VOLUME 80, NUMBER 18 PHYSICAL REVIEW LETTERS 4 MAY 1998 Nonlocal In-Plane Resistance due to Vortex-Antivortex Dynamics in High-Tc Superconducting Films Y. Kopelevich,* F. Ciovacco, and P. Esquinazi Abteilung Supraleitung und Magnetismus, Universität Leipzig, Linnéstrasse 5, D-04103 Leipzig, Germany M. Lorenz Abteilung Halbleiterphysik, Universität Leipzig, Linnéstrasse 5, D-04103 Leipzig, Germany (Received 1 October 1997) In high-Tc superconducting YBa2 Cu3 O72d films and at no applied magnetic field we found both positive and negative in-plane nonlocal resistance in the vicinity of a vortex-antivortex unbinding transition, as it was predicted recently. The sign of the nonlocal resistance depends on the probed region in the current-temperature diagram. Our results indicate that a negative nonlocal resistance is due to the motion of unbounded vortex-antivortex ( V-A), whereas a positive sign is attributed to the motion of a 2D V-A ordered lattice. [S0031-9007(98)06036-0] PACS numbers: 74.76.Bz, 74.40. + k, 74.60.Ge increasing and decreasing current or temperature and at different sweep rates, inverting the current polarity, as well as using an appropriate combination of current-voltage electrodes (I36 , V45 , V12 ). No difference between the results has been observed [5]. Figure 2(a) presents the “secondary” voltage V56 vs current I14 measured in sample 1 at various temperatures. At low enough temperatures V56 is positive, monotonically increasing with current. At higher temperatures, however, V56 shows a complex nonmonotonic behavior. In a certain temperature interval we define three characlow sT d, where V56 becomes negative in teristic currents: I2 the low-current region, I1 sT d where V56 again becomes high positive, and I2 sTd, where V56 again becomes negative at high currents; see inset in Fig. 2(a). Thus, one can define the current-temperature I-T diagram with alternating domains of positive and negative nonlocal resistance as shown in Fig. 3(a). The appearance of a negative nonlocal resistance is expected for a state of unbinding V-A pairs due to the motion of the antivortex dragged by the moving vortex in In conventional resistance measurements the voltage contacts are within the electrical current path. In this work, however, we study the in-plane resistance in highTc superconducting YBa2 Cu3 O72d (Y123) films that arises outside the region in which the current flows. Our results obtained in zero applied magnetic field show that this nonlocal in-plane resistance can be positive or negative and is attributed to vortex-antivortex ( V-A) dynamics in agreement with recently published theoretical predictions [1,2]. Y123 films were obtained by pulsed laser ablation on SrTiO3 substrates as described elsewhere [3]. Structural and superconducting properties of the films were previously characterized by conventional techniques [3,4]; the films show a critical current density at 77 K and zero magnetic field jc , 106 Aycm2 . Several Y123 films of thickness ,400 nm with slightly different critical temperature Tc were measured. Here we focus our attention on the data obtained for three samples: Sample 1 showed a zero-field resistive midpoint transition temperature Tcmid ­ 91.5 K, transition width DTfs10 2 90d%g ­ 2 K, and a normal state resistivity, just above Tc , rn sTc d ­ 110 mV cm. Sample 2 was obtained by slightly deoxygenating sample 1; it showed Tcmid ­ 90.66 K, DT ­ 1.63 K, and rn sTc d ­ 115 mV cm. Sample 3 showed Tcmid ­ 88.8 K, DT ­ 0.8 K, and rn sTc d ­ 76 mV cm. Six low-resistance (,1 mV) gold electrodes were patterned as shown in Fig. 1 with a separation distance of ,200 mm. Copper wires were attached to the electrodes using silver paste. In the experiments the dc current I14 flows between the current leads 1 and 4, whereas the voltage is monitored simultaneously in both the applied current part of the sample V23 and in the currentless part V56 . Measurements of both isothermal V -I characteristics and temperature dependence of the voltage (resistance) at various applied fixed currents up to 100 mA were done. To rule out systematic errors, the measurements were performed with FIG. 1. Geometry of the experiment: I14 is the current flowing between 1 and 4 current leads; V23 and V56 are primary and secondary voltages, respectively. a . b . 