- Email: [email protected]
Superconducting properties in Rh17S15 under magnetic field and pressure
ARTICLE IN PRESS Journal of Physics and Chemistry of Solids 71 (2010) 700–703
Contents lists available at ScienceDirect
Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
Superconducting properties in Rh17S15 under magnetic field and pressure Rikio Settai a,n, Keisuke Katayama a, Hiroshi Muranaka a, Tetsuya Takeuchi b, Arumugam Thamizhavel c, a ¯ Ilya Sheikin d, Y. Onuki a
Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Cryogenic Center, Osaka University, Toyonaka, Osaka 560-0043, Japan c Tata Institute of Fundamental Research, Mumbai 400005, India d GHMFL, CNRS, BP 166, 38042 Grenoble Cedex 09, France b
a r t i c l e in f o
a b s t r a c t
Article history: Received 18 May 2009 Received in revised form 7 October 2009 Accepted 11 October 2009
We have studied superconducting properties by measuring the electrical resistivity and magnetization for a single crystal of Rh17S15 with a superconducting transition temperature Tc = 5.4 K. The upper critical field Hc2(0) and the lower critical field Hc1(0) were obtained as 20.5 and 0.0033 T, respectively. ˚ Correspondingly, the coherence length and the penetration depth were estimated to be 40 and 4900 A, respectively, indicating that Rh17S15 is a typical type-II superconductor with strong correlations of conduction electrons with a 4d-electron character of Rh atoms. The present electron correlations are formed to be enhanced with increasing pressure. & 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Superconductor B. Crystal growth D. Superconductivity
1. Introduction Since the discovery of a heavy fermion superconductor CeCu2Si2[1], heavy fermion superconductivity has been observed in several cerium, praseodymium, uranium, and transuranium compounds with 4f- or 5f electrons [2]. On the other hand, none of heavy fermion superconductor in d-electron compounds is established yet so far. In these heavy fermion superconductors with a large electronic specific heat coefficient g, the superconducting transition temperature Tc is low: Tc = 2.3 K in CeCoIn5 with g =1070 mJ/K2 mol [3] and Tc = 18.5 K in PuCoGa5 with g = 77 mJ/K2 mol [4], for example. The correlation of Tc with the band width might be expanded to a large Tc value in high-Tc cuprates with d electrons, including recent Fe-based superconductors [5]. Recently, superconductivity with strongly correlated 4d electrons with l = 104.8 mJ/K2 mol was reported in Rh17S15 with the superconducting transition temperature Tc = 5.4 K by Naren et al. [6]. Although the present superconductivity in Rh17S15 was previously reported more than 50 years ago [7], Naren et al. found the characteristic superconducting properties such as a large specific heat jump DC/gTc =2 at Tc, and an up-turn curvature of the upper critical field Hc2, which indicates the strong-coupling behavior, and a large upper critical field Hc2(0) estimated to exceed 20 T. In the superconducting properties of Rh17S15
n
Corresponding author. Tel.: + 81 6850 5371; fax: + 81 6850 5372. E-mail address: [email protected] (R. Settai).
0022-3697/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2009.12.070
mentioned above, the strongly correlated electrons with a narrow 4d band, which are derived from a shorter Rh–Rh distance ˚ between Rh(d) and Rh(e) than that for a Rh metal (= 2.58 A) ˚ as shown in Fig. 1, are considered to play an important (= 2.69 A), role of superconductivity. Here, Rh17S15 crystallizes in the cubic crystal structure (space group: Pm3m) with a lattice constant of ˚ 9.909 A. In the present study, we succeeded in growing a single crystal of Rh17S15 and carried out the electrical resistivity and magnetization measurements in order to investigate further the peculiar superconducting properties in Rh17S15. The pressure dependence of the superconducting transition temperature and the upper critical field were also studied.
