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Isotope eﬀect on superconductivity and Raman phonons of Pyrochlore Cd2Re2O7

T

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F.S. Razavi ,a, M. Hajialamdaria, M. Reedyka, R.K. Kremerb a b

Department of Physics, Brock University, St. Catharines, Ontario L2S 3A1, Canada Max-Planck-Institut für Festkörperforschung, Heisenbergstraβe 1, Stuttgart 70569, Germany

A B S T R A C T Cd2Re2O7 is the only α-Pyrochlore exhibiting superconductivity with a transition temperature (Tc) of ∼ 1 K. In this study, we present the eﬀect of oxygen isotope (18O) as well as combined 18O and cadmium isotope (116Cd) substitution on the superconductivity and Raman scattering spectrum of Cd2Re2O7. The change of Tc and the energy gap Δ(T) are reported using various techniques including point contact spectroscopy. The shift in Raman phonon frequencies upon isotope substitution will be compared with measurement of the isotope eﬀect on the superconducting transition temperature.

1. Introduction Amongst the α-Pyrochlore compounds Cd2Re2O7 is the only one exhibiting superconductivity at 1.01 K [1]. Cd2Re2O7 with a 5d2 electronic conﬁguration has a cubic structure with space group Fd3m at room temperature. Below room temperature Cd2Re2O7 undergoes a metal-to-metal second order structural phase transition at TS1 ∼ 200 K to a non-centrosymmetric tetragonal structure with space group I4 m2 followed by a ﬁrst order phase transition at TS2 ∼ 120 K to another tetragonal structure I4122 [2,3]. These two phase transitions have a profound eﬀect on the electronic and magnetic properties of Cd2Re2O7. The resistivity and magnetic susceptibility drop sharply below TS1 [1,4]. The heat capacity also showed rather large electronic heat capacity coeﬃcient (γ = 15 mJ/K2 mol Re) [1]. The band structure calculation for the room temperature cubic structure indicates that the density of states (DOS) at the Fermi level arises mainly from Re-5d states with electron and hole pockets at the diﬀerent symmetry points of the Brillouin zone [5]. Electronic band structure calculations of the low temperature structure indicate localized Cd 4d and itinerant Re 5d electronic states and quasi-two dimensional Fermi surfaces [6]. The results of Re Nuclear quadrupole resonance (NQR) and Cd nuclear magnetic resonance (NMR) at low temperature and in the superconducting state reveal no magnetic or charge ordering in Cd2Re2O7 [7]. The spin lattice relaxation rate obtained from the Re NQR shows that below Tc the relaxation rate between Tc and ∼ 0.8 K is twice larger than that above Tc, and below ∼ 0.8 K the relaxation rate reduces. Based on the Re NQR relaxation rate the superconductivity in Cd2Re2O7 is interpreted as of BCS type with an isotropic energy gap [7]. Vyaselev

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Corresponding author. E-mail address: [email protected] (F.S. Razavi).

https://doi.org/10.1016/j.physc.2018.02.012 Received 12 July 2017; Accepted 28 February 2018 Available online 01 March 2018 0921-4534/ © 2018 Elsevier B.V. All rights reserved.

et al. also calculated the Wilson ratio and obtained a value of 0.34 which implies a strong electron–phonon superconducting coupling in contradiction to their Re NQR results [7]. Recent results of far infrared spectroscopy investigations [8] in the superconducting regime at 0.5 K indicate the existence of two strong absorption peaks near 9.6 and 19.3 cm −1. Recently, we have reported I-V conductance spectra below the superconducting transition temperature of Cd2Re2O7 employing soft point contact spectroscopy [9]. By ﬁtting the spectra to a modiﬁed Blonder–Tinkham–Klapwijk (BTK) theory [10] extended by including the quasiparticle self-energy into the Bogoliubov equations, we were able to derive the temperature dependence and the magnitude of the superconducting order parameter [9]. The magnitude of the gap at T = 0 indicates that Cd2Re2O7 is a strong-coupling superconductor. The temperature dependence of the order parameter is markedly diﬀerent from that expected from weak-coupling BCS theory. To better understand the superconducting state of Cd2Re2O7 in this paper we examined the isotope eﬀect on the Raman phonons, electronic and superconducting properties of single crystals of Cd2Re2O7 by replacing Cd and O with natural isotope composition by isotope enriched 116Cd and 18 O elements. 2. Synthesis Single crystals of Cd2Re2O7, Cd2Re218O7, and 116Cd2Re218O7 were synthesized by ﬁrstly preparing Re2O7 from high purity O2 and Re (Alpha Aesar purity 99.99%) using oxygen with the natural isotope composition or isotope enriched 18O2 (98% isotope enrichment) employing the method by Noddack [11]. After adding high purity Cd

