Magnetoresistance in Gd(Ba2−xPrx)Cu3O7+δ system
Introduction
The magnetic field dependent transport properties of high temperature superconductors (HTSC) have been the subject of a great number of research. Understanding the dissipation mechanism in HTSC is extremely important for its scientific and technological implications.
Among transport properties, one of the most important physical quantities for a superconductor is its superconducting transition temperature variation upon application of the magnetic field. Although, a sharp superconducting transition temperature in HTSC––within the transition width of less than 1 K or so––is generally observed in zero field, it becomes much wider, several K or even more, in a moderate magnetic field intensity ∼1 T [1]. Flux dynamics in the mixed state of HTSC through different transport measuring techniques such as the Hall effect [2] and the field induced broadening of the resistance transition is a pressing scientific concern.
The polycrystalline samples present a pronounced granular character that plays an important role in many of their properties. For instance, the resistance transition of these systems has the characteristic of a two-stage process [3]. At higher temperatures, superconductivity stabilizes in homogenous and mesoscopic regions of the sample i.e., grains, which is the pairing transition. At lower temperatures, close to Tc(ρ=0), a long-range superconducting state with zero resistance is achieved by means of a percolation like process that controls the activation of weak links between grains. Under applied magnetic field, the weak links are affected and therefore, the tail part dissipates in even small fields. In large magnetic fields, due to flux penetration inside the grains the onset part of transition will be broadened. Moreover, as it has been mentioned by Hilgenkamp and Mannhart [4], the grain boundaries misorientation angles has strong effect on the intergranular critical current density. This result has been confirmed recently; magnetic field dependence of the critical current density of various [1 0 0]-tilt grain boundaries in Y-123 bicrystalline films have been measured by Verebelyi et al. [5].
There are some different models for interpretation of resistivity broadening under magnetic field such as thermally activated flux creep [6], phase slip [7], flux line melting [8], flux cutting, curved flux lines [9], and flux entanglement [10]. Some groups such as Batlogg et al. [11], Palstra et al. [12], Malozemoff et al. [13], and Griessen [14] have pointed out that a thermally activated flux creep model can describe the broadening behavior quite well for the resistivity region near Tc(ρ=0). These groups have found a temperature-dependent activation energy, and a very weak magnetic field dependent energy barrier. On the other hand, some resistivity measurements [15], [16], [17], [18], [19], [20] in highly anisotropic HTSC, i.e., Bi2Sr2CaCu2O8+δ, (La,Sr)2CuO4, Tl2Ba2CaCu2O8+δ, and YBa2Cu3O7−δ systems show that the macroscopic Lorentz force plays a minor role in magnetic flux motion, which is in contradiction with flux creep model.
Another approach to the problem of flux dynamics in a magnetic field––leading to induced dissipation behavior of the HTSC––has been achieved by applying the Ambegaokar and Halperin (AH) phase slip model [7] to a medium of Josephson weak links. This model describes the effects of thermal fluctuation of the phases of the order parameters cross a highly damped, current driven Josephson junction. Both granular and single crystals of HTSC have been examined with this model under different magnetic fields and electrical currents. Good agreement has been found between experimental data and the AH theory [21], [22].
Within this theory, when kBT becomes comparable with the Josephson coupling energy, the resistance ρ(T) in the limit of low current, I≪Ic(T), is given bywhere I0 is the modified Bessel function, ρn is the average normal state resistivity of the junction, and γ is the normalized barrier height for thermally activated phase slip, defined as [7]:where U0 is the activation energy, t≡T/Tc is the reduced temperature, H is the applied magnetic field, and A is a constant. In the fitting process, we use ρn, C(H)≡A/H, Tc, and q as free parameters.
In the above mentioned reports on magnetoresistivity (MR) measurements, none have studied the doping effect in a systematic order, especially the Pr effects, on MR in a reasonable domain of doping. Pr atom is the only rare earth (R) with stable orthorhombic 123 structure, which does not superconduct and is an insulator. Although, there have been many experimental and theoretical efforts to justify the insulating behavior of PrBa2Cu3O7−δ (Pr-123), the reports of superconducting Pr-123 by some independent groups [23], [24] have exceeded the complexity of Pr effect in HTSC. So, the real effect of Pr in HTSC, especially in 123 structures, and the corresponding transport properties are an active and intense field of research in superconductivity. Recently, different anomalous effects of Pr doping in HTSC are reviewed by Akhavan [25].
In this paper we will compare the effects of Pr substitution at Ba site i.e., Gd(Ba2−xPrx)Cu3O7+δ (GdBaPr-123) [26], and at R site i.e., (Gd1−xPrx)Ba2Cu3O7−δ (GdPr-123) [27], [28], [29] on magnetoresistance for different amounts of Pr doping. Based on the AH theory, we will investigate the temperature and magnetic field dependences of the pinning energy as a function of Pr doping. The critical current at zero temperature can be derived from the corresponding theory, which will be presented as a function of magnetic field.
Section snippets
Experimental
The Gd(Ba2−xPrx)Cu3O7+δ single phase samples with x=0.0, 0.05, 0.1, 0.15, 0.2, and 0.25 were synthesized by the standard solid state reaction technique. In accordance with the procedures followed in our previous report [30], appropriate amounts of Gd2O3, Pr6O11, BaCO3, and CuO powders with 99.9% purity were mixed, ground, and calcined at 840 °C for 24 h in an air atmosphere. Calcination was repeated twice with intermediate grinding. Then powders were reground, pressed into pellets, and
Results and discussion
The SEM topograph of samples shows the homogenous granular samples with 1–3 μm grain sizes. The XRD patterns show that the single phase 123 structure has been formed. There is no noticeable impurity peak present in the GdBaPr-123 patterns. Formation of some impurity phases such as BaCuO2 is unavoidable in the GdPr-123 samples [33], even for small content [34]. Absence of any impurity phases in the GdBaPr-123 compounds show that the expected stoichiometric 123 structure has been constructed,
Conclusions
Based on the AH phase slip model applied to the GdBaPr-123 and GdPr-123 samples, the power law dependence of γ to magnetic field and temperature has been obtained for different amounts of Pr doping. The dispersivity in the power factors could be due to different angles of grain boundaries, inhomogeneous microstructural grains, different amount of oxygen contents in grains, and various domains of applied magnetic fields in different reports. The critical current density vs. H is consistent with
Acknowledgements
We wish to thank H. Khosroabadi and H. Shakeripour for technical assistance and useful discussions. This work was supported in part by the Offices of Vice President for Research and Dean of Graduate Studies at Sharif University of Technology.
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