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Unconventional resistive transitions in the extreme type-II superconductor Tl2Mo6Se6
Physica C 460–462 (2007) 702–703 www.elsevier.com/locate/physc
Unconventional resistive transitions in the extreme type-II superconductor Tl2Mo6Se6 A. Petrovic´ a
a,*
, Y. Fasano a, R. Lortz a, M. Decroux a, M. Potel b, R. Chevrel b, Ø. Fischer
a
Department of Condensed Matter Physics, University of Geneva, Quai Ernest-Ansermet 24, 1211 Geneva, Switzerland b Laboratoire de Chimie Mine´rale B, Universite´ de Rennes, Avenue du Ge´ne´ral Leclerc, 35042 Rennes, France Available online 4 April 2007
Abstract A study of the resistive transition into the superconducting state of the quasi-1D superconductor Tl2Mo6Se6 (Tc = 5 K) has revealed a broadening effect under applied magnetic field similar to that seen in the high-Tc cuprates. Using anisotropic Ginzburg–Landau theory we calculate a Ginzburg number Gi 1.8 · 105, corresponding to a critical region of width 0.09 mK, which is 18 000 times smaller than the measured DTc2. This proves that fluctuations of the order parameter are not the predominant factor responsible for the broadening of the transition and suggests the possible absence of a macroscopic phase coherence over a wide region of the vortex phase diagram. 2007 Elsevier B.V. All rights reserved. Keywords: Tl2Mo6Se6; Superconducting fluctuations
1. Introduction Molybdenum octahedral clusters are known to form superconductors with a high critical field, such as the Chevrel phases [1]. Tl2Mo6Se6 is formed from a linear condensation of such clusters running along the c (chain) axis, weakly coupled by thallium atoms [2]. It is one of the most strongly quasi-1D superconductors currently known and has a Tc 3–6.5 K depending on sample preparation. Estimates of its effective mass anisotropy e2 = mab/mc give a value of 170–1000 [3,4] where mab and mc are the effective masses perpendicular and parallel to the chains. In certain samples a significant paraconductivity has also been detected just above Tc [5] and attributed to fluctuations of the order parameter. This observation raises the question as to whether there is a wide region of the phase diagram dominated by fluctuations. In this paper we report a
*
Corresponding author. Tel.: +41 22 3796287; fax: +41 22 3796869. E-mail address: [email protected] (A. Petrovic´).
0921-4534/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.03.380
broadening of the superconducting transition with magnetic field from resistivity measurements in Tl2Mo6Se6, analogous to that seen in the high-Tc cuprates. This transition is analysed from a fluctuations perspective by considering the increase of the Ginzburg number Gi = DTc2/Tc2 in a magnetic field and comparing this with our resistive data, revealing whether thermal fluctuations are responsible for the unusual resistive transition broadening. 2. Experimental Gold contacts in a four-point configuration were sputtered onto crystals of dimensions 3.5 · 0.1 · 0.1 mm and 50 lm gold wires glued to these pads with silver epoxy, giving a typical contact resistance <1 X at 300 K. Longitudinal ac resistivity measurements were performed using a Quantum Design PPMS at temperatures down to 0.4 K with a magnetic field H applied either parallel or perpendicular to the chains. The lower critical field measured with H applied perpendicular to c, H c1? , was determined from magnetisation loops performed using a Quantum Design MPMS SQUID magnetometer.