2. Experimental A single crystal of Rh17S15 was grown by mineralization. Powder of 4 N Rh and 5 N S were mixed homogeneously and were changed into pellets under pressure. The pellets in an aluminum crucible were sealed in a quartz ampoule, which was heated up to 1150 1C, cooled down to 1100 1C with 2 1C/h and cooled rapidly down to room temperature. An ingot consists of relatively large single crystal grains. Single crystal samples were obtained from the grains, where the direction of the single crystal sample was determined by the X-ray Laue method, and the sample was cut along the principal directions using a spark erosion cutting machine.
ARTICLE IN PRESS R. Settai et al. / Journal of Physics and Chemistry of Solids 71 (2010) 700–703
The electrical resistivity was measured by a standard dc and ac four-probe technique. The resistivity measurements under magnetic field were performed in a top-loading dilution refrigerator equipped with a superconducting magnet up to 17 T at Osaka University and a resistive magnet up to 28 T at Grenoble High Magnetic Field Laboratory. The magnetization measurement was performed using a SQUID magnetometer (Quantum Design MPMS). The electrical resistivity measurement under pressure was carried out using an MP35N piston-cylinder type pressure cell with a mixture of Daphne oil (7373, IDEMITSU KOSAN) and petroleum ether as a pressure transmitting medium. Pressure was calibrated using the superconducting transition temperature of Sn.
3. Experimental results and discussion Fig. 2 shows the temperature dependence of the electrical resistivity for the current J perpendicular to the /1 1 0S direction of the cubic crystal structure in Rh17S15. The electrical resistivity decreases with decreasing temperature, exhibiting shoulder-like
701
behavior around 100 K, and drops to zero abruptly at Tc =5.4 K, as shown in an inset of Fig. 2. These features are in good agreement with the previous result for a polycrystalline sample [3]. The residual resistivity r0 and the residual resistivity ratio (RRR) ( = rRT/r0; rRT: resistivity at room temperature) are r0 = 3.5 mO cm and RRR= 19, respectively. These values indicate the high purity of the present single crystal compared with the previous polycrystalline sample with r0 = 26.7 mO cm. Next, we show in Fig. 3 (a) and (b) the temperature dependence of the electrical resistivity under several magnetic fields up to 16 T and the magnetic field dependence of the electrical resistivity at 0.5 K, respectively. The superconducting transition temperature decreases with increasing magnetic fields. The upper critical field Hc2 reaches 19.5 T at 0.5 K. Here, we define the superconducting transition temperature as the zero-resistivity even under magnetic fields. In the normal state, the resistivity shows a large magnetoresistance. The present configuration between the directions of the current and magnetic field is perpendicular, indicating a transverse magnetoresistance. The present large magnetoresistance suggests a compensated metal with equal volumes of electron and hole Fermi surfaces. In fact, the unit cell of Rh17S15 consists of 2 molecules of Rh17S15 with 64 atoms, revealing a compensated metal. When all cyclotron orbits are closed, the magnetoresistance increases quadratically as a function of magnetic field. The present speculation is most likely consistent with the data of Hall coefficient, suggesting a semimetallic character [6].
Fig. 1. Crystal structure of Rh17S15.
Fig. 2. Temperature dependence of the electrical resistivity in Rh17S15.
Fig. 3. (a) Temperature dependence of the electrical resistivity under several magnetic fields and (b) magnetic field dependence at 0.5 K for the field along the /1 1 1S direction in Rh17S15.
ARTICLE IN PRESS 702
R. Settai et al. / Journal of Physics and Chemistry of Solids 71 (2010) 700–703
Fig. 4. Temperature dependence of the upper critical field Hc2 for the field along the /1 1 1S direction in Rh17S15. Open circles correspond to zero-resistivity in Fig. 2. A solid line is the calculated one using the WHH theory [9]. A broken line is an Hc2 curve obtained by Naren et al. [6].
