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Fluctuation induced conductivity of polycrystalline MgB 2 superconductor

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We report fluctuation-induced conductivity (FIC) of the polycrystalline MgB2 superconductor in the presence of magnetic field. The results are described in terms of the temperature derivative of the resistivity, dρ/dT. The dρ/dT peak temperature
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  Fluctuation-induced conductivity of polycrystalline Ni dopedCu0.5Tl0.5Ba2Ca2Cu3−yNiyO10−δ y = 0, 0.5, 1.0, 1.5) superconductors Najmul Hassan and Nawazish A. Khan   Citation: J. Appl. Phys. 104 , 103902 (2008); doi: 10.1063/1.3000477   View online: http://dx.doi.org/10.1063/1.3000477   View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v104/i10   Published by the  AIP Publishing LLC.   Additional information on J. Appl. Phys. Journal Homepage: http://jap.aip.org/   Journal Information: http://jap.aip.org/about/about_the_journal   Top downloads: http://jap.aip.org/features/most_downloaded   Information for Authors: http://jap.aip.org/authors   Downloaded 21 Sep 2013 to 183.129.198.245. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions  Fluctuation-induced conductivity of polycrystalline Ni dopedCu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3− y  Ni y  O 10−    „ y  =0, 0.5, 1.0, 1.5 …  superconductors Najmul Hassan and Nawazish A. Khan a   Materials Science Laboratory, Department of Physics, Quaid-i-Azam University, Islamabad 45320, Pakistan  Received 29 April 2008; accepted 28 August 2008; published online 17 November 2008  The fluctuation-induced conductivity of Ni free and Ni doped Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0, 0.5, 1.0, 1.5   samples is investigated for comparison of dimensionality of fluctuations above themean-field critical temperature. The temperature dependence of paraconductivity can be describedby a power law following Aslamazov–Larkin   AL   type equations for these polycrystallinesuperconductors. It is observed from these studies that at higher temperatures, the fluctuations in theorder parameter of the carriers follow two-dimensional   2D   AL behavior, whereas at lowertemperatures   closer to transition temperature   their behavior is three-dimensional   3D   AL. Fromthe analysis of our results, we have also evaluated the exponents of dimensionality, the coherencelengths, and the crossover temperatures. The crossover temperature from 2D to 3D havesubstantially been shifted to lower temperatures with increasing Ni doping, which is most likelyrelated to the scattering of the carriers by remnant spins of Ni atoms. These scattering promote areduction in the coherence length of the carriers along  c -axis. These studies have also shown that thecarrier concentration in the conducting CuO 2  planes is the most essential; the role of antiferromagnetism in the mechanism of superconductivity is secondary. ©  2008 American Instituteof Physics .   DOI: 10.1063/1.3000477  I. INTRODUCTION The electronic properties of high- T  c  superconductors areusually attributed to their layered structure in which electri-cally conducting CuO 2  planes are intercalated by varioussubunits acting as charge reservoirs. 1–7 The layered structureis also believed to be responsible for a large anisotropy of their normal- and superconducting-state properties. Thislarge anisotropy promotes fluctuations in the order parameterdue to competing effects of different coherence lengths  along  c -axis and  ab -plane   during the transport processes.The investigation of the fluctuation-induced conductivity  FIC   is regarded as one of the experimentally accessiblemethods just shedding light on the transport properties of high- T  c  oxides in the normal state. Just above transition tem-perature  T  c  but outside of the critical region, resistivity     T   is affected by superconducting fluctuations resulting in no-ticeable deviation of      T    down from its linear dependence athigher temperatures. Thus there appears a FIC,     T    =      N   T    −     T   /     N   T      T   ,   1  where     T    is the actually measured resistivity and     N   T   =   +   T   is the extrapolated normal state resistivity. Twoforms of fluctuation contributions to      T    are usually con-sidered. The direct Aslamazov–Larkin   AL   contributionarises from excess current carried by fluctuation-createdCooper pairs above  T  c . 8 The additional, indirect Maki–Thompson   MT   contribution reflects the influence of super-conducting fluctuations on the conductivity of normalelectrons. 9 In layered structures such as high- T  c  supercon-ductors the AL term is described by a Lawrence–Doniach  LD   model 10 and predicts a crossover from three-dimensional   3D   electronic state of the system to a two-dimensional   2D   one with increasing temperature. The ALterm dominates close to  T  c  whereas the MT term turns out tobe dependent on phase-relaxation time  t     and gains impor-tance in 2D fluctuation region in the case of moderate pairbreaking. 