Scaling of the equilibrium magnetization in the mixed state of type-II superconductors

We discuss the analysis of mixed-state magnetization data of type-II superconductors using a recently developed scaling procedure. It is based on the fact that, if the Ginzburg-Landau parameter κ does not depend on temperature, the magnetic susceptibility χ(H,T) is a universal function of H/H_c2(T), leading to a simple relation between magnetizations at different temperatures. Although this scaling procedure does not provide absolute values of the upper critical field H_c2(T), its temperature variation can be established rather accurately. This provides an opportunity to validate theoretical models that are usually employed for the evaluation of H_c2(T) from equilibrium magnetization data. In the second part of the paper we apply this scaling procedure for a discussion of the notorious first order phase transition in the mixed state of high-T_c superconductors. Our analysis, based on experimental magnetization data available in the literature, shows that the shift of the magnetization accross the transition may adopt either sign, depending on the particular chosen sample. We argue that this observation is inconsistent with the interpretation that this transition always represents the melting transition of the vortex lattice.     

Dynamical fluctuation of the order parameter and diamagnetism of superconductors. I. Dirty limit

Limiting ourselves to dirty superconductors, we study theoretically the fluctuation-induced diamagnetism above the superconducting transition. We find that the dynamical fluctuation is extremely important except in the immediate vicinity of the transition region [i.e.,TT _c(H) orHH _c2(T), whereH _c2 is the upper critical field] and that this contribution does account for a large discrepancy between previous calculations and the recent experiment by Gollub, Beasley, and Tinkham.     

First and Second Order Phase Transitions and Magnetic Hysteresis in a Superconducting Plate

The self-consistent solutions of the nonlinear Ginzburg–Landau equations, which describe the behavior of a superconducting plate of thickness 2D in a magnetic field H parallel to its surface (provided that there are no vortices inside the plate), are studied. We distinguish two classes of superconductors according to the behavior of their magnetization M(H) in an increasing field. The magnetization can vanish either by a first order phase transition (class-I superconductors), or by a second order (class-II). The boundary S _I–II, which separates two regions (I and II) on the plane of variables (D,), is found. The boundary (D,) of the region, where the hysteresis in a decreasing field is possible (for superconductors of both classes), is also calculated. The metastable d-states, which are responsible for the hysteresis in class-II superconductors, are described. The region of parameters (D,) for class-I superconductors is found, where the supercooled normal metal (before passing to a superconducting Meissner state) goes over into a metastable precursor state (p-). In the limit 1/2 and D( is the London penetration depth) the self-consistent p-solution coincides with the analytic solution, found from the degenerate Bogomolnyi equations. The critical fields H ₁, H ₂, H _p, H _r for class-I and class-II superconducting plates are also found.     

Resistive behavior of the superconducting surface sheath of alloys

Measurements are reported of the surface resistance of dirty type-II superconductors driven into the surface-sheath regime by a static magnetic field,H ₀ parallel or nearly parallel to the sample surfaces and transverse to the microwave current, in which condition the latter can excite fluctuations of the order parameter. A recent calculation by Maki has suggested that the surface resistance would be influenced by the presence of Kulik's vortex state even when the sample surface is polished and is as nearly as possible parallel toH ₀. It is therefore proposed that the sample surface should be decomposed into elements which make different angles withH ₀, and the distribution of these angles described by a Gaussian. ₂ (t) is deduced from the surface-resistance measurements nearH _c3, so interpreted, and a temperature variation, ₂ (t)/₂(1), is found which agrees reasonably with theory and with magnetization data, [₂(1)=lim_{t 1} (₂)]. It is suggested that the anomalously large variation of ₂ (t) reported by Fischer and Maki may have resulted from failure to take Kulik's vortices into account. In magnitude, present ₂(1) data agree with theory but not with magnetization data.     

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.     

