Coherent transition induced by Sr doping on the YBa2Cu3O7-δ single crystal magnetoconductivity

We have studied by magnetoresistivity measurements the influence of the low Sr chemical doping on the conductivity thermodynamic fluctuation regimes (TFR) of a YBa1.98Sr0.02Cu3O7-δ single crystal. The low-current and low-frequency resistivity, ρ(T,H) measurements were performed in a PPMS while DC magnetic fields up to 50kOe were simultaneously applied perpendicular to the ab plane of the single crystal and to the measurement current density. The dρ(T,H)/dT data shows that the superconducting transition of the sample occur is two stages that corresponds to the signature of a granular superconductor. At this scenario is possible to define two critical temperature transitions TC(H) and TC0(H) [TC(H) > TC0(H)]. At TC(H) the superconductivity sets in within the grains and at TC0(H) a coherent transition takes place and a long-range superconducting order takes place over the whole sample. Special attention is reserved to the paracoherent region [TC0(H) ≤ T < TC(H)] of the ρ(T,H) data. The field and the temperature dependence of the paracoherent TFR behavior is characterized by a power law represented by a critical exponent S0 ≈ 3. This exponent is an indicative that the coherence transition of the sample belongs to the 3D-XY universality class with relevant disorder that probably is associated to the low Sr doping.


Introduction
The contribution of the granularity to the superconductor properties of the high temperature superconductors (HTSC) has been an object of the intensity scientific investigation [1,2,3]. In particular AC magnetoresitivity and DC magnetization techniques are successful to characterize its contribution to electrical and magnetic properties of these materials [1,2,3]. The polycrystalline samples prepared by usual solid state reaction techniques are essentially classified as granular superconductors [4,5]. Otherwise the characterization of superconductor single crystals like a granular material is a controversial subject because these are idealized as homogeneous materials [3].
The chemical doping is designated for some works at the literature as an efficient way to introduce an inhomogeneous (granular) character to the superconductor magnetic and electrical properties of YBa 2 Cu 3 O 7-δ single crystals [1,2,3] regime is described by the Almeida-Thouless and the Gabay-Thoulouse power laws that is the magnetic signature of a frustrated and disordered material [2,3]. Otherwise the identification of a magnetoresistivity coherent transition in the electrical property of a superconductor consists in an additional way of characterizes it as a granular material [1,4,5]. As far as we know the report at the literature about magnetoresistivity coherent transition in the HTSC single crystals is scarce [1].
In this work, we report on magnetoresistivity and thermodynamic fluctuation conductivity results of a YBa 1.98 Sr 0.02 Cu 3 O 7-single crystal with the aim of characterizes a granular scenario from the identification of a magnetoconductivity coherent transition.

Sample preparation and experimental methods
The single crystals of YBa 1.98 Sr 0.02 Cu 3 O 7-were grown by self-flux method [1] and the selected ones were submitted to an extra oxygen process with the objective of improve their superconducting temperature transition T C [1].  The four contact ρ(T,H) measurements were performed with AC low current-low frequency PPMS inset while DC magnetic fields up to 50kOe were simultaneously applied parallel to the c axis of the single crystal (H c) and to the measurement current density (H J). The (T,H) was recorded while the temperature was decreased from T > T C . During it measurements the temperature was swept very slowly ( 0.4 k/min) so that a high number of data points could be recorded in the temperature range of the superconducting transition and the temperature derivative of the resistivity [dρ(T)/dT] could be numerically determinate.

Results and Discussion
The upper panels of figures 2 and 3 displays the ρ(T,H) data as well as the lower panels of the figures 2 and 3 displays their correspondent dρ(T,H)/dT data to H 50kOe applied parallel to  figure 3 shows that the resistive transition of the YB(Sr)CO became a two step process to 2.5kOe < H 50kOe.
The T PAR is the paring temperature that in ρ(T,H)/dT plots corresponds approximately to the T C . The observation of a two step process to the resistive superconducting transition is a clear manifestation of the granularity. At this scenario the first step corresponds to establishment of the superconductivity within the grains at T C as well as the second step corresponds to the establishment of a long-range superconducting order over the whole sample resulting in a zero resistivity state. Contrasting the figures 2 and 3 results is reasonable to conclude that the second step resistivity transition could be induced by the magnetic field.    (1) where is the fluctuation conductivity extracted from the experimental data as = -R where = -1 is the measured conductivity and the subtracted regular term ( R = R -1 ) is estimated by extrapolating the high temperature behavior of the (T) data of the figure 1(b).
When the temperature approaches T C from above we assume that diverges as = A(t)where the reduced temperature is t = (T -T C )T C -1 and A and are the criticals amplitude and exponent, respectively. Then, from equation 1 we obtain The existence of asymptotically TFR regimes becomes evident applying the equation (2) in the data of figure 4(c). The extrapolation of the solid line to the temperature axis allows the simultaneously identification of the critical temperature, T C and the critical TFR λ scr .
The λ scr exponent observed close to the T C is related to the critical fluctuations. The [ (T,H)] -1 data for T > T C identify the existence of critical, λ cr and Gaussian, λ G TFR [1,4]. However in this work we are very interesting in the paracoherent TFR behavior of the magnetoconductivity data situated at T C0 (H) T < T C (H). In this particular temperature range, the TFR of [ (T,H)] -1 data is shown to diverge according to the power law = A 0 (t) -S 0 where A 0 is a constant, S 0 is the critical exponent related to the vortex physics [9] and t = (T -T C0 )T Co    In the figure 5 the extrapolation of the solid line of the [ (T,H)] -1 data to the temperature axis allows the simultaneously identification of the critical temperature, T C0 and the critical TFR S 0 to H > 1kOe. The T C0 decreases faster than T PAR as the applied magnetic field is increasing to 50kOe. The open circles correspond to the temperature maximum amplitude of the lower temperature peak of the figure 3. Otherwise their temperature positions coincide with the beginning of the S 0 power law regimes which identifies it as a precursor of the coupling grain process.
In the immediate vicinity of zero resistance of the [ (T,H)] -1 data is possible identify the occurrence of a power law regime corresponding to the averaged exponent . In special, the S 0 3 was observed to a YBa 2 Cu 2.97 Zn 0.03 O 7-single crystal to H 1kOe [1] and to the HTSC polycrystalline samples this exponent converges to 4 as H > 1kOe are applied [4,5]. The where J ij is the Josephson coupling energy between nearest neighbor grains i and j, θ i and θ j are the phases of the parameter order of the grains i and j, respectively and the vector potential A ij is given to 0 is the flux quantum and the line integral is evaluated between the centers of grains i and j. In this scenario the fluctuating phase of the superconductor order parameter in each grain becomes long-range ordered as a consequence of activation of weak links between the grain [5]. This result is the indicative that the coherence transition belongs to the 3D-XY universality class with relevant disorder [9].
According to the results presented in the figures 2, 3 and 5 we suggest that the partial substitution of the 1% of the Ba atoms for Sr atoms introduces a granular character to the superconductor electrical properties of the in the YBa 2 Cu 3 O 7-δ single crystal. This granular character is highlighted by the two step process of the resistive superconducting transition and the characterization of a paracoherent-coherent transition of the granular array represented by the S 0 (H) 3 critical exponent.