Non-ohmic response under low magnetic fields in BSCCO

EI~SEVIER

Physica C 223 (1994) 46-50

Non-ohmic response under low magnetic fields in BSCCO C. P a r a c c h i n i *, L. R o m a n 6 , A. V i o l a n t i Dipartimento di Fisica, Universitd di Parma, Parma, Italy

A. T e b a n o Dipartimento di Ingegneria Meccanica, H Universit6 di Roma - Tor Vergata, Roma, Italy

Received 22 December 1993

Abstract

The influence of low magnetic fields parallel to the c-axis on the vortex-antivortex (v-a) distribution in one BSCCO crystal and in one oriented film is studied by examining the changes of the non-ohmic response near the superconducting transition. The obtained results confirm the non-external magnetic origin of a v-a configuration and are interpreted by a losening and a depairing of the v-a couples in a way similar to that produced by the temperature. Phenomenological dependences of the two effects are proposed.

Several recent results, mainly obtained from the study of non-ohmic behaviors, indicate that in highTc cuprate superconductors (HTSC's) vortex structures are set up when superconducting conditions are attained. The formation of vortex instabilities is peculiar of bidimensional (2D) systems and the layered structure of these compounds seems indeed to allow for the formation of thermally induced supercurrent vortices. In the absence of an external magnetic field the charge neutrality requires that vortices of opposite helicity be equally present. Vortices and antivortices interact with a logarithmic potential which joins them in pairs. The superconducting state corresponds to the paired-vortex configuration and the depairing, which gives rise to electrical dissipation, may be caused by temperature, applied current and magnetic field. The effect of the temperature and of the electrical current on the vortex-antivortex ( v a) distribution is rather well studied and these results * Corresponding author.

are usually explained on the basis of the KosterlitzThouless (KT) theory [ 1 ], though alternative interpretations based on the 2D Coulomb gas model are proposed [ 2 ]. The KT theory, developed for superconductors by Halperin and Nelson [ 3 ], expects that the currentvoltage ( I - V ) characteristics, measured at temperatures below the superconducting transition, exhibit a power dependence: V=AI ~r) .

The exponent a (T) decreases linearly up to a temperature Tk, where it suddenly jumps from 3 to 1 (ohmic state). Such a drop, expressed by the KT "universal jump condition", defines the KT temperature Tk; while the extrapolation of the linear a (T) dependence to a = 1 gives the Ginsburg-Landau temperature Too [4,5]. Several experimental results in BSCCO indicate the existence of a broadened KT transition [ 6-9 ]; in YBCO such an effect is seldomly reported [ 10,11 ] and in most cases it is substituted

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( 1)

47

C. Paracchini et al. / Physica C 223 (1994) 46-50

by a smooth a (T) decrease [ 9,12-14 ], while a more pronounced transition appears in the superlattice structures of the same compound [ 15,16 ]. Recently a modification of the KT theory, which takes into account the quasi-bidimensionality (q2D) of the system, is proposed [ 17 ]. Then the broadening of the KT transition and the slope of the linear a (T) dependence are correlated to the anisotropy of the compound with a good experimental agreement [ 18 ]. On the other hand, the effect of the magnetic field on the v-a distribution is not so widely examined. Martin et al. [ 7 ] and Gorlova et al. [8 ] interpreted the influence of the applied magnetic field with a modified vortex concentration, while Fischer [ 19,20 ] and Artemenko et al. [ 21 ] consider the production of v-a pairs generated by the thermal fluctuations of flux lines. The aim of the present work is to study the influence of an external magnetic field on the v-a distribution by comparing the I-Vmeasurements. The forementioned power I - V dependence is here considered as an indication of the existence of a v-a configuration, either in the presence of the magnetic fields or not. Two BSCCO samples are examined: one single crystal (X) and one film (F), whose deposition plane is perpendicular to the c-axis. Growing procedures and structural data of the samples are described elsewhere [22]. All the electrical measurements are performed with standard four-probes methods and the direction of the external field is parallel to the c-axis of the samples. The temperature (a few degrees below T~o), the applied current ( 0.1-200 mA) and the magnetic fields (0.5-200 G) are kept in the ranges where non-ohmic behavior is observable; other experimental conditions are indicated in the captions of the following figures. Fig. I shows the I- V characteristics of one of the examined samples (F) when the magnetic field is applied at fixed values. The response is typical and a similar one is exhibited by the other sample. The temperature is kept constant below Tk, in order to avoid the thermal contribution of the v-a unbinding. The obtained characteristics exhibit superlinear trends similar to those obtained without applied magnetic fields in the same sample (inset of Fig. 1 ) and in many previously reported HTSC's [6,18 ]. The similarity of the I - V responses at different magnetic fields with those at various temperatures indicates

