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Fluctuation conductivity and the dynamical universality class of the superconducting transition in the high-Tc cuprates
PHYSICA ELSEVIER
Physica C 341-348 (2000) 1911-1912 www.elsevier.nl/loca)e/physc
Fluctuation conductivity and the dynamical universality class of the superconducting transition in the high-To cuprates J. Roa Rojas~'b, A,R. Jurelo e, R. Menegotto Costaa, L. Mendon~a Ferreiraa, P. Pureur~, M . T . D . Orlandod, P. Prietoe and G. Nievar alnstituto de Fisica, UFRGS, P.O. Box 15051, 91501-970 Porto Alegre, Brazil bEscuela Colombiana de Ingenieria, A.A. 14520 Bogota DC, Colombia ¢Departamento de Fisica, UEPG, 84031-510 Ponta Grossa, Brazil dDepartamento de Fisica, UFES, 29060-900 Vit6ria, Brazil ~Departamento de Fisica, Universidad del Valle, A,A. 25360 Cali, Colombia fCentro At6mico Bariloche, CNE& 8400 S.C. de Bariloche, Argentina Systematic measurements of the fluctuation conductivity in several high-temperature superconducting cuprates show the occurrence of a genuine critical regime. The conductivity exponent is consistent with the predictions of the 3D-XY universality class and yields a dynamical critical exponent z = 1.5.
Effects from thermodynamics fluctuations are observed in equilibrium and transport properties of the high-To superconducting cuprates (HTSC) in large temperature intervals near Tc [ 1]. Far above To, Gaussian fluctuations of the order parameter have been identified. Closer to T¢, careful studies of the specific heat [2], penetration depth [3] and electrical conductivity [4] reveal effects of genuine critical fluctuations. There is now a consensus that the static exponents describing the critical thermodynamics of the HTSC are those of the 3D-XY model. However, a controversy still remains about the dynamical universality class of this transition. Some authors propose a dynamical exponent z _~2 [1], which is characteristic of the dissipative dynamics described by the model-A of Hohenberg and Halperin [5]. However, some fluctuation conductivity experiments [4,6] and recent theoretical calculations [7] indicate that z = d/2 = 1.5, as in the model-E of Hohenberg and Halperin. In this communication, we report on fluctuation conductivity experiments in several samples of the HTSC, including single-crystals, thin films and ceramics of RBa2Cu307.8 (R = Y, Gd, Dy, Ho),
Bi2Sr2CaCu2Oy
and
Hgo.s2Reoa 8Ba2Ca2Cu3Ox.
Conductivity measurements were performed with a low-frequency, low-current AC-technique. In some cases, magnetic fields up to 500 mT were apphed parallel to the transport current. The method of analysis is based on the determination of the quantity [4]: zo = -
d enac,
(1)
dT where Ac = c-erR is the fluctuation conductivity. The regular term cR is estimated by extrapolating the high temperature behavior of the total conductivity c to the region of T~. Assuming that Ac diverges as a power law of the reduced temperature, simple identification of a linear behavior in plots of Z~' versus T allows the simultaneous determination of To and the critical exponent, ~ [4]. In Fi~ 1 we show results for epitaxial thin films of RBa2Cu3OT-~ (R = Y, Gd, Ho). In all cases, a straight-line extending about 1 K above To could be fitted to the data. This corresponds to an asymptotic power-law regime where Ac diverges with the
0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII S0921-4534(00)01360-5
1912
J. R o a
Rojas
et al./Physica
C 341-348
(2000)
1911-1912
for YBaCuO rounds off the 3D-XY-E behavior in Ac, suggesting that this regime corresponds to a zero-field scaling. 2
;'.=0,33
90,5
91,0
91,5
;:fo IS
92,5
92,0
Table 1 Critical exponents for the fluctuation conductivity in several samples of the HTSC. Also reported is the interval of validity, A, of the observed critical regimes in plots of X~l versus T.
93.0
¢oo
91.2
i,, f ,
~.6
91.e ' 9 ~ . 0
,
~.0
i
o4.4
' 9~., ' 9~.e ' 93.2
,
i
94.a
TEMPERATURE
,
i
95.2
i
9s.6
(K)
Figure]. Results for Z~,~ versus T in the asymptotic critical irtterva] for RBa2Cu3OT-~ (R = Y, Gd, Ho). The observed power law scalings are indicated by the straight lines and the corresponding exponents are quoted.
