 , which is satisfy with the value predicted for a conventional superconductor [23].
This research is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY14A040007, LY16A040012). References [1] F. Kneidinger, E. Bauer, I. Zeiringer, P. Rogl, C. Blaas-Schenner, D. Reith, R. Podloucky, Phys. Can. 514 (2015) 388–398. [2] K. Togano, P. Badica, Y. Nakamori, S. Orimo, H. Takeya, K. Hirata, Phys. Rev. Lett. 93 (2004) 247004. [3] P. Badica, T. Kondo, T. Kudo, Y. Nakamori, S. Orimo, K. Togano, Appl. Phys. Lett. 85 (2004) 4433. [4] S. Harada, J.J. Zhou, Y.G. Yao, Y. Inada, Guo-qing Zheng, Phys. Rev. B 86 (2012) 220502. [5] P. Badica, T. Kondo, K. Togano, J. Phys. Soc. Jpn. 74 (2005) 1014. [6] M. Nishiyama, Y. Inada, G.Q. Zheng, Phys. Rev. Lett. 98 (2007) 47002. [7] H.Q. Yuan, D.F. Agterberg, N. Hayashi, P. Badica, D. Vandervelde, K. Togano, M. Sigeist, M.B. Salamon, Phys. Rev. Lett. 97 (2006) 17006. [8] Lingwei Li, Katsuhiko Nishimura, Jyungo Ishiyama, Katsunori Mori, Phys. Can. 468 (2008) 244–248. [9] Mojammel A. Khan, A.B. Karki, T. Samanta, D. Browne, S. Stadler, I. Vekhter, Abhishek Pandey, P.W. Adams, D.P. Young, S. Teknowijoyo, K. Cho, R. Prozorov, D.E. Graf, Phys. Rev. B 94 (2016) 144515. [10] D.A. Mayoh, J.A.T. Barker, R.P. Singh, G. Balakrishnan, D. McK. Paul, M.R. Lees, Phys. Rev. B 96 (2017) 064521. [11] K. Matano, R. Yatagai, S. Maeda, Guo-qing Zheng, Phys. Rev. B 94 (2016) 214513. [12] R.P. Singh, A.D. Hillier, B. Mazidian, J. Quintanilla, J.F. Annett, D. McK. Paul, G. Balakrishnan, M.R. Lees, Phys. Rev. Lett. 112 (2014) 107002. [13] Bin Chen, Yang Guo, Hangdong Wang, Qiping Su, Qianhui Mao, Jianhua Du, Yuxing Zhou, Jinhu Yang, Minghu Fang, Phys. Rev. B 94 (2016) 024518. [14] D. Singh, J. A. T. Barker, A. Thamizhavel, D. McK. Paul, A. D. Hillier, R. P. Singh, arXiv:1710.08598v1. [15] A.C. Larson, R.B. Von Dreele, Los Alamos National Laboratory Report LAUR 86 (2000) 748. [16] B.H. Toby, EXPGUI, a graphical user interface for GSAS, J. Appl. Cryst 34 (2001) 210. [17] A.A. Castro, O. Olicn, R. Escamilla, F. Morales, Solid State Commun. 255–256 (2017) 11–14. [18] J. Chen, L. Jiao, J.L. Zhang, Y. Chen, L. Yang, M. Nicklas, F. Steglich, H.Q. Yuan, Phys. Rev. B 88 (2013) 14. [19] L.N. Bulaevskii, O.V. Dolgov, M.O. Ptitsyn, Phys. Rev. B 38 (1988) 11290–11295. [20] T. Kita, M. Arai, Phys. Rev. B 70 (2004) 224522. [21] P. deGennes, M. Tinkham, Physics 1 (1964) 107. [22] L. Coffey, K. Levin, K.A. Muttalib, Phys. Rev. B 32 (1985) 4382–4391. [23] H.D. Yang, S. Mollah, W.L. Huang, P.L. Ho, H.L. Huang, C.-J. Liu, J.-Y. Lin, Y.-L. Zhang, R.-C. Yu, C.-Q. Jin, Phys. Rev. B 68 (2003) 092507.
4. Conclusion In summary, we prepared polycrystalline samples of (Re1−x Fex )6 Hf for x ≤ 0.22 by arc-melting method successfully. We measured resistivity and magnetic susceptibility for each sample and found that TC is suppressed with the increase of Fe content. A linear behavior was observed in Hc2 (T), deviating from the prediction of the WHH theory. The TC was suppressed a bit under the external pressure up to 2.5 GPa, with a rate dlnTC /dP of 0.01 GPa−1 .
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