Flux dynamics and low-field magnetic properties of the heavy-fermion superconductor CeCu2Si2

Strong flux creep effects are observed in CeCu₂Si₂ at low magnetic inductions and temperatures in the range 6 mK<T<T _c . Measurements of flux creep in single crystal as well as polycrystalline specimens show that the magnetization in CeCu ₂ Si ₂ decays following a power law time dependence of the typeM(t)t ^– for 1<t<10 ⁵ sec, where the exponent a ranges between 0.015 and 0.06. The activation energy values obtained from the relaxation rates are around 2–3 meV. The flux creep data give clear evidence of the existence of different types of pinning centers in CeCu ₂ Si ₂ : a large number of shallow potential barriers that characterize the vortex dynamics at short times and few strong pinning centers responsible for the long-time relaxation behavior. Quantum tunneling of flux lines through weak pinning centers probably gives rise to the non-thermally activated relaxation observed at the lowest temperatures. The physical origin of weak and strong pinning centers in CeCu ₂ Si ₂ is discussed. From isothermal dc magnetization measurements we estimate the lower critical fieldH _c1 as well as the critical current densityJ _c . TheH _c1 versusT curve shows an anomalous positive curvature for temperatures close toT _c .     

Some Remarks on Vortex Matter in High-T c Superconductors

We show that some experimentally observed features of vortex matter in high-T _c superconductors may be interpreted in simpler ways than it is usually done. In particular, we consider magnetic flux creep at low temperatures as well as the irreversibility line in the H–T phase diagram. We also discuss a new approach to the analysis of the equilibrium magnetization in the mixed state of type-II superconductors and we suggest an alternative configuration for the mixed state in magnetic fields close to the upper critical field.     

Magnetization curves and Bean''s model in high-Tcsuperconductors

High-T _c superconductors have critical currents that decay sharply with increasing magnetic field. We solve Bean's model forJ _c decaying exponentially withH and obtain qualitative agreement with existing magnetization data. We show thatH _c1 cannot be obtained from the linear part of the magnetization curve; it can only be inferred from a low-field anomaly in the hysteresis curve. Presently quoted values ofH _c1 ,based on the linear part of the magnetization curve, are gross overestimates.     

A Comparative Study of High-Field Diamagnetic Fluctuations in Deoxygenated YBa2Cu3O7-x and Polycrystalline (Bi–Pb)2Sr2Ca2Cu3O10

We studied three single crystals of YBa₂Cu₃O_7-x, (Y123) with superconducting transition temperature, T_c=62.5, 52, and 41 K, and a highly textured polycrystalline specimen of (Bi–Pb)₂Sr₂Ca₂Cu₃O₁₀ (Bi2223), with T_c=108K. Isofield magnetization data were obtained as a function of temperature, with the magnetic field applied parallel to the c axis of each sample. The reversible magnetization data for all samples exhibited a rounded transition as magnetization tended toward zero. The reversible data were interpreted in terms of two-dimensional diamagnetic lowest-Landau-level (LLL) fluctuation theory. The LLL scaling analysis yielded consistent values of the superconducting transition temperatures T_c(H) for the various samples. The resulting scaling data were fit well by the two-dimensional LLL expression for magnetization obtained by Tesanovic and colaborators, producing reasonable values of κ but the fitting parameter ∂H_c2/∂T produced values that were larger than the experimentally determined ones. We performed simultaneous scaling of Y123 data and Bi2223, obtaining a single collapsed curve. The single curve was obtained after multiplying the x and y axis of each scaling curve by appropriate sample-dependent scaling factors. An expression for the two-dimensional x-axis LLL scaling was extracted from theory, allowing comparison of theoretical values of the x-axis scaling factors with the experimental values. The comparison between the values of the x-axis produced a deviation of 40% which suggests that the hypothesis of universality of the two-dimensional LLL fluctuations is not supported by the studied samples. We also observe that Y123 magnetization data for temperatures above T_c obbey a universal scaling obtained for the diamagnetic fluctuation magnetization from a theory considering non-local field effects. The same scaling was not obbeyed by the corresponding magnetization calculated from the two-dimensional LLL theory.     