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log I ( A ) Fig. 1. Logarithmic plot of I- Vcharacteristics of sample F at 82.5 K under a magnetic field of (from down to up) 0.5, 1, 2, 4, 8, 16, 32, 64 G. Inset: logarithmic plot of I- Vcharacteristics of sample F at different applied temperatures without magnetic field (from down to up): 82.1, 82.3, 82.6, 82.8 K. that thermal and magnetic energy influence the " c a distribution in qualitatively similar ways. In particular, it is evident that the steepness of the non-ohmic behavior decreases at higher applied fields as it happens for the temperature. The straight lines obtained indicate that also with low applied magnetic fields the non-ohmic behaviors are satisfactorily approximated by power functions like Eq. ( 1 ), where the exponent a must now be considered both temperature and field dependent. According to the theory, a - 1 is a measure of the v-a coupling and its decrease indicates a loosening of the v-a interaction [4,5 ]. The relative lowering of the v-a coupling is given by the the ratio (ol(H) - 1 )/ ( a ( 0 ) - 1 ), whose dependence versus H is expected to start from 1 at H = 0 and to approach 0 (ohmic response) at larger H. For small fields a reasonable approximation is here obtained with a(H)-1 =exp(_ H) o~(O)-- I

(2)

as shown in Fig. 2. Eq. (2) is in agreement with the dependence of the supercarrier density n, on the applied magnetic field as obtained by Minnagen in the framework of the 2D Coulomb gas model [2]. A smoother dependence is observed at larger fields. The obtained values of a and a (0) are reported in Table 1.

48

C. Paracchini et al. /Physica C 223 (1994) 46-50

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Fig. 2. In lot(H) - 1 ] vs. H for the examined samples. (Circles are for X, crosses for F. )

Although all the measurements are here performed in the presence of magnetic fields (at least some component of earth magnetism) the extrapolation of the data in Fig. 2 to H = 0 assures that the I - Vpower dependence is exhibited also when the field is quite absent. In this way such an I - V dependence should not be explained with magnetic field induced mechanisms and it supports the existence of thermally induced v - a pairs favored by the bidimensionality of the system. By defining R = V/l, Eq. ( 1 ) may be rewritten as: or--1

,

Fig. 3. Logarithmic plot of the ratio R = V/I vs. H for sample F at 82.5 K at different applied currents: (from down to up) 5.8× 10 -4, 8X 10 -4, 1.8× 10 -3, 3X 10 -3, 4.6X 10 -3) 7.1 X 10 -3, 1 X 10 -2 A. The lines are obtained from Eq. (5) with the parameters listed in Table 1.

is kept constant as in Fig. 1 and the current is applied at fixed values. At small fields the R values are strongly affected by the applied current, while they approach the same value when H increases. No analytic approximation of these experimental trends is immediately found, nevertheless the data of Fig. 3 plotted versus 1 / H in Fig. 4 indicate that at higher magnetic fields R is exponentially dependent on 1/ H:

(3) .

where A" = A I g - 1oc 2n~(Tk) 2RN, RN being the normal resistance, ~ the coherence lenght and Io the Ginsburg-Landau critical current evaluated at irk [ 5 ]. In Eq. (3) the dependence of R on H is included in c t - 1, as indicated in Eq. (2). The effect of the applied magnetic field on the electrical dissipation is shown in Fig. 3, where R is plotted versus H on a logarithmic scale. The temperature

where B and b are current-independent parameters, since all curves collapse on a single straight line when the field is increased and the current decreased. The B value gives R when H ~ ~ , while b gives the slope of the straight line limit. Eq. (4) gives the better approximation at larger fields and smaller currents, while Eq. (3) is more significant for larger H values.

Table 1

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a (G)

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b (G)

bo (kG)

T~o (K)

43 35

140 17

7.8 a 5.7 a

46 23

12 430

550 a 240 a

16 7.3

76.7 85.3

a The indicated values of or(0) and b refer to 74.1 K for X and to 82.5 K for F.

C. Paracchini et al. / Physica C 223 (1994) 46-50

Then two field contributions to the dissipation are suggested: one through the current, the other directly by the field. A dependence of R versus H over the whole examined range may be obtained by adding Eqs. (3) and (4). This approach is in agreement with the Halperin-Nelson model, where the resistivity is due to free vortices released by the current and the field [ 3 ]. Then

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where the first term, prevailing at low fields, indicates a loosening of the v-a couples to be disrupted by the current; the second, more effective at larger H, gives the direct field-induced pair breaking. This equation contains six current independent parameters which can be evaluated from the data fo Figs. 1, 2 and 4. The point where the I - V characteristics of Fig. 1 converge givesA', that is the ratio of Vo/Io, and Io [23], while the intercept and the slope of the straight line in Fig. 2 give o r ( 0 ) - 1 and a respectively; finally B and b are given in the same way by Fig. 4. The values of all these parameters for the examined samples are listed in Table 1. In Fig. 3 the lines show the trends of Eq. (5) obtained by using the forementioned parameters, giving evidence for the good agreement with the experimental points obtained for different applied currents. A further agreement between Eq. (5) and experiment is achieved by considering the R-H measurements at different temperatures below Tk, as shown in Fig. 5. The applied current is here kept constant

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log H (G) Fig. 5. Logarithmic plot of the ratio R = V/I vs. H for sample F at constant applied current ( 1.5 X 10 -4 A) and at different temperatures: (from down to up) 81.5, 82.5, 83, 83.5, 84 K. The lines are obtained from Eq. (5) where a, B and b are tempera. ture-dependent parameters as discussed in the text.