200 mm, w . 1.6 mm. 4048 © 1998 The American Physical Society 0031-9007y98y80(18)y4048(4)$15.00 VOLUME 80, NUMBER 18 PHYSICAL REVIEW LETTERS 4 MAY 1998 FIG. 3. Current-reduced temperature diagram obtained for (a) sample 1 and (b) sample 2. spd: Ic std, shd: I2low std, s±d: I1 std, s3d: Ix std, s1d: If std, and s≤d: I2high std. The shaded regions correspond to a positive nonlocal resistance. The lines are only a guide to the eyes. FIG. 2. (a) Secondary voltage V56 vs I14 measured in sample 1 at various temperatures near the unbinding transition temperature Tub . 89 K. The numbers near the data indicate the following temperatures: 1: 88.5 K, 2: 88.7 K, 3: 88.75 K, 4: 88.9 K, 5: 88.95 K, 6: 89 K, and 7: 89.25 K. The inset shows V56 sI14 d measured at temperatures where a negative nonlocal voltage occurs in the high current limit. ( b) Primary voltage V23 vs current I14 . The numbers at the curves correspond to the temperatures of (a). Solid lines are obtained from Eq. (1). Arrows indicate the crossover current Ix sT d above which the V -I characteristic is described by a power law V ~ I a with a . 1 above Tub . The inset shows the temperature dependence of the exponent a near Tub . The solid line is obtained from asT d ­ 3 1 2fbs1 2 T yTub dg1y2 , with Tub ­ 88.97 K, and b ­ 23. the applied current region [1]. Therefore, it is tempting to search for features in the “primary” voltage V23 vs I [see Fig. 2(b)] that may provide some hints for a V-A unbinding transition. We found that at low enough temperatures V23 sId can be well described by the equation V ­ csT dIfI 2 Ic sT dgasTd21 (1) [solid lines in Fig. 2(b)]. This form for V -I characteristics has been suggested in Ref. [6] to describe a current-induced V-A unbinding in high-Tc superconductors, where the threshold current Ic sTd originates from a finite Josephson interplane coupling and csT d is a fitting parameter. According to theory, at a V-A unbinding transition temperature Tub the exponent asT d jumps from a ­ 3 to 1 in the low-current limit. The occurrence of such a jump in the measured film is clear at T . 89 K [see inset in Fig. 2(b)] which is similar to the results obtained for Y123 films [7] and Y123 single crystals [8]. Slightly below this temperature asT d can be fitted by asT d ­ 3 1 2fbs1 2 T yTub dg1y2 [9], taking Tub ­ 88.97 K and the nonuniversal parameter b ­ 23. It is also expected that near Tub the threshold current Ic sTd becomes very small. A diminishing Ic sT d manifests itself as an apparent disappearance of the negative curvature on a logsV d 2 logsId plot at temperatures near Tub ; see Fig. 2(b). We note that the obtained transition temperature Tub ­ 88.97 K is close to the temperature T ­ 88.9 K, where the negative secondary voltage first appears. This strongly suggests an intimate relationship between a V-A unbinding transition and the occurrence of the negative nonlocal resistance. We should stress, however, that the here observed V-A unbinding transition may not be a true Kosterlitz-Thouless transition due to sample size effects; see Ref. [10] for more details. This issue requires further investigations. Above some current Ix sT d, marked by arrows in Fig. 2(b), and at T . Tub , V23 , I a with a . 1, that corresponds to a regime of bound V-A pairs on the probed length scale [11]. The temperature dependence of Ix sT d is shown in Fig. 3(a). As can be seen, Ix sT d and I1 sT d are very close. This observation, together with the results obtained at T , Tub , suggests that the positive nonlocal resistance originates from the motion of bound V-A pairs. At I . If sT d, the local V -I characteristics become linear [V ~ I, see, e.g., the results for sample 2 in Fig. 4(b); 4049 VOLUME 80, NUMBER 18 PHYSICAL REVIEW LETTERS FIG. 4. (a) Secondary voltage V56 vs I14 for sample 2 at the following various temperatures near the unbinding transition temperature Tub ­ 88.5 K: 1: 88 K, 2: 89 K, 3: 89.2 K, 4: 89.3 K, 5: 89.5 K, 6: 90 K, 7: 90.5 K, 8: 91 K, and 9: 91.5 K. ( b) Primary voltage V23 vs current I14 . The numbers at the curves correspond to the