Fluctuation-induced diamagnetism in type II superconductors above H c2

The fluctuation-induced diamagnetism in strong magnetic fields in type II superconductors is studied theoretically. It is shown that the fluctuation-induced diamagnetism at low temperatures (i.e., TT _c0) is described in terms of a universal function of [B \s- H _c2(T)]/H_s(T) for both dirty and pure superconductors, where H _s(T), the scaling field, is proportional to (T/T _c0)H_c2(0).Work supported by the National Science Foundation under Grant DMR 76-21032.     

AC-measured shifts inT c of high temperature superconductors: The effect of interlayer structure

The apparentT _c of some high temperature superconductors such as BiSrCaCuO and TlBaCaCuO measured by low (10–20,000 Hz) a.c. inductance techniques is shifted downward by up to 30K in the presence of modest (400 Oe) d.c. magnetic fields. Dc magnetization (SQUID) measurements of the same samples show no such shifts in the same magnetic fields. Other materials like YBaCuO and TlPbSrCaCuO do not show such shifts ofT _c in a.c. inductance measurements in d.c. magnetic fields. While BiSrCaCuO and TlBaCaCuO are known to exhibit flux creep/flux flow phenomena resulting in low irreversibility line behaviour as measured by both a.c. and SQUID techniques, the aboveT _c shift is apparently a new phenomenon. Materials exhibiting this property contain two or more layers of metal ions between the CuO conductance layers (2212, 2223 structure). Materials with only one metal ion layer between the CuO layers (123, 1223 structure) do not show the apparentT _c shift, suggesting that the phenomenon is a result of the properties of magnetically-isolated CuO layers. Implications of the latter will be discussed.     

A New Method for the Estimation of Hc2 Anisotropy in Polycrystalline MgB2 Samples

By using isothermal magnetization measurements in polycrystalline MgB₂ samples, we estimate the H ^c _c2 in the interval [0, T _c]. By combining these measurements to the estimated H ^ab _c2 from the onset of the diamagnetic transition in isofield and isothermal magnetic measurements, an estimation of the anisotropy parameter can be achieved. The H ^c _c2 values coming from high quality polycrystalline samples agrees nicely to those obtained on single crystals. Our results show a temperature variation of the (T ) = H ^ab _c2/H^c2 with (T _c) 3.     

A study of the flux density distribution in type II superconductors rotating in a magnetic field

Torque measurements on type II superconductors rotating in a magnetic field H ₀ directed perpendicular to the rotational axis can be used to determine pinning and viscous friction of vortices. The exact analysis of these measurements requires a knowledge of the vortex configuration in the rotating specimen, which is studied for the case of a circular cylinder of infinite length. A method is developed to calculate numerically the vortex configuration if the dependence of critical current density J _c and flux flow conductivity _f on flux density B and if the equilibrium magnetization curve are known. An inverse procedure also allows us to determine these material parameters from the measured torque and magnetization of the rotating sample. Results obtained by applying this procedure to different materials are reported.     

Detailed Physical Characterizations of Cu-rich and Ru-poor (Ru0.9Cu0.1)Sr2YCu2O7.9