Specific heat and magnetization of superconducting niobium in the mixed state

The thermodynamics of the mixed state of niobium is reconsidered. Critical fieldsH _c (t),H _c1(t),and H _c2(t), Maki parameters ₁ and ₂, magnetization, and specific heat are measured with a computer-controlled magnetometer and calorimeter. The results show quantitative discrepancies with the isotropic Gorkov-Brandt theory over almost the whole mixed state. Computations based on Fermi surface anisotropy using a scaling ofH _c2 provide a much better agreement with the experimental magnetization curves already in the limit of weak nonlocality, thus suggesting a numerical evaluation of the anisotropic terms in the Gorkov-Brandt theory.     

Upper Critical Field and Specific Heat of Cuprates

A representative set of magnetotransport measurements in novel superconductors is analyzed. The resistive upper critical field, H _c2 (T) of many cuprates, of superconducting spin-ladders, and organic (TMTSF)2X systems has a universal nonlinear temperature dependence H _c2 (T_c – T)^3/2 in a wide temperature interval near T _c, while its low-temperature behavior depends on the chemical formula and sample quality. The unusual H _c2(T) is described as the Bose–Einstein condensation field of preformed pairs. Its universal temperature dependence follows from the scaling arguments. Controversy in the determination of H _c2 (T) from the resistivity and specific heat measurements is resolved in the framework of the charged Bose-gas model with the impurity scattering. It is shown that specific heat shows two anomalies. The high-temperature anomaly is strong and shows only weak shift with applied field. The low-temperature anomaly corresponds to resistive transition and is very weak in agreement with the experiments. Both anomalies coincide at H = 0.     

Weak Coupling Theory of Clean (d+s)-Wave Superconductors

The properties of weakly coupled clean anisotropic (orthorhombic) superconductors with pure d and (d+s) pairing symmetry are considered. We derive analytical and universal results for generalized BCS-Mühlschlegel parameters like the zero temperature gap and the specific heat discontinuity at the transition even for the most general situation of (d+s) pairing symmetry. The properties of the gas of thermal excitations, the Bogoliubov quasiparticles, is studied through the temperature dependence of the quasiparticle entropy _B ⁰ (T), the specific heat C_B(T), the spin susceptibility _B(T), and the quasiparticle contribution K _B(T) to the electronic supercurrent response (magnetic field penetration depth). In particular we present analytical results for these quantities in the asymptotic low temperature limit T0. The experimental relevance of these results for hole-doped cuprate superconductors with orthorhombic crystal symmetry is discussed.     

Hall-Effect study of YNi2B2C superconductor

Hall-effect and critical magnetic fields H_c2(T) have been studied for YNi₂B₂C (prepared using high pressure technique) at H130 kOe and 1.6T300K. The normal state Hall coefficient R_H was found to be negative (R_H=–1.43.10^–11 cm/Oe at T=4.2 K and H=130 kOe) and slightly growing in absolute value with increase of temperature. The dependence of the Hall voltage on magnetic field in the mixed superconducting state shows no sign reversal as was observed earlier for some high-T_c systems. The values of ¦H_c2/ T¦and H_c2(0) are found to be 4.8 kOe/K and 47 kOe respectively.     

Flux motion in anisotropic type-II superconductors nearH c 2 with arbitrary vortex orientation

Flux motion in anisotropic type-II superconductors near H_{c 2} is studied in the framework of the time-dependent Ginzburg-Landau (TDGL) theory for the case that the average flux densityB is oriented in an arbitrary direction relative to the principal axes of the sample. The linearized TDGL equation for a uniformly translating order parameter is solved and expressions for all elements of the flux-flow resistivity tensor _ij (including the off-diagonal Hall elements) are obtained. The diagonal elements _ii show the angular scaling property that _ii(B) = _ii(B/H_{c 2}(, ø)), whereas the Hall elements _ij (i j) have additional angular dependences that are not contained in H_c2. For the case that the normal state Hall elements _ij ⁽ⁿ⁾ B _k with i j k, the ratios _ij/ _ij ⁽ⁿ⁾ are functions of B/H_c2 (, ) only.     