11 Consequently, measurements of fluctuation con-ductivity provide a sufficiently simple method of getting re-liable information about    c  T   ,  t    , and dimensionality of theelectronic system of the superconductor. In view of a veryshort Ginzburg–Landau coherence length    GL  0   in high- T  c oxides      T    should be observed at temperatures well above T  c . The crossover phenomena analyzed in terms of the LDmodel have been reported by many research groups but theMT contribution was found to be uncertain 12–16 thus exclud-ing the possibility to evaluate  t    .We have recently synthesized Ni dopedCu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0, 0.5, 1.0, 1.5   super-conductors at normal pressure and achieved superconductiv-ity in these compounds over a wide composition range  i.e.,  y =1.5  . 17 These research findings have not only shownthat superconductivity and ferromagnetism can coexist butalso that the presence of antiferromagnetic aligned Cu atomsin CuO 2  planes is not essential for the mechanism of super-conductivity; contrary to the theory of antiferromagnetismfor superconductors. The FIC studies to the order parameterof the Ni doped superconductors, therefore, becomes essen-tial for the determination of ultimate mechanism of super-conductivity in these compounds. II. EXPERIMENTAL The samples were synthesized by standard solid-state re-action method. The samples are characterized by various a  Electronic mail: nawazishalik@yahoo.com. JOURNAL OF APPLIED PHYSICS  104 , 103902   2008  0021-8979/2008/104  10   /103902/6/$23.00 © 2008 American Institute of Physics 104 , 103902-1 Downloaded 21 Sep 2013 to 183.129.198.245. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions  techniques such as x-ray diffraction, ac susceptibility, and dcresistivity. The resistivity of the samples was measured byfour probe method. The rectangular bar shaped samples of dimensions 2  10 mm 2 were used for resistivity measure-ments. The contacts are made by silver paint and a constantcurrent of 1 mA is passed through the sample during resis-tivity measurements in four probe method. All of these mea-surements indicated that the samples were predominantlyCuTl-1223 phase with nominal traces of CuTl-1234 andCuTl-1234 phases. Details of preparation and these investi-gations have been given previously. 17 III. BRIEF THEORETICAL BACKGROUND The excess conductivity      in the lower anisotropyCu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0, 0.5, 1.0, 1.5   super-conductors have been calculated using AL model involvingmicroscopic approach in the mean field region. According tothis approach, the excess conductivity in two dimensions andthree dimensions are given by formula    2D  =   e 2 / 16  d    −1 ,   2     3D  =   e 2 / 32    c  0   −1 / 2 ,   3  where    c  0   and  d   are the coherence length along the  c -axisat 0 K and the interlayer separation, respectively.    is thereduced temperature and given by the relation  =   T   −  T  c mf   / T  c mf  ,where  T  c mf  is the mean field critical temperature obtainedfrom the point of inflection of      versus  T   curve in our case.The dimensional exponent    is found from the slope of the ln       versus ln     plot. All physical parameters dependon the critical fluctuation dimensionality    D  , which is ex-pressed as  D  = 2  2 +   It is seen that the 2D to 3D crossover is mainly foundabove the critical temperature at a particular temperature  T  o ,which is different for different samples. However, the cross-over temperature is not very unique. Rather, the dimensionalcrossover takes place over a temperature regime. It is re-ported that there is a temperature regime where the supercon-ductor is neither 2D nor 3D and the extent of this regime iscontrolled by the ratio of the Josephson coupling strengths inthe biperiodic model. 18,19 In some other cases, the fractalcharacteristics are reported in the fluctuation conductivity of high- T  c  superconductors, and recently two band effects havealso been considered for modifying the amplitude and cross-over places in such data analysis. Lawrence and Doniachintroduced the concept of interlayer coupling in the vicinityof the critical temperature via Josephson coupling  J  . 10 TheFIC      is expressed as     =   e 2 / 16  d    −1  1 +   2   c  0  / d   2  −1 / 2 ,where    c  0   and  d   are the coherence length along the  c -axisand the interlayer separation, respectively. The above equa-tion reduces to the AL equation with the approximations   c     d   and    c     d   in 2D and 3D regions, respectively. Acharacteristic temperature  T  0  is obtained, which is called acrossover temperature. Below and above this temperature,the system has 3D and 2D fluctuations, which can be de-scribed by the relevant AL equations. The expression forcrossover temperature according to LD model is 20–22 T  o  =  T  c  1 +   2   c  0  / d   2  .   4  The FIC analysis is mainly done on the basis of the ALequations. 