The optimized nominal composition, (Ru_0.9Cu_0.1) Sr₂YCu₂O_7.9 sample, has been prepared through high-pressure and high-temperature solid-state densification method. The obtained material has been studied by X-ray (laboratory) diffraction powder technique, magnetization and detailed magneto-transport measurements. The title compound indicates bulk magneto-superconducting properties under field strengths of H=10, 100, 500 and 1000 Oe. It shows diamagnetic transition at T _d=54, 38, 20 and 8 K for H=10, 100, 500 and 1000 Oe, respectively, in the zero-field-cooled susceptibility measurements. The high-field (H=5 and 10 kOe) molar susceptibility measurements show sharp ferromagnetic transition at ∼150 K with reduced molar susceptibility values. The various field dependence of magnetization, M(H), isotherm curves recorded at constant temperatures (5, 10, 25, 50, 100 and 150 K) indicate ferromagnetic saturation, whereas the MH curves measured at 200 and 300 K conditions reveal the paramagnetic state of the compound. Though the sample showed onset transition temperature, T_c^onsetT_{\mathrm{c}}^{\mathrm{onset}}, at ∼34 K under different field strengths (H=0, 10, 30, 50, 70 and 90 kOe), no T_c^R=0T_{\mathrm{c}}^{R=0} is seen down to 2 K. Even under relatively low applied field (ΔH=10 kOe) the title compound shows large negative magnetoresistance (MR) of about 68% at 2 K and increases with increasing the field strength up to ΔH=90 kOe (MR=77% at 2 K). This value is amazing and probably higher than other 1212 type ruthenocuprates. The title compound which shows little negative MR (about 1%) in the high temperature regions (125–300 K) is not affected much by different field strengths. Among the different fixed temperature MR(H) isotherms, the MR(H) curve measured at 5 K shows maximum negative MR of about 47% at 90 kOe compared to other four (T=50, 100, 200 and 300 K) MR(H) curves.     

Studies onin situ Cu-Nb composites

As part of a program of developing Cu-Nb₃Sn composite superconductors through in situ techniques, systematic investigations have been performed on Cu-Nb composites containing niobium up to 30 at %. These alloys, prepared by an arc melting technique, show excellent filamentary morphology when reduced to fine wires. TheT _c (midpoint) of these composite wires is 8.8 K with a T _c =0.12 K. The self-field overallJ _c of 0.21-mm-diameter wires of these composites at 4.2 K is 2.5×10⁵ A cm^–2. TheJ _c increases with area reduction ratio up to a value of 2000 and has not attained saturation. Kramer plots (J _c ^1/2 H _c ^1/4 versusH) of the compsite wire yield a value of effective upper critical fieldH _c2 ^* of 1.1 T, significantly higher than for pure niobium wire. Enhancement ofH _c2 ^Emphasis>* is attributed to the increase of the normal resistivity of the niobium filaments. In situ tapes show large critical current anisotropy with applied field direction, strongly indicating that surface flux pinning at the interface boundaries between the superconducting filament and matrix is important in these materials. The peak in the volume pinning force, versus reduced field plots occurs for Cu-Nb (20 at %) composites consistently at 0.25, very close to the predicted value on the basis of surface flux pinning.     

Anisotropy of the generalized Ginzburg-Landau parameters x 1 and x 2 in clean,cubic, type II superconductors

From the nonlocal GLAG theory expressions are derived for x₁ and x₂ of a clean, cubic crystal with a general Fermi surface. In the region of weak nonlocality near T _cthe correction terms in H _c2, x₁, and x₂ due to the nonspherical Fermi surface are expressed by two dimensionless Fermi surface averages. For highly purified Nb single crystals and polycrystalline Nb samples, x₁ and x₂ were determined from magnetization measurements in the temperature range (0.3–0.95)T _c. The experimental data show that the orientation dependence in x₂ is twice as large as in x₁, in agreement with the theoretical result near T _c. The two Fermi surface averages that characterize the anisotropy of H _c2, x₁, and x₂ near T _care estimated from experimental data for Nb and V.     

Flux entry fields in amorphous superconductors

We have measured the flux entry fields (lower critical fieldsH _c1) of homogeneous and inhomogeneous extreme type II amorphous superconductors based on zirconium. Samples are prepared by melt quenching at both ambient and elevated substrate temperatures. The degree of homogeneity is classified according to the widths of both inductive and resistive transitions. TheH _c1 (T) curves for powdered homogeneous samples with weak flux pinning are found to be in good agreement with Maki's theory. Taking into account the electron-phonon renormalization effect, we deduce the zero-temperature energy gap values 2_o/k _B T _c to be BCS like. On the other hand, anomalousH _c1 (T) curves are observed in powdered inhomogeneous samples and strips from homogeneous samples parallel to the applied field. Appreciable irreversibility effects are also observed. The latter results are discussed qualitatively in terms of bulk and surface inhomogeneity effects.Research supported by National Science Foundation grant DMR-82-02624.     