The temperature dependence of Hc2 is shown in Fig. 4. The slope of the upper critical field is –dHc2/dT= 5.6 T/K at Tc = 5.4 K, and the upper critical field at 0 K is estimated to be Hc2(0) = 20.5 T. The orbital limiting field Horb c2 (0) [= 0.73( dHc2/dT)Tc] for the clean limit is obtained to be 22.1 T [8], which is in good agreement with the present experimental result. A solid line is a guide for eyes based on the WWH theory [9]. A broken line in Fig. 3 is the fitted formula Hc2(T)= Hc2(0)[1 (T/Tc)3/2]3/2; Hc2(0) = 23.5 T to reproduce the experimental result by Naren et al. [6]. The present Hc2 data are approximately explained by the standard WHH theory, although the Hc2 data indicate an up-turn curvature in the temperature range from 5.4 to 3.8 K, reflecting a strong-coupling superconducting property [6], namely DC/gTc = 2, as mentioned in Introduction. The Ginzburg–Landau (GL) coherence length xGL(0) is estimated to be xGL(0) =40 A˚ with the formula Hc2( = F0/2px2GL) =20.5 T, where F0 is the flux quantum. Next, we show in Fig. 5 the temperature dependence of Hc2 for the field along the /1 1 0S direction under pressures of 1.3 and 2.7 GPa. With increasing pressure, Tc decreases as dTc/dP= 0.17 K/ GPa. The slope of the Hc2 curve –dHc2/dT slightly increases from 6.0 T/K at 0 GPa to 6.3 T/K at 2.7 GPa, reflecting a slight increase of density of states at the Fermi level. Finally, we show in Fig. 6(a) the magnetization curve, which indicates the typical type-II superconducting behavior. The lower critical field Hc1 in Fig. 6(b) was obtained as the field deviating from the linear line in the magnetization curve. The lower critical field at zero temperature Hc1(0) is estimated to be 0.0033 T from the formula Hc1(T)= Hc1(0)[1 (T/Tc)2], as shown in a solid line in Fig. 6(b). The penetration depth lGL(0) is estimated to be lGL(0)= 4900 A˚ by the formula Hc1 = F0/4plGL2 ln k, where k ¼ lGL~ xGL is the GL parameter and k = 120, indicating that Rh17S15 is a typical type-II superconductor. The thermal critical field Hc(0) ispffiffifficalculated to be 0.12 T using the formula Hc ð0Þ ¼ Hc2 ð0Þ= 2 kð0Þ. These superconducting parameters are summarized in Table 1.
Fig. 5. Temperature dependence of the upper critical field Hc2 for the field along the /1 1 0S direction in Rh17S15 at ambient pressure and under pressures of 1.3 and 2.7 GPa.
Fig. 6. Temperature dependence of the magnetization under several constant temperature in the superconducting state and (b) the temperature dependence of the lower critical field Hc1 for the magnetic field along the /1 1 1S direction in Rh17S15.
ARTICLE IN PRESS R. Settai et al. / Journal of Physics and Chemistry of Solids 71 (2010) 700–703
Table 1 Superconducting parameters for Rh17S15. The direction of the magnetic field is /1 1 1S. Transition temperature, Tc Upper critical field, Hc2(0) Lower critical field, Hc1(0) Thermodynamic critical field, Hc(0) Coherence length, xGL(0)
5.4 K 20.5 T 33 10 4 T 0.12 T 40 A˚
Penetration depth, lGL(0)
4900 A˚ 120
Ginzburg–Landau parameter, k(0)
4. Summary We have studied superconducting properties by measuring the electrical resistivity and magnetization for a single crystal of Rh17S15. The upper critical field Hc2(0) and the lower critical field Hc1(0) are determined to be 20.5 and 0.0033 T, respectively. The coherence length and the penetration depth ˚ respectively, indicating are estimated to be 40 and 4900 A, Rh17S15 is a typical type-II superconductor with k = 120. The temperature dependence of Hc2 is approximately explained by the standard WHH theory, although the Hc2 data indicate an up-turn curvature in the temperature range from 5.4 to 3.8 K, reflecting a strong-coupling superconducting property. A large value of Hc2(0) =20.5 T for Tc =5.4 K is mainly due to strong correlations of conduction electrons with a 4d-electron character of Rh atoms. The transition temperature Tc is found to decrease with increasing pressure, although the slope of Hc2 slightly increases with increasing pressure. This might suggest that the g value increases as a function of pressure, and strong
703
correlations of conduction electrons are enhanced with increasing pressure.