Physica C: Superconductivity and its applications 549 (2018) 11–14

F.S. Razavi et al.

(99.9975%, Alfa Aesar) with the natural isotope composition or isotope enriched 116Cd (98.7% isotope enrichment, Chemotrade Handelsgesellschaft (Düsseldorf, Germany)) to Re2O7, crystals were grown by chemical vapor transport in an oxygen atmosphere [12]. X-ray studies indicate a very good single crystalline nature of the samples with lattice parameters 1.028(5) nm similar to that of published results [1]. Within experimental error we did not observe any diﬀerence in lattice parameter of natural and isotope-substituted samples.

Table 1 Observed center frequencies in cm −1 for the Eg, A1g, T 2g − 1 and T 2g − 2 modes in the Cd2Re2O7 samples. The ﬁnal row gives the expected center frequencies for an 18O-substituted sample given the observed frequencies in the sample with 16O (ﬁrst row) if complete oxygen isotope substitution were achieved. T 2g − 1

A1g

T 2g − 2

Cd2Re16 2 O7

219

453

489

676

nat

Cd2Re18 2 O7

208

427

462

637

Cd2Re18 2 O7 Complete 18O sub.

207

426

462

638

206

427

461

637

nat

116

3. Raman Scattering

Eg

Room temperature polarized Stokes Raman scattering measurements of the Cd2Re2O7 single crystals were performed in a back-scattering geometry using a Jobin Yvon V 010 LabRAM single grating spectrometer with a 632.8 nm Helium–Neon laser, an edge ﬁlter to eliminate the laser line and a Peltier cooled CCD camera. The measurements were carried out with the beam focussed to a one micron spot and a laser power of less than 1 mW. As discussed above, at room temperature Cd2Re2O7 is in the cubic Fd3m phase, and is expected from a factor group analysis [13,14] to exhibit six Raman active phonon modes: A1g+Eg+4T2g. All modes should appear in the z(x’x’)z scattering geometry that was employed in our measurement. The results for the isotope-substituted samples are shown in Fig. 1. The two sharpest modes are identiﬁed as the Eg and A1g modes as assigned by Bae et al. [14] based on their behavior in diﬀerent polarization geometries [13,14]. Both modes appear at lower Raman shift when 16O (lower curve) is substituted with 18O (upper two curves). This is expected since both modes involve only the motion of the oxygen atoms in the ReO6 octahedra [13,14]. Note that the mode forming a shoulder on the lowshift side of the A1g mode as well as the mode near 650 cm −1 also shift with oxygen isotope substitution and are thus ascribed to T2g modes which involve motion of the oxygen in the ReO6 octahedra or the oxygen bonded to Cd [14]. Since the phonon resonance frequencies vary as 1/ m the degree of shift is strong evidence for nearly complete oxygen isotope substitution. Table 1 gives the center frequency of the Eg, A1g, T 2g − 1 and T 2g − 2 modes for each of the samples as determined by ﬁtting the Raman spectra to a sum of Lorentzians. The ﬁnal row gives the values that would be expected if complete oxygen isotope substitution were achieved and was calculated by multiplying the values observed for the 16O sample by 16/18 = 0.9428. Note that there is an additional mode near 350 cm −1. A similar mode has been observed in structurally identical Pyrochlore molybdenum oxides [13]. It is rather broad and has been attributed to a two-phonon excitation of an infrared active oxygen bending mode. However, our results show that this mode does not shift with oxygen isotope substitution, and thus is

