Kopelevich and Esquinazi Reply:

Abstract

Kopelevich and Esquinazi Reply: In their Comment, Miu, Jakob, and Adrian [1] have questioned a nonlocal origin of the in-plane voltage measured in YBa 2 Cu 3 O 72x (Y123) high-T c films with electrodes situated outside the electrical current path [2].(1) The authors [1] claim that the nonlocal voltage V 56 ͑I, T ͒ due to vortex-antivortex dynamics should be undetectable in the configuration used in [2]. In particular, a very short characteristic range for the vortexantivortex interaction L 2l L ͑T ͒ 2 ͞l c was calculated, i.e., L͑T ϳ T ub ͒ ϳ 4 mm assuming the effective correlation length along the c axis l c equal to the film thickness t Ӎ 400 nm. T ub is the vortex-antivortex unbinding temperature (88.97 K for sample 1 and 88.5 K for sample 2 [2]). However, in the vicinity of T ub the threshold current I c ͑T ͒, due to a finite Josephson interplane coupling, is negligibly small [2], suggesting that at T ϳ T ub the decoupling of the superconducting CuO 2 layers takes place. Hence, the correlation length l c at T ϳ T ub should be much smaller than the film thickness t. At large enough measuring currents and/or T . T ub the correlation along the c axis disappears (see Ref.[12] in [2]), l c reduces to the spacing between the superconducting layers s ϳ 1 nm, and one gets L . 1.5 mm at T . T ub for both samples 1 and 2, which is comparable to the length of the films. Therefore the nonlocal voltage V 56 ͑I, T ͒ should be detectable at T ϳ T ub , as was found [2]. We stress that the sample characteristics such as, e.g., O content, may influence the correlation length. Our measurements, performed on Y123 films having a finite I c ͑T ͒ up to T c0 (sample 3 in [2]) and hence larger l c , have revealed a much smaller nonlocal V 56 ͑I, T ͒ signal indeed (see Fig. 5 in Ref. [2]).(2) The authors [1] pointed out that the mixed state that is supposed to arise from the magnetic field generated by the applied current I 14 may influence the measurements. Let us assume that at large enough currents the measured V 23 ͑I 14 ͒ characteristics originate from the flow of the field-induced vortices. Then, we have, e.g., at T 91 K, the linear "flux flow" resistivity r L 96 mV cm (see Fig. 4 in Ref. [2]). The local current I 14 100 mA generates a self-field (in the region between contacts 1 and 4) H 2I 14 ͞c p wt͞2 Ӎ 11 Oe [3], where w is the film's width. According to Bardeen-Stephen and Nozieres-Vinen models r ff r n ͑H͞H c2 ͒, where the upper critical field near the superconducting transition temperature H c2 ͑T ͒ Ӎ ͑dH c2 ͞dT͒ ͑T c0 2 T͒, and r n is the normal state resistivity. With T c0 92 K, the onset superconducting transition temperature [at T , 92 K, nonlinear I-V characteristics were measured at intermediate currents (Fig. 4 in Ref.[2]), indicating that the film is in the superconducting state], r n ͑T ϳ T c0 ͒ 115 mV cm, and dH c2 ͞dT 2 T͞K [4,5], we calculate r ff ϳ 6.3 3 10 22 mV cm at T 91 K, which is several orders of magnitude smaller than the measured resistivity r L

Effect of the sample geometry on the second magnetization peak in single crystalline BaKBiO thick film

“…It is interesting to note that the SMP was essentially suppressed reducing the lateral sample size to ∼ 100 µm also in Nb films [2] and Bi 2 Sr 2 CaCu 2 O 8 single crystals [3], suggesting (within the framework of the GV theory) a similar scale length L in these otherwise different superconductors. It is tempting to associate this fact with the irregular fractal-type flux penetration observed at low fields in various superconductors such as, e. g., Nb films [14], [16], and assume L as a characteristic width of flux droplets or fingers of size ∼ 10 .…”

“…Recently, the dependence of the second magnetization peak (SMP) -a maximum in the width of the magnetization hysteresis loop -on the sample geometry has been reported for Nb films [1,2] and Bi 2 Sr 2 CaCu 2 O 8 single crystals [3]. In particular, it was found that the SMP vanishes in both superconductors for small enough dimensions of the samples.…”

“…Thus, the interpretations of SMP given in Refs. [1][2][3][4] are fundamentally different from those based on an increase of the critical current density, implying that a careful distinction between the different approaches is necessary. The study of the sample geometry dependence of SMP is one of the experimental instruments allowing for such a distinction.…”

“…[1][2][3][4] treat the SMP as resulting from either a TMI effect [1][2][3] or from a non-uniform current flow due to material inhomogeneities [4] which takes place at H < H SMP . According to the TMI theory, the condition for thermomagnetic stability is achieved for an effective sample dimension s eff < s crit = 10H fj /4πj c [11], where H fj is the field at which the first magnetization jump (or reduction of the isothermal critical state magnetization which can occur in a rather smooth fashion even in Nb films [1]) takes place. Within our interpretation (see also Refs.…”

“…Within our interpretation (see also Refs. [1][2][3]), H fj ≃ H fp . Thus, taking the experimental values for µ 0 H fp ∼ 0.1 T and j c ∼ 10 9 A/m 2 , we get s crit ∼ 100 µm.…”