exponent % = 0.34. Table 1 lists the critical exponents obtained from our fluctuation conductivity experiments. Also specified in the table is the width of the temperature interval, A, where the corresponding critical regimes are observed. One notes that A is shorter for the more anisotropic Hg-based and Bi-based superconductors. The critical exponent for fluctuation conductivity is given by ~, = u ( 2 + z - d + r l ) ,
(2)
where u is the critical exponent for the coherence length, z is the dynamical critical exponent, d is the dimensionality and r 1 is the exponent for the order-par~eter correlation function. Renormalization group calculations for the 3D-XY model give u ~- 0.67 and 71 = 0.03 [8]. Thus, our result, k ~ 0.34, implies that z = 1.5 in Eq. (2). This value is characteristic of model-E, which is the dynamical universality class for the superfluid transition in 4He and also for extreme type II superconductors in the absence of screening [7]. We also notice that the application of magnetic fields above 10 mT for Bi2Sr2CaCu2Oy and above 100 mT
Sample type YBaCuO SC YBaCuO SC YBaCuO F YBaCuO P GdBaCuO F GdBaCuO P HoCaCuO F DyBaCuO P Bi-2212 SC Hg(Re)-1223 P SC: single crystal; F: epitaxial P: polycrystalline sample
;L 0.34 0.33 0.33 0.33 0.34 0.35 0.35 0.34 0.33 0.32 thin film;
A(K) 0.7 0.4 1.1 0.5 0.7 0.5 0.8 0.6 0.13 0.3
Recently, a fluctuation conductivity regime beyond 3D-XY, with exponent ;~=0.17, was identified in the close vicinity of Tc in a YBaCuO single-erystal [9]. Owing to this small value for L, it was suggested that the ultimate critical behavior for this superconductor might be that of a weakly first-order transition. REFERENCES
1. D.S. Fisher, M.P.A. Fisher and D.A. Huse, Phys. Rev. B 43 (1991) 130. 2. N. Overend, M.A. Howson and I.D. Lawrie, Phys. Rev. Lett. 72 (1994) 3238. 3. S. Kamal, D.A. Bonn, N. Goldenfeld, P.J. Hirschfeld, R. Lian and W.N. Hardy, Phys. Rev. Lett. 73 (1994) 1845. 4. P. Pureur, R. Menegotto Costa, P. Rodrigues Jr., J. Schaf and J.V. Kunzler, Phys. Rev. B 47 (1993) 11420. 5. P.C. Hohenberg and B.I. Halporin, Rev. Mod. Phys. 49 (1977) 435, 6. W. Holm, Yu. Eltsev and O. Rapp, Phys. Rev. B 51 (1995) 11992. 7. H. Weber and H.J. Jensen, Phys. Rev. Lett. 76 (1977) 2620; J. Lidmar, M. Wallin, C. Wengel, S.M. Girvin and A.P. Young, Phys. Rev. B 58 (1998) 2827. 8. J.C. Le Guillou and J. Zinn-Justin, Phys. Rev. B 21 (1980) 3976. 9. R. Menegotto Costa, P. Pttreur, M. Gusnfio, S. Senoussi and K. Behnia, Solid State Commun. 113 0999) 23.
Physica C 341-348 (2000) 1911-1912 www.elsevier.nl/loca)e/physc
Fluctuation conductivity and the dynamical universality class of the superconducting transition in the high-To cuprates J. Roa Rojas~'b, A,R. Jurelo e, R. Menegotto Costaa, L. Mendon~a Ferreiraa, P. Pureur~, M . T . D . Orlandod, P. Prietoe and G. Nievar alnstituto de Fisica, UFRGS, P.O. Box 15051, 91501-970 Porto Alegre, Brazil bEscuela Colombiana de Ingenieria, A.A. 14520 Bogota DC, Colombia ¢Departamento de Fisica, UEPG, 84031-510 Ponta Grossa, Brazil dDepartamento de Fisica, UFES, 29060-900 Vit6ria, Brazil ~Departamento de Fisica, Universidad del Valle, A,A. 25360 Cali, Colombia fCentro At6mico Bariloche, CNE& 8400 S.C. de Bariloche, Argentina Systematic measurements of the fluctuation conductivity in several high-temperature superconducting cuprates show the occurrence of a genuine critical regime. The conductivity exponent is consistent with the predictions of the 3D-XY universality class and yields a dynamical critical exponent z = 1.5.
Effects from thermodynamics fluctuations are observed in equilibrium and transport properties of the high-To superconducting cuprates (HTSC) in large temperature intervals near Tc [ 1]. Far above To, Gaussian fluctuations of the order parameter have been identified. Closer to T¢, careful studies of the specific heat [2], penetration depth [3] and electrical conductivity [4] reveal effects of genuine critical fluctuations. There is now a consensus that the static exponents describing the critical thermodynamics of the HTSC are those of the 3D-XY model. However, a controversy still remains about the dynamical universality class of this transition. Some authors propose a dynamical exponent z _~2 [1], which is characteristic of the dissipative dynamics described by the model-A of Hohenberg and Halperin [5]. However, some fluctuation conductivity experiments [4,6] and recent theoretical calculations [7] indicate that z = d/2 = 1.5, as in the model-E of Hohenberg and Halperin. In this communication, we report on fluctuation conductivity experiments in several samples of the HTSC, including single-crystals, thin films and ceramics of RBa2Cu307.8 (R = Y, Gd, Dy, Ho),
Bi2Sr2CaCu2Oy
and
Hgo.s2Reoa 8Ba2Ca2Cu3Ox.