temperatures of (a). The inset shows the hysteretic jump in V23 sId measured at T ­ 89.25 K. If is the current at which the differential resistance dV ydI saturates] that means that only dissociated V-A pairs are present. In this regime one should expect the reentrance of a negative nonlocal resistance. Indeed, we observed high sT d as well as a negative nonlocal resistance at I . I2 high the coincidence of I2 sT d and If sT d; see Fig. 3. Figure 3(b) shows the I-T diagram for sample 2 constructed from the V sId measurements shown in Fig. 4. As follows from Fig. 3 the I-T diagrams are similar for both samples 1 and 2. However, for the slightly deoxygenated sample 2, the threshold current Ic , 0 at all measured temperatures, reflecting a reduced Josephson coupling as compared to the virgin film (sample 1). It is worth noting that the obtained I-T diagrams are reminiscent of the theoretical predicted I-T phase diagram proposed for layered superconductors [12]. There is another intriguing feature found in sample 2, namely, I1 sTd lies just above a hysteretic jump measured in both primary V23 sI14 d and secondary V56 sI14 d characteristics at temperatures slightly above Tub [see Fig. 4 and inset of Fig. 4(b)]. At higher temperatures the jump transforms into a minimum in V56 sId measured in both samples 1 and 2. A similar hysteretic jump in the V -I characteristics has been measured in an applied magnetic field 4050 4 MAY 1998 in high-Tc [13] and conventional low-Tc superconductors [14,15]. This was interpreted as a current-induced vortex crystallization transition [16] or as a current-induced depinning related to the dynamics of an elastic medium [17]. On the other hand, the formation of a V-A crystal has been recently proposed [18]. Taking into consideration these results we propose the dynamic crystallization of the V-A matter at I $ I1 sT d. The motion of the “center of mass” [2] of the V-A crystal would lead then to a positive nonlocal resistance. Within this scenario the Ohmic (local) V -I characteristics measured at low currents just above the unbinding transition would be due to the motion of dissociated V-A pairs in the solid, similar to the thermally activated plastic motion in a vortex solid with dislocations [16,19]. Next, we compare V23 sTd and V56 sTd measured in samples 1 [Fig. 5(a)] and 3 [ Fig. 5(b)] with an applied current I14 ­ 50 mA. V56 sT d of sample 1 shows a pronounced “positive peak” at T ­ 89.8 K as well as “negative peaks” at T . 89 K and . 91 K. However, V56 sTd of sample 3 shows only a small positive peak at T . 88.4 K. It is also found that the ratio V56 yV23 at the positive peak temperature is 300 times smaller in sample 3 as compared to sample 1. The reason for such a difference is explained as follows. First, the unbinding transition was not observed in sample 3, which naturally explains the FIG. 5. Temperature dependent voltages V23 sTd and V56 sTd measured with a constant current I14 ­ 50 mA in sample 1 (a) and sample 3 ( b). Symbols correspond to measurements increasing T and lines decreasing. The inset shows the secondary voltage V56 against reduced temperature TyTc0 , where Tc0 is the superconducting transition temperature (onset). Numbers at the curves correspond to the sample numbers. VOLUME 80, NUMBER 18 PHYSICAL REVIEW LETTERS absence of negative peaks in V56 sT d associated with the motion of unbound V-A pairs. Second, V -I characteristics of sample 3 are described by Eq. (1) up to temperatures close to Tc . Because Ic originates from a finite Josephson interplane coupling [6], this would imply that in-plane nonlocal effects are reduced in a strongly coupled system. Also, the essential reduction of the nonlocal resistance can be understood assuming stronger vortex pinning in sample 3. As known from collective pinning theory [20], the quenched disorder (pinning) destroys the long range positional order in the vortex lattice beyond a characteristic length Rc , m3y2 yW (m is the rigidity modulus of the V-A lattice [18], and W the pinning strength). Thus, in a system with pinning, the nonlocal response due to the motion of the V-A lattice would vanish at distances R . Rc . This consideration suggests