Acknowledgements This work was supported by a Grant-in-Aid for Scientific Research on Specially Promoted Research (No. 20001004), Priority Area of New Materials Science Using Regulated Nano Spaces, and Osaka University Global COE Program ‘‘Core Research and Engineering of Advanced Materials—Interdisciplinary Education Center for Materials Science’’ (No. G10) and Grant-in-Aid for Scientific Research on Innovative Areas ‘‘Heavy Electrons’’ (20102002) from the Ministry of Education, Culture, Sports, Science and Technology, Japan. Part of this work has been supported by EuroMagNET II under the EU contract. References [1] F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz, H. Scafer, Phys. Rev. Lett. 43 (1979) 1892. ¯ [2] Y. Onuki, Y. Kitaoka (Eds.), Frontiers of Novel Superconductivity in Heavy Fermion Compounds: Reprints from special topics section, J. Phys. Soc. Jpn. 76 (2007). [3] C. Petrovic, P.G. Pagliuso, M.F. Hundley, R. Movshovich, J.L. Sarrao, J.D. Thompson, Z. Fisk, P. Monthoux, J. Phys.: Condens. Matter 13 (2001) L337. [4] J.L. Sarrao, L.A. Morales, J.D. Thompson, B.L Scott, G.R. Stewart, F. Wastin, J. Rebizant, P. Boulet, E. Colineau, G.H. Lander, Nature (London) 420 (2002) 297. [5] Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Am. Chem. Soc. 130 (2008) 3296. [6] N.R. Naren, A. Thamizhavel, A.K. Nigam, S. Ramakrishnan, Phys. Rev. Lett. 100 (2008) 026404. [7] B.T. Matthias, E. Corenzwit, C.E. Miller, Phys. Rev. 93 (1954) 1415. [8] E. Helfand, N.R. Werthamer, Phys. Rev. 147 (1966) 288. [9] N.R. Werthamer, E. Helfand, P.C. Hohenberg, Phys. Rev. 147 (1966) 295.
Contents lists available at ScienceDirect
Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
Superconducting properties in Rh17S15 under magnetic field and pressure Rikio Settai a,n, Keisuke Katayama a, Hiroshi Muranaka a, Tetsuya Takeuchi b, Arumugam Thamizhavel c, a ¯ Ilya Sheikin d, Y. Onuki a
Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Cryogenic Center, Osaka University, Toyonaka, Osaka 560-0043, Japan c Tata Institute of Fundamental Research, Mumbai 400005, India d GHMFL, CNRS, BP 166, 38042 Grenoble Cedex 09, France b
a r t i c l e in f o
a b s t r a c t
Article history: Received 18 May 2009 Received in revised form 7 October 2009 Accepted 11 October 2009
We have studied superconducting properties by measuring the electrical resistivity and magnetization for a single crystal of Rh17S15 with a superconducting transition temperature Tc = 5.4 K. The upper critical field Hc2(0) and the lower critical field Hc1(0) were obtained as 20.5 and 0.0033 T, respectively. ˚ Correspondingly, the coherence length and the penetration depth were estimated to be 40 and 4900 A, respectively, indicating that Rh17S15 is a typical type-II superconductor with strong correlations of conduction electrons with a 4d-electron character of Rh atoms. The present electron correlations are formed to be enhanced with increasing pressure. & 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Superconductor B. Crystal growth D. Superconductivity
1. Introduction Since the discovery of a heavy fermion superconductor CeCu2Si2[1], heavy fermion superconductivity has been observed in several cerium, praseodymium, uranium, and transuranium compounds with 4f- or 5f electrons [2]. On the other hand, none of heavy fermion superconductor in d-electron compounds is established yet so far. In these heavy fermion superconductors with a large electronic specific heat coefficient g, the superconducting transition temperature Tc is low: Tc = 2.3 K in CeCoIn5 with g =1070 mJ/K2 mol [3] and Tc = 18.5 K in PuCoGa5 with g = 77 mJ/K2 mol [4], for example. The correlation of Tc with the band width might be expanded to a large Tc value in high-Tc cuprates with d electrons, including recent Fe-based superconductors [5]. Recently, superconductivity with strongly correlated 4d electrons with l = 104.8 mJ/K2 mol was reported in Rh17S15 with the superconducting transition temperature Tc = 5.4 K by Naren et al. [6]. Although the present superconductivity in Rh17S15 was previously reported more than 50 years ago [7], Naren et al. found the characteristic superconducting properties such as a large specific heat jump DC/gTc =2 at Tc, and an up-turn curvature of the upper critical field Hc2, which indicates the strong-coupling behavior, and a large upper critical field Hc2(0) estimated to exceed 20 T. In the superconducting properties of Rh17S15
n
Corresponding author. Tel.: + 81 6850 5371; fax: + 81 6850 5372. E-mail address: [email protected] (R. Settai).