Heat capacities were measured on pieces of single crystal with weights between ∼ 15 and ∼ 40 mg in a PPMS System (Quantum Design) equipped with a 3He continuous ﬂow system. The samples were attached to the sapphire platform with a minute amount of Apiezon N vacuum grease. The addenda heat capacities of the grease and the platform were measured in preceding runs and subtracted from the total heat capacities. All heat capacities quoted in the following are related to one formula unit of Cd2Re2O7. The inset to Fig. 2 displays the heat capacities Cp(T)/T including electronic and lattice contributions in the vicinity of the superconducting transition. The red solid line is a ﬁt of the data to the predictions of a single band α-model [15] assuming a BCS-type temperature dependence of the gap, Δ(T) with a ratio 2Δ(0)/ kB Tc = 3.3(19) consistent with the expected value for weak coupling BCS of 3.54. Tc was ﬁtted to Tc = 0.99(2) K in good agreement with ﬁndings by other groups [16]. The ﬁtting algorithm included a Gaussian-type broadening [17,18] of Tc of ∼ 2.7% (FWHM) indicating the high quality of the sample. The main frame of Fig. 2 enlarges the region near Tc for a sample containing the natural isotopic compositions of Cd and Oxygen and a sample prepared from 18-Oxygen. The heat capacity of Cd2Re18 2 O7 exhibits a small downshift compared to the sample containing the natural abundances. The diﬀerence in Tc is small and amounts to less than 5(1) mK (taken at the midpoint) indicating an oxygen isotope coeﬃcient of αO ≤ 0.04. Since the Raman scattering results indicate essentially complete oxygen isotope substitution it can be concluded that the oxygen modes do not participate strongly in the superconductivity.

Fig. 1. Room temperature Raman scattering spectra of isotope-substituted Cd2Re2O7 single crystals in z(x’x’)z scattering geometry. The spectra are displaced vertically for clarity.

Fig. 2. Comparison of the heat capacities of Cd2Re2O7 and Cd2Re18 2 O7 as indicated in the vicinity of Tc. The inset displays the full superconducting heat capacity anomaly of Cd2Re2O7 in comparison with the results of a ﬁt to the α-model with parameters given in the text. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

not likely a two-phonon excitation of a mode involving the motion of oxygen atoms. Since the Re and Cd atoms with site-symmetry D3d do not give rise to Raman-active modes in theFd3m space group [14] this mode may be electronic in origin. 4. Heat capacity

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F.S. Razavi et al.

116 Fig. 3. Heat capacities of Cd2Re18 Cd2Re18 2 O7 and 2 O7. The inset shows a Sommerfeld plot of the heat capacity of Cd2Re18 2 O7. The dashed black line is a linear ﬁt of the data above Tc with coeﬃcients quoted in the text.

Fig. 5. Comparison of superconducting energy gap Δ0 of with BCS gap energy.

116

Cd2Re18 2 O7 and Cd2Re2O7

conductance data we modiﬁed the BTK theory [10] such that the selfenergy of the quasiparticles is inserted directly into the Bogoliubov equations [9]. Within the experimental error due to the variation of temperature during the measurement ( ± (2–5 mK)) the Δ0 of 116 Cd2Re18 2 O7 agrees well with that of Cd2Re2O7 for injecting current in the [111] plane (see Fig. 5). The Δ0 for both compounds rises rapidly compared to the BCS curve for temperatures just below Tc and below 0.8 K the Δ0 approaches the zero temperature BCS value. 6. Conclusion

Fig. 4. Temperature dependence of normalized conductance of perature is shown on right hand side in Kelvin.

In conclusion, while the oxygen isotope has minimal eﬀect on the superconductivity of Cd2Re2O7 compared to the expected isotope eﬀect, the isotope eﬀect of Cd is a more signiﬁcant fraction of that expected. The fact that we did not observe a full isotope eﬀect using Cd and oxygen isotopic enrichment implies that the Re atoms may also contribute to the superconductivity in Cd2Re2O7.