that Rc (sample 1) ¿ Rc (sample 3). From Figs. 5(a) and 5(b) and the inset of Fig. 5(b) one can also see a temperature independent negative V56 voltage which is equal for these two samples in the normal state. This nonlocal voltage decays below the resolution limit at distances much shorter as in the superconducting state. It is also found that the sign of the normal state nonlocal voltage oscillates with the distance between electrodes 4 and 5 (note that this was not observed in the superconducting state) suggesting its nontrivial origin, and it will be reported in a future work. Figure 5 clearly illustrates the fact that both “positive” and “negative” peaks in V56 sTd are essentially related to the superconducting state. Finally, we would like to note that positive nonlocal zero-field c-axis resistance has been measured in Bi2 Sr2 CaCu2 O8 high-Tc single crystals at T . Tub [21] and attributed to the Josephson interaction between thermal vortex excitations in adjacent superconducting layers. Our measurements indicate, however, the importance of 2D V-A dynamics in the occurrence of both positive and negative in-plane nonlocal resistance. To conclude, nonlocal in-plane resistance of Y123 superconducting films in the vicinity of a V-A unbinding transition reveals an I-T phase diagram with alternating domains of positive and negative nonlocal resistance. The negative nonlocal resistance is associated with the motion of unbounded V-A pairs, whereas the positive nonlocal resistance is attributed to the motion of the 2D vortex-antivortex crystal. These novel phenomena indicate that nonlocal measurements in “planar” geometry open new possibilities for the study of vortex dynamics in superconductors. One of us (Y. K.) acknowledges the support of the Innovationskolleg “Phänomene an den Miniaturisierungsgrenzen” (DFG IK 24yA1-1) and F. C. the support of 4 MAY 1998 the German-Israeli Foundation for Scientific Research and Development (Grant No. G-303-114.07y93). *On leave from Instituto de Fisica, Unicamp, 13083-970 Campinas, Sao Paulo, Brasil. [1] R. Wortis and D. A. Huse, Phys. Rev. B 54, 12 413 (1996). [2] C.-Y. Mou, R. Wortis, A. T. Dorsey, and D. A. Huse, Phys. Rev. B 51, 6575 (1995). [3] M. Lorenz, H. Hochmuth, D. Natusch, H. Börner, K. Kreher, and W. Schmidt, Appl. Phys. Lett. 68, 3332 (1996), and references therein. [4] M. Wurlitzer, F. Mrowka, M. Lorenz, and P. Esquinazi, Phys. Rev. B 55, 11 816 (1997); Appl. Phys. Lett. 70, 898 (1997). [5] For a detailed discussion on the contribution of thermoelectric and self-heating effects and why these cannot mimic our results, see Y. Kopelevich et al., J. Low Temp. Phys. (to be published). [6] H. J. Jensen and P. Minnhagen, Phys. Rev. Lett. 66, 1630 (1991). [7] Q. Y. Ying and H. S. Kwok, Phys. Rev. B 42, 2242 (1990). [8] N.-C. Yeh and C. C. Tsuei, Phys. Rev. B 39, 9708 (1989). [9] This is a result for vortex unbinding when V ~ I a [see A. M. Kadin, K. Epstein, and A. M. Goldman, Phys. Rev. B 27, 6691 (1983)], and is probably applicable to our case [ Eq. (1)]. [10] J. M. Repaci, C. Kwon, Q. Jiang, T. Venkatessan, R. Glover III, C. J. Lobb, and R. S. Newrock, Phys. Rev. B 54, R9674 (1996). See also S. T. Herbert et al., Phys. Rev. B 57, 1154 (1998). [11] G. Blatter, M. V. Feigel’man, V. B. Geshkenbein, A. I. Larkin, and V. M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994) see especially p. 1293. [12] S. W. Pierson, Phys. Rev. Lett. 74, 2359 (1995). [13] J. A. Fendrich, U. Welp, W. K. Kwok, A. E. Koshelev, G. W. Crabtree, and B. W. Veal, Phys. Rev. Lett. 77, 2073 (1996). [14] R. Wördenweber and P. H. Kes, Phys. Rev. B 34, 494 (1986). [15] S. Bhattacharya and M. J. Higgins, Phys. Rev. B 52, 64 (1995). [16] A. E. Koshelev and V. M. Vinokur, Phys. Rev. Lett. 73, 3580 (1994). [17] S. Scheidl and V. M. Vinokur, Phys. Rev. Lett. 77, 4768 (1996). [18] M. Gabay and A. Kapitulnik, Phys. Rev. Lett. 71, 2138 (1993). [19] S. Ryu, M. Hellerqvist, S. Doniach, A. Kapitulnik, and D. Stroud, Phys. Rev. Lett. 77, 5114 (1996). [20] A. I. Larkin and Yu. N. Ovchinnikov, J. Low Temp. Phys. 34, 409 (1979). [21] Y. M. Wan, S. E. Hebboul, D. C. Harris, and J. C. Garland, Phys. Rev. Lett. 71, 157 (1993). 4051