The upper critical field of thin superconducting films with large resistance

The influence of the electron-electron interaction on the upper critical fieldH _c2 of thin superconducting films with large resistance and of layered superconductors is investigated theoretically. The orbital effect only is taken into account. It is shown that the electron-electron interaction in the diffusion and Cooper channels influencesH _c2 in different manners. The interaction in the diffusion channel (dynamically screened Coulomb interaction) leads to essential deviations from the standard BCS dirty limitH _c2 (T) curve at low temperatures and as a result upward curvature inH _c2 (T) is possible. The interaction in the Cooper channel is significant only at temperaturesT _c–TT_c and enlarges the slopedH _c2 (T)/dt atT=T _c.     

The determination of pinning forces from magnetization curves of wires

Methods are developed for the numerical calculation of pinning forces resp. critical current densitiesJ _cfrom experimental magnetization curves of cylinders. Application to Pb-Tl and Pb-In samples indicates a general lawJ _c=I _O(1 – H/H_c2)µ for well-annealed samples and largeH nearH _c2, where the constant depends on the composition and possibly the temperature. The application of the method to neutron-irradiated Nb samples shows that the peak effect is much more pronounced in theJ _c(H) curve than in the magnetization curve.     

Magnetization curves and Bean's model in high-T c superconductors

High-T _c superconductors have critical currents that decay sharply with increasing magnetic field. We solve Bean's model forJ _c decaying exponentially withH and obtain qualitative agreement with existing magnetization data. We show thatH _c1 cannot be obtained from the linear part of the magnetization curve; it can only be inferred from a low-field anomaly in the hysteresis curve. Presently quoted values ofH _c1 ,based on the linear part of the magnetization curve, are gross overestimates.     

Pinning Energy of High-Tc (Bi, Pb)2Sr2Ca2Cu3Oy

The flux pinning potential energy of silver (Ag) sheathed high-T _c Bi-2223 tapes determined from measured current densities, J(T,H), is reported in this paper. Measurements of the transport current density, J, of the Ag sheathed Bi-2223 tapes were performed with an applied magnetic field directions parallel (H‖ab) and perpendicular (H‖c) to the tape’s board surface from 0 to 3 T, at temperatures from 23 to 77 K. To obtain the pinning potential energy of the Bi-2223 superconductor, an empirical scaling of J(T,H) is introduced in this study. Under the flux dynamics, the effective pinning energy, U _eff(T,H,J), can be formulated using the measured current density, J(T,H). Furthermore, the pinning potential energies, U(T,H), for both H‖ab and H‖c were quantitatively determined by the scaling of J(T,H). The two energies, U(T,H), exhibit as a function that is inversely proportional to both temperature and logarithmic magnetic field. The magnitude of U(T,H) for H‖ab is three or more times larger than that for H‖c under the considered conditions. The U(T,H) is sensitive to the temperature, but insensitive to the magnetic field. This characteristic of insensitiveness towards magnetic field is an advantage for applications on the conditions of high current density, high magnetic field, and low temperature.     

Neutron Scattering from the Flux Line Lattice in the Cubic (K, Ba)BiO 3 Superconductor

Small Angle Neutron Scattering has been used to observe diffraction from the flux line lattice in the fully isotropic (K, Ba)BiO ₃ high T _c superconductor. We show that the flux lines are ordered into a hexagonal lattice at low field (H < H _e 0.6T H _g (0) where H _g is the second order vortex glass transition field). The diffracted intensity continuously drops to zero as the field is increased towards H _e . Those observations are in good agreement with recent theoritical works which suggested that the formation of dislocations becomes favorable above H _e leading to a glassy structure. The field H _e lies close to the onset of the second peak in magnetization measurements indicating that this peak is related to the change in the vortex structure.     

