A paper presented at the 2 nd Physics Symposium May 8-9, 2007

1. Ac susceptibility measurements and extraction of inter- and intra-grain superconductive transitions in polycrystalline RuSr2GdCu2O8superconductorM. M. Abu-Samreh1,4, R. M-L Kitaneh2, H. F. Braun3, and A. M. Saleh2,*1 Physicsand Electronic Department, Faculty of Applied Sciences, Palestine Polytechnic University, Wadi-Alhariah, Hebron, West Bank, Israel 2 Physics Department, College of Science and Technology, Al-Quds University, East Jerusalem, Abu-Dis, P O Box 20002, West Bank, Israel.3 Physikalisches Institut, Universitiit Bayreuth, 95440 Bayreuth, Germany4 Permanent address: Physics Department, College of Science and Technology, Al-Quds University, East Jerusalem, Abu-Dis, P O Box 20002, West Bank, Israel A paper presented at the 2nd Physics Symposium May 8-9, 2007 Organized by the Physics Department An-Najah National University Faculty of Science Nabuls, Palestine May 8-9, 2007

2. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine Abstract • Systematic measurements of the AC magnetic susceptibility of polycrystalline RuSr2GdCu2O8 (Ru-1212) samples are reported for various frequencies and magnetic field amplitudes. The study covered frequency range from 22 Hz to 12.5 kHz and field amplitudes between 0.5 to 25 Gauss. Both of the susceptibility components χ', and χ'' are greatly affected by frequency and applied field depending on the relevant range under consideration. • In addition, the measured data of the susceptibility components were employed to extract inter- and intra-grain superconductive transition temperatures as well as the average transition temperature in magnetic superconductor RuSr2GdCu2O8. The intra- and inter-granular components of the granular susceptibility components were also estimated. It was found that both of the intra- and inter-granular transition temperatures increase by increasing field frequencies and decrease by increasing the field amplitudes. This might be an indication that the grains of RuSr2GdCu2O8 behave differently from a homogenous bulk superconductor. The nature of curves indicated the presence of a superconducting transition between grains, coupled by weak links with a distribution of critical temperatures, and the superconducting transition within the grains. The two transitions observed are linked to the typical intra- and intergrain transitions of a granular superconductor. The weak coupling between grains might be modeled in terms of Josephson-junction arrays.

3. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine Introduction • The discovery of superconductivity (SC) (Tc=8– 46 K) coexisting with spatially uniform ferromagnetism (FM) (TCurie124-136 K) in the polycrystalline hybrid ruthenate-cuprate material RuSr2GdCu2O8 (Ru-1212 Gd) had presented a remarkable achievement in the study of competing magnetism and SC and had opened an interesting and promising era for new research topics in the field of superconductivity • The ACS technique was successfully employed to extract some electronic and magnetic properties of Ru-1212Gd polycrystalline superconductor such as its transition temperature (TC), magnetization, critical current density (CCD), JC(T), ordering parameters, penetration depth, and conductivity • It is well known that the fundamental complex ACS (χac=χ΄-χ˝) has a clear physical meaning. The real part of ACS,, corresponds to the dispersion of magnetic into the medium that measures the response of the system to the probing field, and hence reflecting the supercurrent shielding effect in the case of superconducting samples

4. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • Besides, the imaginary part, , corresponds to energy dissipation that represents the bulk pinning hysteresis losses of type-II superconductors that arises from the viscous flux flow motion and hysteresis due to the pinning of flux vortices • Several models have been proposed and developed to explore the main features of χac(T) data and their dependencies on ac field amplitudes, Hac, and frequencies [19-32]. The simplest and oldest critical state models (CSMs) are the Bean critical state model (BCSM) and Kim-Anderson model (KAM) • In this work, the ACS data of Ru-1212 Gd polycrystalline magnetic-superconductor were analyzed over the temperature range (6–50 K) in order to investigate the applicability of the ACS analytical models. In other words, the main aim of the present paper is to check the general agreement between the theoretical predictions ofand relations with experimental data that may include additional loss mechanisms like flow or flux-creep (FC).

5. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine Experimental • Samples of Ru-1212 polycrystalline superconductor were prepared following the two-step procedure reported previously [1,2,8]. In the first step, Sr-2116 was prepared from stoichiometric quantities of RuO2, Gd2O3, and SrCO3. Then the mixed powders were ground, calcined at 950 0C in air, reground, milled, pressed into pellets and fired for 16 h at 1250 0C in air. In the second step, the obtained Sr-2116 was mixed with CuO and the mixture was ground, milled, pressed into pellets and fired for 720 h at 1060 0C in flowing oxygen atmosphere. • The ACS measurements were performed by a homemade susceptometer using a standard lock-in amplifier technique. The measurements covered a wide range of frequency (20-12500) Hz for different field amplitudes that range between 0.5-25 G.

6. Results and discussion 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine

7. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • This type of transition, which is characterized by a steep drop in the χ' component of ACS, is known as the intragrain transition. In general, the intragrain transition corresponds to paramagnetic-superconductive (PM-SC) transition. Besides, this type of dependence represents the transition from near-perfect screening to complete penetration of external. ac magnetic field into the sample. Moreover, the linear decrease of below the intra-grain temperature,,can be interpreted on the basis of decreasing the JJ penetration depth .

8. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine The temperature can be extracted from χ΄ dependencies on the frequencies of the applied ac field using the crossing point of the two extrapolated linear parts of above and below the transition (of the two straight lines of Fig. 2)

9. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • A typical dependence of on ac field frequencies is shown in Fig. 3A. The measured data showed almost a power-law behavior.

10. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • Additionally, the general behavior of curves shown in Fig. 3B, which represents the dependence of on field amplitude, are quite different from that expected for a bulk superconductor, i.e., from Ginzburg-Landau theory

11. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • Particularly, the uncommonly strong decrease of the intragrain of at low field cannot be explained by means of the bulk and homogeneous superconductivity inside the grains. The observed suppression rates for in Ru-1212 compound are an indication of the intragrain superconductivity is attributed to the phase-lock transition of nanoscale JJA’s. • Similarly, the peak of positive magnetoresistance observed in Ru-1212 was quantitatively explained under this assumption

12. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • More information about the intragrain superconducting state and its corresponding average transition temperature, Tave, can be obtained from the temperature derivatives of χ΄curves, i.e. . The dependence of on temperature between 10-50 K at different field frequencies and constant field amplitude of 0.5 G is displayed in Fig. 4. The location of the average transition temperature, Tave, is generally represented by the maximum of versus temperature curves. The nature of curves indicate the presence of a superconducting transition between grains coupled by weak links, with a distribution of critical temperatures, TC, and the superconducting transition within the grains. The superconducting transition is generally connected with a magnetic phase transition.

13. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • The peak positions of plots in Fig. 4 occurred around T ~ 27.8 K, 25.4 K, 22 K for f = 12.5 kHz, 5 kHz, and 100 Hz, respectively. The obtained values of Tave were found to range from 22 to 30 K. The low frequency values were found to be in a good agreement with the values obtained from the specific heat measurements. • Typical log-log plot of the frequency dependence of Tave is exhibited in Fig. 5. Clearly, the general behavior of the log-log dependence on Tave is almost linear. It should be pointed out that Tave was defined as the intragrain transition temperature based on both the size and the ac field amplitude dependencies of the measured ACS in the same sample. • The outcome of this study had shown that Tintra and Tave exhibited the same field dependence, but the obtained values of Tintra are higher than Tave by almost 2 K. This is a clear indication that the two transition temperatures are different and the samples might possess a weak-coupling limit similar to that between JJA’s.

14. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • The temperature transition width, ΔT, between points on curve had been chosen to represent half of the maximum value of the first derivative and thus it can be considered as a good quantitative measure of the transition width. At fixed field amplitude, this width depends on the frequency where it decreases by increasing the frequency. In the present data ΔT = 12 K at 100 Hz while at 12.5 kHz the width, ΔT, is about 9.6 K.

15. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • The imaginary part of the ACS, , dependence on temperatures at different field frequencies and constant field amplitude (0.5 G) is exhibited in Fig. 6A, while Fig. 6B displayed the dependence of χ˝(T) on field amplitudes at 1 K Hz. Generally, a peak around a certain temperature, known as the inter-grain transition temperature,, is characterized by most of χ˝(T) curves. The observed peak in χ˝(T) curve represents the losses to the shielding current flowing in between individual grains . The can be simply extracted from χ˝ dependencies on field amplitudes and frequencies. The inter-grain transition for Ru-1212 was found to occur within 8 - 30 K. This relatively weak intergrain coupling may partially be attributed to heat treatment conditions.

16. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine

17. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine The dependencies of on field frequencies at of 0.5 G and its dependence on field amplitudes at 1 KHz are displayed in Figs. 7A and 7B, respectively. The dependencies of on frequencies and field amplitudes are similar to those of. The results had shown that by increasing the frequency is increased, while it is decreased by increasing field amplitude. The frequency

18. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • According to explanation of the FC model by Tinkham and Müller, when the frequency is increased, the intergranular vortices have less time to relax and then penetrate the superconductor during each cycle. In order to reach full flux penetration, the effective intergranular pinning force density must be weakened. Since the pinning force density is weakened by increasing temperature, the, must increase with increasing frequency. • It appears from Fig. 7B that decreases steeply with an initial slope of ~ 8 K/G by increasing ac field amplitude. It should be pointed out here that the maximum loss always takes place when the magnetic flux lines just penetrate to the center of the sample. As the driving field amplitude increases, larger screening currents are required to shield the applied field and consequently decreasing This fraction of available links diminishes as the external field is increased leading to sharper transitions. Such type of behavior is typical for a granular superconductor with weak intergranular JJA’s coupling. This is an indication that Ru-1212 exhibits a strong intragrain granularity effects. Granularity of Ru-1212 have been previously reported in the temperature dependence of the resistivity measurement, which is more sensitive to weak links across the grain boundaries, and it was attributed to either structural defects or possible phase separation [7,12,17,30-31]. Accordingly, a JJAs model should be invoked to interpret the present data. • An attempt has been made to fit the dependence of and on frequency and field amplitudes. The dependence of both temperatures on angular frequency, ω = 2πf, is found to fit an empirical equation of the form:

19. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • The experimental inter-granular matrix susceptibility could be extracted from the measured susceptibility components and using the following equations [32-34]: • Here is effective volume fraction of superconducting grains excluding a shell of thickness of order of the London penetration depth and are the intragrain susceptibility components. The values were estimated using the method introduced by Ravi. The estimated values of at T = 22, 24, 28 K are 0.31, 0.33, 0.34, respectively. As it could be noted the fraction of susceptibility χ′g or χ′i will depend mostly on the quality of the sample; that is the grain size and grain contribution. The average of the volume fraction of the grains fg in this study is taken as 0.33. Using the value in eq. (3), the experimental values were determined. Accordingly, the ACS components can be rewritten as the summation of granular susceptibility components: . Therefore, the ACS component is divided as 1:2 between the granular ACS components (the intra- and the inter-). The granular ACS components of the investigated samples are displayed in Fig. 8.

20. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine

21. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • . Conclusion • The inter-, intra-transition temperatures are determined for the magnetic Ru-1212 polycrystalline superconductor from ACS measurements as function of temperature, frequency and field amplitude. The inter- and intra-transition temperatures were found to decrease with increasing field amplitudes and to increase by increasing the field frequencies. This sort of behavior is explained by assuming that the intragrain superconductivity is due to a phase-lock transition of a nanoscale JJA’s. The intra- and inter-grain transitions are attributed to the paramagnetic-superconductive (PM-SC) transition. • The nature of the temperature derivative of the real part of the ACS curves indicated the presence of a superconducting transition between grains, coupled by JJA’s weak links with a distribution of critical temperatures, and the superconducting transition within the grains. The observed suppression rates of the transition temperatures in Ru-1212 magnetic superconductor compound are in compatible of the nanoscale JJA’s. This means that the ruthenate-cuprate grains were actually JJA’s, in agreement with the phase separation model [30]. Generally, the overall behavior of is very different from what might be expected for a bulk superconductor, i.e., from Ginzburg-Landau theory.

22. 2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine • Thank You For Your Attendence