Angular dependence of the critical magnetic field in granular superconducting films

The critical magnetic fieldH _c () of granular Al films has been measured as a function of the angle between the field direction and the plane of the film at temperatures nearT _c0 .The film thicknessd is smaller than the temperature-dependent coherence length (T), the bulk electron mean free path1 is smaller than the BCS coherence length ₀, and 1 d. The experimental data onH _c () are well fitted by the Tinkham formula. However, the observed values ofH _c/H _care not always consistent with and increase with1/d. This fact suggests that the boundary scattering of electrons at the film surface enhancesH _c () and that the enhancement ofH _cis larger than that ofH _c.On leave from Department of Physics, Faculty of Science, Kyushu University, Fukuoka, Japan.     

Upper Critical Field Hc2 on c Axis of Ag/Bi-2223 Polycrystal Tape

The upper critical field H _c2, based on Ginzburg–Landau theory at medial magnetic fields, can be calculated from the relationship of the magnetization intensity M(H) versus magnetic field H if M is linear with ln₀ H. For Ag/Bi-2223 tapes, the measured M(H) was found to be linear with ln₀ H. In this case, the values of H _c2(T) may in principle be determined. To do this, we will meet another problem in that the obliquity of crystal planes is not equal for different grains in tapes, and values of grain-oblique angle will appear in the calculated H _c2. Obviously, for Ag/Bi-2223 tapes is an uncertain parameter and hard to determine. To avoid the effects of , we only study the H _c2 in the c axis direction and the projections of H onto the c axis is taken as the actual applied fields. Thus, the effects of grain-oblique angle may be counteracted when measuring critical current density J, if the external magnetic fields are applied to the tape along both the parallel to and perpendicular to the c axes directions (on the narrow surfaces of the tape). On medial fields (H = 0 – 3 T), the upper critical fields H _c2(T) on c axis for the Ag/Bi-2223 tape are obtained and fitted as ₀ H _c2(T) = 830 e ^–0.07T . The average slope d[₀ H _c2(T)]/dT – 8T/K is found to be as large as that of Bi-2212. On extrapolating the relation to T = 0 K, the value of ₀ H _c2(0) 800T. The coherence length _ab is determined from H _c2(c), and _ab (0) = 0.63 nm at T = 0 K.     

Specific Heat Near Hmetamag=18 T in UPd2Al3

We have measured the specific heat vs. temperature in fields to 20 T of UPd₂Al₃ in order to try to determine the reason for the disagreement in the magnetic phase diagram as determined by magnetization and _ac vs. resistivity measurements, with the resistivity measurements showing the magnetic anomaly trending towards T=0 as HH _metamag. Our data show a slight monotonic suppression of T _N with increasing field in agreement with both previous magnetoresistance and magnetization data until HH _metamag. However, as field exceeds 17 T the specific heat shows a peak (presumably in a narrow field range connected with both antiferromagnetism and the H>H _metamag magnetization anomaly) that is suppressed with further increases in field no lower in temperature than 11.7 K (in contrast to the feature in the magnetoresistivity which, e.g., occurs at 8.4 K in 18 T) before it starts to move up in temperature with increasing field at H18 T (H _metamag). Possible causes of the specific heat anomaly for H>H _metamag, as well as for the discrepancy between the specific heat and the resistivity as HH _metamag, are discussed.     

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.     

Resistivity of Lightly Doped Ferromagnetic Semiconductors

In metallic magnets with a low carrier density, scattering from magnetic fluctuations above and near the transition temperature T _c provides a large contribution to the electrical resistance. Because the fluctuations can be suppressed by a magnetic field, a large negative magnetoresistance ensues. In a simple model, we find the low field magnetoresistance scales with the ratio of field induced magnetization m(H) to the saturation magnetization m _sat: /=((T, 0)–(T, H))/(T, 0)C(m/m _sat)². At very low carrier densities magnetic polarons should form in a range of temperatures above T _c. The CMR perovskite manganites cannot be explained without strong coupling of the magnetic order to lattice distortions (of the Jahn–Teller type) above T _c.     