0022-3697/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2009.12.070
mentioned above, the strongly correlated electrons with a narrow 4d band, which are derived from a shorter Rh–Rh distance ˚ between Rh(d) and Rh(e) than that for a Rh metal (= 2.58 A) ˚ as shown in Fig. 1, are considered to play an important (= 2.69 A), role of superconductivity. Here, Rh17S15 crystallizes in the cubic crystal structure (space group: Pm3m) with a lattice constant of ˚ 9.909 A. In the present study, we succeeded in growing a single crystal of Rh17S15 and carried out the electrical resistivity and magnetization measurements in order to investigate further the peculiar superconducting properties in Rh17S15. The pressure dependence of the superconducting transition temperature and the upper critical field were also studied.
2. Experimental A single crystal of Rh17S15 was grown by mineralization. Powder of 4 N Rh and 5 N S were mixed homogeneously and were changed into pellets under pressure. The pellets in an aluminum crucible were sealed in a quartz ampoule, which was heated up to 1150 1C, cooled down to 1100 1C with 2 1C/h and cooled rapidly down to room temperature. An ingot consists of relatively large single crystal grains. Single crystal samples were obtained from the grains, where the direction of the single crystal sample was determined by the X-ray Laue method, and the sample was cut along the principal directions using a spark erosion cutting machine.
ARTICLE IN PRESS R. Settai et al. / Journal of Physics and Chemistry of Solids 71 (2010) 700–703
The electrical resistivity was measured by a standard dc and ac four-probe technique. The resistivity measurements under magnetic field were performed in a top-loading dilution refrigerator equipped with a superconducting magnet up to 17 T at Osaka University and a resistive magnet up to 28 T at Grenoble High Magnetic Field Laboratory. The magnetization measurement was performed using a SQUID magnetometer (Quantum Design MPMS). The electrical resistivity measurement under pressure was carried out using an MP35N piston-cylinder type pressure cell with a mixture of Daphne oil (7373, IDEMITSU KOSAN) and petroleum ether as a pressure transmitting medium. Pressure was calibrated using the superconducting transition temperature of Sn.
3. Experimental results and discussion Fig. 2 shows the temperature dependence of the electrical resistivity for the current J perpendicular to the /1 1 0S direction of the cubic crystal structure in Rh17S15. The electrical resistivity decreases with decreasing temperature, exhibiting shoulder-like
701
behavior around 100 K, and drops to zero abruptly at Tc =5.4 K, as shown in an inset of Fig. 2. These features are in good agreement with the previous result for a polycrystalline sample [3]. The residual resistivity r0 and the residual resistivity ratio (RRR) ( = rRT/r0; rRT: resistivity at room temperature) are r0 = 3.5 mO cm and RRR= 19, respectively. These values indicate the high purity of the present single crystal compared with the previous polycrystalline sample with r0 = 26.7 mO cm. Next, we show in Fig. 3 (a) and (b) the temperature dependence of the electrical resistivity under several magnetic fields up to 16 T and the magnetic field dependence of the electrical resistivity at 0.5 K, respectively. The superconducting transition temperature decreases with increasing magnetic fields. The upper critical field Hc2 reaches 19.5 T at 0.5 K. Here, we define the superconducting transition temperature as the zero-resistivity even under magnetic fields. In the normal state, the resistivity shows a large magnetoresistance. The present configuration between the directions of the current and magnetic field is perpendicular, indicating a transverse magnetoresistance. The present large magnetoresistance suggests a compensated metal with equal volumes of electron and hole Fermi surfaces. In fact, the unit cell of Rh17S15 consists of 2 molecules of Rh17S15 with 64 atoms, revealing a compensated metal. When all cyclotron orbits are closed, the magnetoresistance increases quadratically as a function of magnetic field. The present speculation is most likely consistent with the data of Hall coefficient, suggesting a semimetallic character [6].