A. Petrovic´ et al. / Physica C 460–462 (2007) 702–703
3. Results and discussion Resistive transitions with H perpendicular to c are shown for two samples in Fig. 1a and b. Unusually for a crystal of this type, sample B displays two distinct steps at the transition, indicating some form of inhomogeneity. However, both samples display the same characteristic broadening in a magnetic field, confirming that disorder or inhomogeneity are not responsible for this effect. As previously observed [5], H c2? does not appear to saturate down to low temperature. Fig. 1c displays transitions with H applied parallel to c for sample B: the anisotropy in Hc2 can be seen clearly in the larger fields required to suppress superconductivity. At high fields the main transition splits further into three steps. This can be explained by considering the high sensitivity of Hc2k to the field angle [3]. Each sample may contain regions in which the chain alignment differs very slightly, leading to Hc2 varying for each
703
Table 1 Measured and derived anisotropic parameters for Tl2Mo6Se6 Parallel ðkÞ
Perpendicular (?) Measured
Tc Hc2(0) Hc1(0) (SQUID) Hc(0) (Specific heat)
5.0 K 100 000 Oe
7100 Oe 19 ± 2 Oe 207 Oe Derived
e n(0) k(0) j Hc(0)
14 ˚ 800 A 0.14 lm 340
˚ 57 A 1.9 lm 1.7 208 ± 10 Oe
zone. We model Tl2Mo6Se6 as a uniaxial superconductor and apply anisotropic Ginzburg–Landau theory [6] to calculate the superconducting parameters summarized in Table 1. Extrapolating H c2? and Hc2k linearly to T = 0, the coherence lengths are given by H c2k ¼ U0 =2pn2? and H c2? ¼ p U0 =2pn? nk . The lower critical field H c1? ¼ U0 lnð j? jk þ 0:08Þ=4pk? kk , where j? ¼ kk =nk and jk ¼ k? =n? . Thep calculated thermodynamic critical field Hc(0) = U0/ 8pnk (with k and n measured in the same direction) is in good agreement with the value extracted from specific heat data. 2 2 The Ginzburg parameter Gi ¼ 0:5ðk B T c =H c ð0Þ n2? nk Þ ¼ 1:8 105 , giving a fluctuation-dominated temperature range GiTc 0.09 mK. This is smaller than the transition width observed in zero field by a factor of 18 000. Furthermore, Gi exhibits a weak field dependence 2=3 Gi ðH Þ G1=3 . Our measured DTc2 does not i ðH =H c2 Þ follow this trend and clearly diverges as H increases, confirming that conventional thermal fluctuations cannot be responsible for this behaviour. 4. Conclusions Three-dimensional thermal fluctuations within anisotropic Ginzburg–Landau theory fail to describe the transition broadening seen in a magnetic field in Tl2Mo6Se6. It remains to be investigated whether a quasi-1D fluctuations model could explain these phenomena, or if there is a wide region in the vortex phase diagram where a macroscopic phase coherence along the chains is unstable. References
Fig. 1. Resistive transitions in Tl2Mo6Se6 for (a) Sample A, H?c; (b) Sample B, H?c; (c) Sample B, H kc . Insets: Upper critical temperature Tc2(H) and transition width DTc2(H) determined by averaging and subtracting temperatures at 10% and 90% of the transition, respectively.
[1] [2] [3] [4] [5] [6]
R. Chevrel, The`se de Doctorat d’Etat, Universite´ de Rennes (1974). M. Potel et al., Acta. Crystallogr. 36 (1980) 1545. J.C. Armici et al., Solid State Commun. 33 (1980) 607. R. Brusetti et al., Solid State Commun. 66 (1988) 187. R. Brusetti et al., Phys. Rev. B 49 (1994) 8931. J.R. Waldram, Superconductivity of Metals and Cuprates, IOP Publishing., Bristol and Philadelphia, 1996.
Unconventional resistive transitions in the extreme type-II superconductor Tl2Mo6Se6 A. Petrovic´ a
a,*
, Y. Fasano a, R. Lortz a, M. Decroux a, M. Potel b, R. Chevrel b, Ø. Fischer
a
Department of Condensed Matter Physics, University of Geneva, Quai Ernest-Ansermet 24, 1211 Geneva, Switzerland b Laboratoire de Chimie Mine´rale B, Universite´ de Rennes, Avenue du Ge´ne´ral Leclerc, 35042 Rennes, France Available online 4 April 2007
Abstract A study of the resistive transition into the superconducting state of the quasi-1D superconductor Tl2Mo6Se6 (Tc = 5 K) has revealed a broadening effect under applied magnetic field similar to that seen in the high-Tc cuprates. Using anisotropic Ginzburg–Landau theory we calculate a Ginzburg number Gi 1.8 · 105, corresponding to a critical region of width 0.09 mK, which is 18 000 times smaller than the measured DTc2. This proves that fluctuations of the order parameter are not the predominant factor responsible for the broadening of the transition and suggests the possible absence of a macroscopic phase coherence over a wide region of the vortex phase diagram. 2007 Elsevier B.V. All rights reserved. Keywords: Tl2Mo6Se6; Superconducting fluctuations
1. Introduction Molybdenum octahedral clusters are known to form superconductors with a high critical field, such as the Chevrel phases [1]. Tl2Mo6Se6 is formed from a linear condensation of such clusters running along the c (chain) axis, weakly coupled by thallium atoms [2]. It is one of the most strongly quasi-1D superconductors currently known and has a Tc 3–6.5 K depending on sample preparation. Estimates of its effective mass anisotropy e2 = mab/mc give a value of 170–1000 [3,4] where mab and mc are the effective masses perpendicular and parallel to the chains. In certain samples a significant paraconductivity has also been detected just above Tc [5] and attributed to fluctuations of the order parameter. This observation raises the question as to whether there is a wide region of the phase diagram dominated by fluctuations. In this paper we report a
*
Corresponding author. Tel.: +41 22 3796287; fax: +41 22 3796869. E-mail address: [email protected] (A. Petrovic´).