8 These equations are formulated for the crystal-lites, not for the polycrystalline sample. Therefore, theseequations cannot be directly used to analyze the FIC of thepolycrystalline samples. For the case of polycrystallinesamples such as ours, Ghosh  et al. 22 proposed a model toanalyze the FIC that takes into count the polycrystalline na-ture of the samples. It is modified form of AL equations thatcan be applied to the polycrystalline samples. According tothis model, the equations for 2D and 3D fluctuations are asfollows:    2D  = 1 / 4  e 2 / 16  d   −1  1 +   1 + 8   c 4  0  / d  2   ab 2  0   −1  ,  5     3D  =  e 2 / 32     p  0   −1 / 2 ,   6  where     p  0   is effective characteristic coherence length andis given by1 /    p  0   = 1 / 4  1 /   c  0   +   1 /   c 2  0   + 8 /   ab 2  0  1 / 2  ,with the assumption of the high anisotropic nature of thesample and by using the Eqs.   3   and   4  , the crossover tem-perature is given approximately by T  o  =  T  c  1 +     p 2  0  / d  2  1 +     p 2  0  / 16   ab 2  0  .   7  We have employed above formulation to interpret the data onFIC of our samples. As our samples are low anisotropic, wehave used Eq.   4   for the estimation of crossover tempera-ture. IV. RESULTS AND DISCUSSIONS The x-ray diffraction scans of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0, 0.5, 1.0   supercon-ductor samples, prepared at 850 °C, are shown in Fig. 1  a  .The x-ray diffraction scan of   y =1.5 is reported elsewhere. 17 Most of the diffraction lines could be indexed according te-tragonal structure following  P 4 / mmm  space group. The Nisubstituted nominal derivative phasesCu 0.5 Tl 0.5 Ba 2 CaCuNiO 10−    and Cu 0.5 Tl 0.5 Ba 2 Ca 3 Cu 2 Ni 2 O 10−   are also marked in the diffraction scans. The lengths of   a  and c  axes decrease with increased Ni doping inCu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0.5, 1.0, 1.5  . For thesesamples, there is no remarkable structural transition with in-creased Ni content. The  a  and  c  lattice parameters of thesamples decrease monotonously with increasing Ni concen-tration presumably due to the lower ionic size of Ni +2 ascompared to Cu +2 . The variation of length of axes with Niconcentration is given in the inset of Fig. 1  a  . Figure 1  b  depicts the surface micrograph of one of the representativeCu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 1.5 Ni 1.5 O 10−    sample. The grains appearwhite while the epoxy appears as a black background. Grains 103902-2 N. Hassan and N. A. Khan J. Appl. Phys.  104 , 103902   2008  Downloaded 21 Sep 2013 to 183.129.198.245. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions  are seemed to be oriented randomly but well connected. Theaverage grain size was calculated at different spots of thesamples and found to lie between 2 and 6    m.The resistivity measurements of Ni free and Ni dopedCu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0, 0.5, 1.0, 1.5   samplesare shown in the inset of Fig. 2  a  –2  d  . The resistivity varia-tions are metallic from room temperature down to the onsetof superconductivity. In the inset of these figures, the peakcurves show the derivatives of the resistivities in the regionof transition for all the samples. The transition width   T  c ,evaluated from the  dp / dT   plots using the full width at half maximum of the peaks, comes out to be lying between 4 and5 K for all samples, indicating a sharp transition. Generally,for the high  T  c  systems,   T  c  has been found between 3 and 5K in good quality samples. It is well known that these sys-tems consist of multiphases and these mechanism of  growthinvolves intergrowth of two phases simultaneously. 23 There-fore, it is difficult to synthesize a material with a sharp tran-sition and small   T  c . It is believed that the presence of im-purities, even in traces, results in broadening of    T  c . Theposition of this peak on temperature axis provides  T  c mf   K   . T    K    is the temperature related to pseudogap regime whereonset of fluctuations in the order parameter of superconduct-ors set in. The  T  o  K    is the temperature at which a crossoverin the fluctuations to the order parameter from 2D to 3D takeplace. All the samples have shown linear dependence of re-sistivities      T   =   +   T    with temperature above 157 K. Lin-ear fits to the data at high temperatures are shown by thestraight lines. The values of      and     are listed in Table I andaforementioned temperatures are included in Tables I and II. The deviations from the linear dependence of resistivitiesstart from  T    K    pseudogap temperature  . A. Fluctuations induce conductivities The FIC is derived using the expression   1  . In order tocompare the experimental data with the theoretical expres-sions for superconducting fluctuating behavior, we plotln       versus ln     for the Ni free and Ni doped samples for2D and 3D cases of polycrystalline samples, Fig. 2  a  –2  d  .    2D  and     3D  have been calculated by using    c  0  =4 Åand    ab  0  =16 Å for Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3 O 10−    samples. 24 We have taken  d  , the effective separation between the CuO 2 layers, to be equal to 9.3 Å for this analysis. 