Impact of Tuning Molar Ratio in the Starting Materials: <Emphasis Type="Italic">Magneto</Emphasis>-Transport Features of Hybrid YSr<Subscript>2</Subscript>Ru<Subscript>0.9</Subscript>Cu<Subscript>2.1</Subscript>O<Subscript>7.9</Subscript>

The impact of slightly tuning molar ratio in the starting materials on the physical properties of 1212-type rutheno-cuprate, YSr₂Ru_0.9Cu_2.1O_7.9 (nominal) samples prepared under four synthesis approaches are reported. Interestingly, all samples clearly show the differences in the physical properties of the samples prepared under different synthetic protocols. However, neither XRD nor EDX reveal any notable differences in the crystal structure or sample composition. All the samples exhibit magneto-superconducting properties (H _ext=5 Oe) which are slightly varied with synthetic approaches. The high field (H _ext=10 kOe) temperature dependence of magnetization data shows a sharp ferromagnetic transition around 150 K and all the samples obey Curie–Weiss linear behavior above 180 K. The experimental effective paramagnetic moment for the various samples is in the range of 2.5 and 2.7μ _B/Ru which are in line with the literature report. The magnetization, M(H) isotherm curves measured at 5 K and −10 kOe≤H≤10 kOe conditions reveal weak ferromagnetic-like hysteresis loops for all samples with returning moment (M _r) and coercive field (H _c), whereas the high field M(H) loops indicate soft ferromagnetic behaviors with magnetic saturation. The saturation moment of the samples is slightly varied with the synthesis approaches. None of the samples showed bulk superconductivity (T_c^{R = 0})T_{\mathrm{c}}^{R = 0}) down to 2 K, while all samples show onset transitions (T_c^onsetT_{\mathrm{c}}^{\mathrm{onset}}) except the sample prepared by approach-3. The latter approach sample shows semiconducting behavior down to 2 K. The T_c^onsetT_{\mathrm{c}}^{\mathrm{onset}} noticed at 34 K, 12 K, and 6 K for the sample prepared by approach-1, 2, and 4, respectively. The nearly linear dependence suggests that hopping conduction is dominant in certain temperature range for all samples. The magneto-transport features of these samples exhibit maximum magnetoresistance (MR) at low temperatures. Remarkably, the sample prepared by approach-1 shows largest −MR about 77% at low temperature 2 K and H=90 kOe which stimulates for further investigations. Among the four synthesis approaches employed in the present study, we can probably suggest that the approach-1 (0.5Y₂O₃+0.5SrO₂+1.5SrCuO₂+0.9RuO₂+0.6CuO) is the preferable method to achieve the best sample (in terms of magneto-transport features).     

A New Method for the Estimation of H c2 Anisotropy in Polycrystalline MgB2 Samples

By using isothermal magnetization measurements in polycrystalline MgB₂ samples, we estimate the H ^c _c2 in the interval [0, T _c]. By combining these measurements to the estimated H ^ab _c2 from the onset of the diamagnetic transition in isofield and isothermal magnetic measurements, an estimation of the anisotropy parameter can be achieved. The H ^c _c2 values coming from high quality polycrystalline samples agrees nicely to those obtained on single crystals. Our results show a temperature variation of the γ(T ) = H ^ab _c2/H^c2 with γ(T _c) ≈ 3.     

Equilibrium magnetization properties of irreversible superconducting niobium with peak effect

Measurements of the equilibrium magnetization curve of type II superconductors have usually only been possible on reversible specimens. In this paper, a method to measure the equilibrium magnetization curve of irreversible type II superconductors is described. Results obtained by this method from a hysteretic Nb specimen exhibiting the peak effect are reported. They show an irregularity in the shape of the equilibrium magnetization curve in the neighborhood ofH _c2 which corresponds to a minimum of the compressional modulusK of the flux line lattice. The minimum ofK also corresponds with the maximum of the critical current densityj _c, which strongly suggests that in this case the peak effect is originated by a “soft point” of the flux line lattice. The observed anomaly ofK is discussed in terms of a possible first-order phase transition in the flux line lattice.