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and the results are similar to those previously reported [ 7 ]. As far as the temperature dependence of the forementioned parameters is concerned, the inset of Fig. 1 assures that A' and I0 are temperature independent; the KT theory gives: a ( 0 ) - 1 oc ( 1 - T/Too) [ 5 ] and the temperature dependence of B and b is given by the plot ofln R versus 1/H, as shown in Fig. 6. The obtained straight lines converge in a single point at 1 / H = O, suggesting that B is temperature independent, while the inset of Fig. 6 indicates b = bo( 1- T/T~o), giving to this parameter the meaning of a critical field. By using these dependences a

50

C. Paracchini et aL /Physica C 223 (1994) 46-50

good analytical fitting is obtained also for the data of Fig. 5, as shown by the c o n t i n u o u s lines. The good agreement of the experimental points in Figs. 3 a n d 5 with the lines obtained from Eq. (5) supports the proposed model. In conclusion the influence of the magnetic field on the n o n l i n e a r electrical response in BSCCO suggests that low magnetic fields do not generate nor destroy the v - a configuration, b u t they contribute with temperature a n d current to the change of the v - a distribution: in particular lower fields loosen the v - a coupling, favoring the current depairing, while higher fields contribute directly to the v - a dissociation. The proposed formulas for these two effects have, at the m o m e n t , no theoretical justification, b u t they should be useful to clarify the role of the magnetic field on the v - a interaction in HTSC's.

Acknowledgements The authors are grateful to G. Calestani for the preparation of the crystal used in the experiments. This work is supported by the "Progetto Finalizzato Tecnologie Superconduttive e Criogeniche" a n d by CISM.

References [ 1] J.M. Kosterlitzand D.J. Thouless,J. Phys. C 6 ( 1973) 1181.

[2] P. Minnagen, Rev. Mod. Phys. 59 (1987) 1001; D.P. Norton and D.H. Lowndes, Phys. Rev. B 48 (1993) 6460. [3] B.I. Halperin and D.R. Nelson, J. Low Temp. Phys. 36 (1979) 599. [4 ] J.E. Mooij, in: Percolation, Localization and Superconductivity, eds. A.M. Goldman and S. Wolf (Plenum, New York, 1983). [ 5] A.M. Kadin, K. Epstein and A.M. Goldman, Phys. Rev. B 27 (1983) 6691. [6] S.N. Artemenko, I.G. Gorlova and Yu.I. Latyshev, Pis'ma Zh. Eksp. Teor. Fiz. 49 (1989) 566 [JETP Lett. 49 (1989) 654]. [7 ] S. Martin, A.T. Fiory, R.M. Fleming,G.P. Espinosaand A.S. Cooper, Phys. Rev. Lett. 62 (1989) 677. [8] I.G. Goriova and Yu.I. Latyshev, Pis'ma Zh. Eksp. Teor. Fiz. 51 (1990) 197 [JETP Lett. 51 (1990)224]. [9 ] C. Paracchini, L. Roman6 and L. Francesio, Physica C 175 (1991) 324. [ 10] N.C. Yeh and C.C. Tsuei, Phys. Rev. B 39 (1989) 9078. [ 11 ] Q.Y. Ying and H.S. Kwok, Phys. Rev. B 42 (1990) 2242. [12] P.C.E. Stamp, L. Forro and C. Ayache, Phys. Rev. B 38 (1988) 2847. [13] C. Paracchini and L. Francesio, Progr. in High Temp. Supercond. 25 (1990) 257. [ 14] C. Paracchini and L. Roman6, Physica C 184 ( 1991 ) 29. [ 15] S. Vadlamannati, Q. Li, T. Venkatesan, W.L. McLean and P. Lindenfeld, Phys. Rev. B 44 (1991) 7094. [16]X.G. Qiu, B.R. Zhao, S.Q. Guo, J.L. Zhang and L. Li, Physica C 197 (1992) 195. [ 17] C. Paracehini and L. Roman6, Physica C 191 ( 1992) 72. [ 18 ] C. Paracchini and L. Romanr, Physica C 207 ( 1993) 143. [ 19] K.H. Fischer, Physica C 178 ( 1991 ) 161. [20] K.H. Fischer, Physica C 193 (1992) 401. [21 ] S.N. Artemenko, I.G. Gorlova and Yu.I. Latyshev, Physica C 193 (1992) 47. [22] G. Balestrino, M. Marinelli, E. Milani, A. Paoletti and P. Paroli, J. Appl. Phys. 70 ( 1991 ) 6939. [23 ] To be published.