Fig. 1. Crystal structure of Rh17S15.
Fig. 2. Temperature dependence of the electrical resistivity in Rh17S15.
Fig. 3. (a) Temperature dependence of the electrical resistivity under several magnetic fields and (b) magnetic field dependence at 0.5 K for the field along the /1 1 1S direction in Rh17S15.
ARTICLE IN PRESS 702
R. Settai et al. / Journal of Physics and Chemistry of Solids 71 (2010) 700–703
Fig. 4. Temperature dependence of the upper critical field Hc2 for the field along the /1 1 1S direction in Rh17S15. Open circles correspond to zero-resistivity in Fig. 2. A solid line is the calculated one using the WHH theory [9]. A broken line is an Hc2 curve obtained by Naren et al. [6].
The temperature dependence of Hc2 is shown in Fig. 4. The slope of the upper critical field is –dHc2/dT= 5.6 T/K at Tc = 5.4 K, and the upper critical field at 0 K is estimated to be Hc2(0) = 20.5 T. The orbital limiting field Horb c2 (0) [= 0.73( dHc2/dT)Tc] for the clean limit is obtained to be 22.1 T [8], which is in good agreement with the present experimental result. A solid line is a guide for eyes based on the WWH theory [9]. A broken line in Fig. 3 is the fitted formula Hc2(T)= Hc2(0)[1 (T/Tc)3/2]3/2; Hc2(0) = 23.5 T to reproduce the experimental result by Naren et al. [6]. The present Hc2 data are approximately explained by the standard WHH theory, although the Hc2 data indicate an up-turn curvature in the temperature range from 5.4 to 3.8 K, reflecting a strong-coupling superconducting property [6], namely DC/gTc = 2, as mentioned in Introduction. The Ginzburg–Landau (GL) coherence length xGL(0) is estimated to be xGL(0) =40 A˚ with the formula Hc2( = F0/2px2GL) =20.5 T, where F0 is the flux quantum. Next, we show in Fig. 5 the temperature dependence of Hc2 for the field along the /1 1 0S direction under pressures of 1.3 and 2.7 GPa. With increasing pressure, Tc decreases as dTc/dP= 0.17 K/ GPa. The slope of the Hc2 curve –dHc2/dT slightly increases from 6.0 T/K at 0 GPa to 6.3 T/K at 2.7 GPa, reflecting a slight increase of density of states at the Fermi level. Finally, we show in Fig. 6(a) the magnetization curve, which indicates the typical type-II superconducting behavior. The lower critical field Hc1 in Fig. 6(b) was obtained as the field deviating from the linear line in the magnetization curve. The lower critical field at zero temperature Hc1(0) is estimated to be 0.0033 T from the formula Hc1(T)= Hc1(0)[1 (T/Tc)2], as shown in a solid line in Fig. 6(b). The penetration depth lGL(0) is estimated to be lGL(0)= 4900 A˚ by the formula Hc1 = F0/4plGL2 ln k, where k ¼ lGL~ xGL is the GL parameter and k = 120, indicating that Rh17S15 is a typical type-II superconductor. The thermal critical field Hc(0) ispffiffifficalculated to be 0.12 T using the formula Hc ð0Þ ¼ Hc2 ð0Þ= 2 kð0Þ. These superconducting parameters are summarized in Table 1.