Second Magnetization Peak at Low Fields due to Thermomagnetic Flux-Jump Instability

Magnetization measurements performed on a Nb thin film have revealed the existence of a second magnetization peak (SMP) well below the upper critical field boundary H _c2 (T). The results of this work provide clear evidence that the SMP originates from a thermomagnetic flux-jump instability. The similarity of the magnetization loops measured in Bi ₂ Sr ₂ CaCu ₂ O ₈ high-T _c superconducting crystals to those in Nb, as well as their dependence on the crystal size and field step indicate that a common mechanism is responsible for the SMP in these superconductors.     

Effect of magnetic field and temperature on the voltage-current characteristics of YBCO superconductor

Voltage-current characteristics of YBCO superconductor was studied under magnetic field up to 0.4 T at different temperatures below T_c. The critical temperature decreases and the transition width broadens under magnetic field. V-I data below T_c were fitted to a power law expression V I^(T,B) in which (T,B) is found to decrease with increase of magnetic field and temperature, gradually approaching unity as T approaches T_c, being independent of magnetic field. Similarly, (T,B) approaches unity as magnetic field increases being independent of temperature.     

Does Vortex Lattice of YBa2Cu3O6.94 in H⊥c Melt Below Intrinsic-Pinning Irreversibility Line?

Vortex lattice melting in the Hc configuration of an YBa ₂ Cu ₃ O _6.94 single crystal has been investigated by means of the ac susceptibility – i and the magnetic torque . The melting transition of vortex lattice occurs in Hc, too. Since the torque curve shows a sharp peak in the irreversible torque at _c 90° due to intrinsic pinning at lower temperatures, we can determine the irreversibility line for the intrinsic pinning. The melting transition in the Hc configuration appears at temperatures where the intrinsic-pinning peak is absent. We consider that the intrinsic pinning does not affect the nature of the vortex melting transition in the Hc configuration.     

Type II superconductors containing magnetic impurities

A theoretical study is made on the equilibrium as well as on the dynamical properties of type II superconductors containing magnetic impurities. The Kondo effect associated with the impurity spins is taken into account within the pole approximation, which has been used previously by Müller-Hartmann and Zittarz in their calculation of the superconducting transition temperature. In this approximation we have still the additive law of the different pair-breaking mechanisms for the transition temperature; the sum of the pair-breaking parameters due to magnetic impurities and due to magnetic fields is a universal function of the temperature. Since the pair-breaking parameter arising from magnetic impurities has the maximum atTT _K , the upper critical fieldH _c2 (T) reflects the Kondo effect in the system. The ₂(T) parameter, which describes the magnetization as well as the flux-flow resistivity of the vortex state, is obtained. WhenT _K /T _c0 >1, ₂(T) increases as the temperature decreases, but whenT _K /T _c0 <1, ₂(T) first increases as the temperature decreases, then passing a maximum and decreasing at low temperatures, which is in sharp contrast to that obtained previously where the impurity scattering was treated with the Born approximation (i.e., the Kondo effect was completely neglected.) A brief discussion of the density of states in the gapless region is also given, which reflects the Kondo effect in an interesting way.     

A theory of the upper critical field in antiferromagnetic superconductors

A generalized Ginzburg-Landau approach is used to study the nonmonotonic temperature dependence of the upper critical field H _c 2(T) in antiferromagnetic superconductors RE(Mo)₆S₈; RE = Dy, Tb, Gd. It is found that electrodynamic effects incorporated through screening and indirect coupling between the staggered magnetization M _Q (T) and superconducting order parameter cannot explain the observed nonmonotonicity. This suggests that the direct coupling between the two order parameters should be considered to understand the experimental results, a finding which is consistent with recent microscopic calculations.