25 Like all hightemperature superconductors   HTSCs  , all our samples haveshown 2D character at higher temperatures and 3D behaviorat lower temperatures   closer to the transition temperatureregions  . Ni free samples have shown 2D AL behavior up to152.5 K whereas the Ni doped samples    y =0.5, 1.0, 1.5  have shown 2D AL description at much lower temperaturesi.e., 117, 109, and 116 K, respectively. The shift of 2D ALcharacter to very low temperatures could be looked in termsof associated spins of Ni atoms in mixed CuO 2 / NiO 2  planes.In oxide superconductors, it is widely believed that 3 d  9 shells of Cu atoms are associated with antiferromagneticalignment of spins within the CuO 2  planes. This antiferro-magnetic alignment of spin somehow provides 2D fluctua-tions to the order parameter of the carriers up to 152.5 K,whereas in the Ni doped samples, the disruption of antifer- FIG. 1.   a   X-ray diffraction pattern of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0, 0.5, 1.0   superconductor samples. “  x  ” and “  ” are the representation of CuTl-1234 and CuTl-1212 phases respectively. Length of “ a ” and “ c ” axesvs Ni content is given in the inset.   b   Surface micrograph of theCu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =1.5   sample. 103902-3 N. Hassan and N. A. Khan J. Appl. Phys.  104 , 103902   2008  Downloaded 21 Sep 2013 to 183.129.198.245. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions  romagnetic alignment of spin array within the CuO 2 / NiO 2 planes possibly provides more 2D character, which survivesto the much lower temperature. Close to the transition tem-perature, 3D AL fluctuation becomes dominant. The 2D ALcharacter starts where conductivity deviations from the linearbehavior begin. This is the temperature where cooper pairformation set in. The deviation from the linear behavior in Nifree samples set in around 158 K and in the Ni dopedsamples around 160 K, which shows that cooper pair forma-tion in Ni doped samples starts at slightly higher tempera-tures. The asymmetric or inharmonic scattering offered bythe spin lattice of doped Ni +2 atoms probably shifts the coo-per pair formation to slightly higher temperatures. The 3DAL behavior in Ni free samples begins around 152.5 K andterminates around 102 K, whereas in Ni doped samples thisregime set in around 109–117 K and terminates around 99 K.The spread of 3D fluctuations in Ni free samples is about 50K while in Ni doped samples are around 18 K, which is threetimes smaller than Ni free samples. It is most likely that thesmaller spread of 3D AL regimes in the Ni doped samples (a) (c)(b) (d) FIG. 2.   a   ln       vs ln     plot of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0   sample. The scattered points are experimentally found FIC of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0   with the help of Eq.   1   Solid line   3DAL   through experimental points has slope −0.45   −3.5  ln     −0.6  . Dash line  2DAL   of slope −0.84 through the experimental FIC in the region ln     0.03. In the inset of figure, the resistivity measurement of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0   sample and its derivative curve are shown.   b   ln       vs ln     plot of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0.5   sample.The scattered points are experimentally found FIC of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0.5   with the help of Eq.   1   Solid line   3DAL   through experimentalpoints has slope −0.52   −3.3  ln     −1.4  . Dash line   2DAL   of slope −0.95 through the experimental FIC in the region ln     −0.86. In the inset of figure,the resistivity measurement of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =0.5   sample and its derivative curve are shown.   c   ln       vs ln     plot of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =1.0   sample. The scattered points are experimentally found FIC of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =1.0   with the help of Eq.   1   Solid line   3DAL   through experimental points has slope −0.58   −3.4  ln     −1.6  . Dash line   2DAL   of slope −1.25 through the experimental FICin the region ln     −0.8. In the inset of figure, the resistivity measurement of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =1.0   sample and its derivative curve areshown.   d   ln       vs ln     plot of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =1.5   sample. The scattered points are experimentally found FIC of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =1.5   with the help of Eq.   1   Solid line   3DAL   through experimental points has slope −0.48   −3.6  ln     −1.5  . Dashline   2DAL   of slope −1.15 through the experimental FIC in the region ln     −0.861. In the inset of figure, the resistivity measurement of Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3−  y Ni  y O 10−      y =1.5   sample and its derivative curve are shown. 103902-4 N. Hassan and N. A. Khan J. Appl. Phys.  104 , 103902   2008  Downloaded 21 Sep 2013 to 183.129.198.245. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions
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