Fig. 5. Temperature dependence of the upper critical field Hc2 for the field along the /1 1 0S direction in Rh17S15 at ambient pressure and under pressures of 1.3 and 2.7 GPa.
Fig. 6. Temperature dependence of the magnetization under several constant temperature in the superconducting state and (b) the temperature dependence of the lower critical field Hc1 for the magnetic field along the /1 1 1S direction in Rh17S15.
ARTICLE IN PRESS R. Settai et al. / Journal of Physics and Chemistry of Solids 71 (2010) 700–703
Table 1 Superconducting parameters for Rh17S15. The direction of the magnetic field is /1 1 1S. Transition temperature, Tc Upper critical field, Hc2(0) Lower critical field, Hc1(0) Thermodynamic critical field, Hc(0) Coherence length, xGL(0)
5.4 K 20.5 T 33 10 4 T 0.12 T 40 A˚
Penetration depth, lGL(0)
4900 A˚ 120
Ginzburg–Landau parameter, k(0)
4. Summary We have studied superconducting properties by measuring the electrical resistivity and magnetization for a single crystal of Rh17S15. The upper critical field Hc2(0) and the lower critical field Hc1(0) are determined to be 20.5 and 0.0033 T, respectively. The coherence length and the penetration depth ˚ respectively, indicating are estimated to be 40 and 4900 A, Rh17S15 is a typical type-II superconductor with k = 120. The temperature dependence of Hc2 is approximately explained by the standard WHH theory, although the Hc2 data indicate an up-turn curvature in the temperature range from 5.4 to 3.8 K, reflecting a strong-coupling superconducting property. A large value of Hc2(0) =20.5 T for Tc =5.4 K is mainly due to strong correlations of conduction electrons with a 4d-electron character of Rh atoms. The transition temperature Tc is found to decrease with increasing pressure, although the slope of Hc2 slightly increases with increasing pressure. This might suggest that the g value increases as a function of pressure, and strong
703
correlations of conduction electrons are enhanced with increasing pressure.
Acknowledgements This work was supported by a Grant-in-Aid for Scientific Research on Specially Promoted Research (No. 20001004), Priority Area of New Materials Science Using Regulated Nano Spaces, and Osaka University Global COE Program ‘‘Core Research and Engineering of Advanced Materials—Interdisciplinary Education Center for Materials Science’’ (No. G10) and Grant-in-Aid for Scientific Research on Innovative Areas ‘‘Heavy Electrons’’ (20102002) from the Ministry of Education, Culture, Sports, Science and Technology, Japan. Part of this work has been supported by EuroMagNET II under the EU contract. References [1] F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz, H. Scafer, Phys. Rev. Lett. 43 (1979) 1892. ¯ [2] Y. Onuki, Y. Kitaoka (Eds.), Frontiers of Novel Superconductivity in Heavy Fermion Compounds: Reprints from special topics section, J. Phys. Soc. Jpn. 76 (2007). [3] C. Petrovic, P.G. Pagliuso, M.F. Hundley, R. Movshovich, J.L. Sarrao, J.D. Thompson, Z. Fisk, P. Monthoux, J. Phys.: Condens. Matter 13 (2001) L337. [4] J.L. Sarrao, L.A. Morales, J.D. Thompson, B.L Scott, G.R. Stewart, F. Wastin, J. Rebizant, P. Boulet, E. Colineau, G.H. Lander, Nature (London) 420 (2002) 297. [5] Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Am. Chem. Soc. 130 (2008) 3296. [6] N.R. Naren, A. Thamizhavel, A.K. Nigam, S. Ramakrishnan, Phys. Rev. Lett. 100 (2008) 026404. [7] B.T. Matthias, E. Corenzwit, C.E. Miller, Phys. Rev. 93 (1954) 1415. [8] E. Helfand, N.R. Werthamer, Phys. Rev. 147 (1966) 288. [9] N.R. Werthamer, E. Helfand, P.C. Hohenberg, Phys. Rev. 147 (1966) 295.