Cd2Re18 2 O7. The tem-

116

Acknowledgments Fig. 3 shows a comparison of the heat capacities of Cd2Re18 2 O7 and 116 Cd2Re18 2 O7. The Tc downshift induced by the increased mass of the Cd isotope (116 vs 112.41 for natCd) is similarly small ( ∼ 14(3) mK, midpoint) as for the oxygen isotope enriched sample. In addition, the steep increase at Tc is somewhat more rounded for 116Cd2Re18 2 O2 as compared to the data collected for Cd2Re18 2 O2. Taking all possible errors into account we arrive at a Cd isotope coeﬃcient of αCd ∼ 0.4(1), indicating that Cd related vibrations may play a signiﬁcant role for superconductivity in Cd2Re2O7. The inset to Fig. 3 shows a Sommerfeld2 type plot of the heat capacity of Cd2Re18 2 O7, Cp/T = γ + βT . The Sommerfeld coeﬃcient γ amounts to γ = 30.2(3) mJ/mol K2, and the coeﬃcient of the Debye-type lattice contribution, β, to β = 0.223(33) mJ/mol K4, in good agreement with values found previously for Cd2Re2O7 [19].

Financial support for this work was partially provided by the Natural Sciences and Engineering Research Council of Canada grants DDG-2017-00043 and the Canadian Foundation for Innovation CFI24411. We thank G. Siegle for expert assistance with the heat capacity experiments. References [1] M. Hanawa, Y. Koraoka, T. Tayama, T. Sakakibara, J. Yamaura, Z. Hiroi, Phys. Rev. Lett. 87 (2001) 187001. [2] Z. Hiroi, M. Hanawa, Y. Muraoka, H. Harima, J. Phys. Soc. Jpn. 72 (2003) 21. [3] K. Arai, K. Kobayashi, K. Kodama, O. Vyaselev, M. Takigawa, M. Hanawaa, H. Hiroi, J. Phys. 14 (2002) L461. [4] M. Sakai, K. Yoshimura, H. Ohno, H. Kato, S. Kambe, R.E. Walstedt, T.D. Matsuda, Y. Haga, Y. Onuki, J. Phys. 13 (2001) L785. [5] D.J. Singh, P. Blaha, K. Schwarz, J.O. Sofo, Phys. Rev. B 65 (2002) 155109. [6] S.W. Huang, H.-T. Jeng, J.Y. Lin, W.J. Chang, J.M. Chen, G.H. Lee, H. Berger, H.D. Yang, K.S. Liang, J. Phys. 21 (2009) 195602. [7] O. Vyaselev, K. Arai, K. Kobayashi, J. Yamazaki, K. Kodama, M. Takigawa, M. Hanawaa, H. Hiroi, Phys. Rev. Lett. 89 (2002) 017001. [8] M. Hajialamdari, F.S. Razavi, D.A. Crandles, R.K. Kremer, M. Reedyk, J. Phys. 24 (2012) 505701. [9] F.S. Razavi, Y. Rohanizadegan, M. Hajialamdari, M. Reedyk, R.K. Kremer, B. Mitrovic, Can. J. Phys. 93 (2015) 1648. [10] G.E. Blonder, M. Tinkham, T.M. Klapwijk, Phys. Rev.B 25 (1982) 4515. [11] W.Z. Noddack, Z. Elecktrochem 34 (1928) 628. [12] N.B. sić, L. Forró, D. Mandrus, R. Jin, J. He, P. Fazekas, Phys. Rev. B 67 (2003) 245112. [13] K. Taniguchi, T. Katsufuji, S. Iguchi, Y. Taguchi, H. Takagi, Y. Tokura, Phys. Rev. B 70 (2004) 100401. [14] J.S. Bae, H.K. Ko, I.-S. Yang, Y.S. Lee, T.W. Noh, R. Jin, J. He, D. Mandrus, J. Korean

5. Point-Contact spectroscopy Point-contact spectra were measured by employing the soft pointcontact spectroscopy method developed and reviewed in detail by Gonnelli et al. [20]. The conductance of a single crystal of 116Cd2Re18 2 O7 was measured by varying the voltage between ± 1.5 meV. To avoid heating of the samples they were fully immersed in liquid 3He and stabilized between ( ± (2–5 mK)) to the particular temperatures by carefully adjusting the vapor pressures. For further details see [9]. The conductance spectra normalized to the spectra collected at 1.06 K above the superconducting transition temperature are shown in Fig. 4. In order to obtain the gap values at diﬀerent temperatures from the 13

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