Conductivity measurements were performed with a low-frequency, low-current AC-technique. In some cases, magnetic fields up to 500 mT were apphed parallel to the transport current. The method of analysis is based on the determination of the quantity [4]: zo = -
d enac,
(1)
dT where Ac = c-erR is the fluctuation conductivity. The regular term cR is estimated by extrapolating the high temperature behavior of the total conductivity c to the region of T~. Assuming that Ac diverges as a power law of the reduced temperature, simple identification of a linear behavior in plots of Z~' versus T allows the simultaneous determination of To and the critical exponent, ~ [4]. In Fi~ 1 we show results for epitaxial thin films of RBa2Cu3OT-~ (R = Y, Gd, Ho). In all cases, a straight-line extending about 1 K above To could be fitted to the data. This corresponds to an asymptotic power-law regime where Ac diverges with the
0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII S0921-4534(00)01360-5
1912
J. R o a
Rojas
et al./Physica
C 341-348
(2000)
1911-1912
for YBaCuO rounds off the 3D-XY-E behavior in Ac, suggesting that this regime corresponds to a zero-field scaling. 2
;'.=0,33
90,5
91,0
91,5
;:fo IS
92,5
92,0
Table 1 Critical exponents for the fluctuation conductivity in several samples of the HTSC. Also reported is the interval of validity, A, of the observed critical regimes in plots of X~l versus T.
93.0
¢oo
91.2
i,, f ,
~.6
91.e ' 9 ~ . 0
,
~.0
i
o4.4
' 9~., ' 9~.e ' 93.2
,
i
94.a
TEMPERATURE
,
i
95.2
i
9s.6
(K)
Figure]. Results for Z~,~ versus T in the asymptotic critical irtterva] for RBa2Cu3OT-~ (R = Y, Gd, Ho). The observed power law scalings are indicated by the straight lines and the corresponding exponents are quoted.
exponent % = 0.34. Table 1 lists the critical exponents obtained from our fluctuation conductivity experiments. Also specified in the table is the width of the temperature interval, A, where the corresponding critical regimes are observed. One notes that A is shorter for the more anisotropic Hg-based and Bi-based superconductors. The critical exponent for fluctuation conductivity is given by ~, = u ( 2 + z - d + r l ) ,
(2)
where u is the critical exponent for the coherence length, z is the dynamical critical exponent, d is the dimensionality and r 1 is the exponent for the order-par~eter correlation function. Renormalization group calculations for the 3D-XY model give u ~- 0.67 and 71 = 0.03 [8]. Thus, our result, k ~ 0.34, implies that z = 1.5 in Eq. (2). This value is characteristic of model-E, which is the dynamical universality class for the superfluid transition in 4He and also for extreme type II superconductors in the absence of screening [7]. We also notice that the application of magnetic fields above 10 mT for Bi2Sr2CaCu2Oy and above 100 mT
Sample type YBaCuO SC YBaCuO SC YBaCuO F YBaCuO P GdBaCuO F GdBaCuO P HoCaCuO F DyBaCuO P Bi-2212 SC Hg(Re)-1223 P SC: single crystal; F: epitaxial P: polycrystalline sample
;L 0.34 0.33 0.33 0.33 0.34 0.35 0.35 0.34 0.33 0.32 thin film;
A(K) 0.7 0.4 1.1 0.5 0.7 0.5 0.8 0.6 0.13 0.3
Recently, a fluctuation conductivity regime beyond 3D-XY, with exponent ;~=0.17, was identified in the close vicinity of Tc in a YBaCuO single-erystal [9]. Owing to this small value for L, it was suggested that the ultimate critical behavior for this superconductor might be that of a weakly first-order transition. REFERENCES
1. D.S. Fisher, M.P.A. Fisher and D.A. Huse, Phys. Rev. B 43 (1991) 130. 2. N. Overend, M.A. Howson and I.D. Lawrie, Phys. Rev. Lett. 72 (1994) 3238. 3. S. Kamal, D.A. Bonn, N. Goldenfeld, P.J. Hirschfeld, R. Lian and W.N. Hardy, Phys. Rev. Lett. 73 (1994) 1845. 4. P. Pureur, R. Menegotto Costa, P. Rodrigues Jr., J. Schaf and J.V. Kunzler, Phys. Rev. B 47 (1993) 11420. 5. P.C. Hohenberg and B.I. Halporin, Rev. Mod. Phys. 49 (1977) 435, 6. W. Holm, Yu. Eltsev and O. Rapp, Phys. Rev. B 51 (1995) 11992. 7. H. Weber and H.J. Jensen, Phys. Rev. Lett. 76 (1977) 2620; J. Lidmar, M. Wallin, C. Wengel, S.M. Girvin and A.P. Young, Phys. Rev. B 58 (1998) 2827. 8. J.C. Le Guillou and J. Zinn-Justin, Phys. Rev. B 21 (1980) 3976. 9. R. Menegotto Costa, P. Pttreur, M. Gusnfio, S. Senoussi and K. Behnia, Solid State Commun. 113 0999) 23.