0921-4534/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.03.380
broadening of the superconducting transition with magnetic field from resistivity measurements in Tl2Mo6Se6, analogous to that seen in the high-Tc cuprates. This transition is analysed from a fluctuations perspective by considering the increase of the Ginzburg number Gi = DTc2/Tc2 in a magnetic field and comparing this with our resistive data, revealing whether thermal fluctuations are responsible for the unusual resistive transition broadening. 2. Experimental Gold contacts in a four-point configuration were sputtered onto crystals of dimensions 3.5 · 0.1 · 0.1 mm and 50 lm gold wires glued to these pads with silver epoxy, giving a typical contact resistance <1 X at 300 K. Longitudinal ac resistivity measurements were performed using a Quantum Design PPMS at temperatures down to 0.4 K with a magnetic field H applied either parallel or perpendicular to the chains. The lower critical field measured with H applied perpendicular to c, H c1? , was determined from magnetisation loops performed using a Quantum Design MPMS SQUID magnetometer.
A. Petrovic´ et al. / Physica C 460–462 (2007) 702–703
3. Results and discussion Resistive transitions with H perpendicular to c are shown for two samples in Fig. 1a and b. Unusually for a crystal of this type, sample B displays two distinct steps at the transition, indicating some form of inhomogeneity. However, both samples display the same characteristic broadening in a magnetic field, confirming that disorder or inhomogeneity are not responsible for this effect. As previously observed [5], H c2? does not appear to saturate down to low temperature. Fig. 1c displays transitions with H applied parallel to c for sample B: the anisotropy in Hc2 can be seen clearly in the larger fields required to suppress superconductivity. At high fields the main transition splits further into three steps. This can be explained by considering the high sensitivity of Hc2k to the field angle [3]. Each sample may contain regions in which the chain alignment differs very slightly, leading to Hc2 varying for each
703
Table 1 Measured and derived anisotropic parameters for Tl2Mo6Se6 Parallel ðkÞ
Perpendicular (?) Measured
Tc Hc2(0) Hc1(0) (SQUID) Hc(0) (Specific heat)
5.0 K 100 000 Oe
7100 Oe 19 ± 2 Oe 207 Oe Derived
e n(0) k(0) j Hc(0)
14 ˚ 800 A 0.14 lm 340
˚ 57 A 1.9 lm 1.7 208 ± 10 Oe
zone. We model Tl2Mo6Se6 as a uniaxial superconductor and apply anisotropic Ginzburg–Landau theory [6] to calculate the superconducting parameters summarized in Table 1. Extrapolating H c2? and Hc2k linearly to T = 0, the coherence lengths are given by H c2k ¼ U0 =2pn2? and H c2? ¼ p U0 =2pn? nk . The lower critical field H c1? ¼ U0 lnð j? jk þ 0:08Þ=4pk? kk , where j? ¼ kk =nk and jk ¼ k? =n? . Thep calculated thermodynamic critical field Hc(0) = U0/ 8pnk (with k and n measured in the same direction) is in good agreement with the value extracted from specific heat data. 2 2 The Ginzburg parameter Gi ¼ 0:5ðk B T c =H c ð0Þ n2? nk Þ ¼ 1:8 105 , giving a fluctuation-dominated temperature range GiTc 0.09 mK. This is smaller than the transition width observed in zero field by a factor of 18 000. Furthermore, Gi exhibits a weak field dependence 2=3 Gi ðH Þ G1=3 . Our measured DTc2 does not i ðH =H c2 Þ follow this trend and clearly diverges as H increases, confirming that conventional thermal fluctuations cannot be responsible for this behaviour. 4. Conclusions Three-dimensional thermal fluctuations within anisotropic Ginzburg–Landau theory fail to describe the transition broadening seen in a magnetic field in Tl2Mo6Se6. It remains to be investigated whether a quasi-1D fluctuations model could explain these phenomena, or if there is a wide region in the vortex phase diagram where a macroscopic phase coherence along the chains is unstable. References
Fig. 1. Resistive transitions in Tl2Mo6Se6 for (a) Sample A, H?c; (b) Sample B, H?c; (c) Sample B, H kc . Insets: Upper critical temperature Tc2(H) and transition width DTc2(H) determined by averaging and subtracting temperatures at 10% and 90% of the transition, respectively.
[1] [2] [3] [4] [5] [6]
R. Chevrel, The`se de Doctorat d’Etat, Universite´ de Rennes (1974). M. Potel et al., Acta. Crystallogr. 36 (1980) 1545. J.C. Armici et al., Solid State Commun. 33 (1980) 607. R. Brusetti et al., Solid State Commun. 66 (1988) 187. R. Brusetti et al., Phys. Rev. B 49 (1994) 8931. J.R. Waldram, Superconductivity of Metals and Cuprates, IOP Publishing., Bristol and Philadelphia, 1996.