Magnetization of high-T c superconductors

We have tried to understand the field dependence of magnetization of high temperature superconductors in the light of phenomenological theory. Especially, the field dependence of dM/d lnB of polycrystalline Bi(2212) is understood by incorporating the overlap of vortices in the London theory.     

Modelling harmonic generation measurements in solids

Harmonic generation measurements typically make use of the plane wave result when extracting values for the nonlinearity parameter, β, from experimental measurements. This approach, however, ignores the effects of diffraction, attenuation, and receiver integration which are common features in a typical experiment. Our aim is to determine the importance of these effects when making measurements of β over different sample dimensions, or using different input frequencies. We describe a three-dimensional numerical model designed to accurately predict the results of a typical experiment, based on a quasi-linear assumption. An experiment is designed to measure the axial variation of the fundamental and second harmonic amplitude components in an ultrasonic beam, and the results are compared with those predicted by the model. The absolute β values are then extracted from the experimental data using both the simulation and the standard plane wave result. A difference is observed between the values returned by the two methods, which varies with axial range and input frequency.     

Measurement and understanding of magnetization in AC and DC fields and the determination of intragrainH c1 in highT c RBa2Cu3O7 superconductors

We present DC and low frequency AC magnetization measurements on various RBa₂Cu₃O₇ superconductors. We identify features intrinsic to these compounds, and establish the features originating from intergranular links in sintered pellets. The isothermal magnetization curves, and the temperature dependence of magnetization in field-cooled and zero field-cooled states are shown to be consistent with the calculations done following a recent extension of Bean’s model. Low field anomalies predicted within this model are observed, and yieldH _c1 values of a few Oe. These values are shown to be consistent with the temperature variation of magnetization. A comparison is made with the other existing data and it is demonstrated that earlier quoted values ofH _c1 are gross overestimates.     

Electronic structure of high-T c superconductors and related compounds

We study a 5-band Hubbard model for the CuO₂ planes in cuprate super-conductors using Hartree-Fock mean-field theory including spiral spin density waves. For the half-filled case we recover a ZSA-like phase diagrambut with an additional new region characterized by strong covalency effects, which we call a covalent insulator region. We also provide a nonperturbative calculation ofJ _eff, the effective in-plane antiferromagnetic interaction, as a function of parameters of the model. We suggest that the high-T _c cuprates are in or very close to the covalent insulator region and within this we show that a consistent explanation of apparently conflicting high energy spectroscopic and magnetic measurements of the high-T _c cuprates can be given.     

Magnetic phase diagram of anisotropic layered superconductors via magnetization measurements forH‖c in Bi2212

The Bi₂Sr₂CaCu₂O₈ system is viewed as an archetypal of superconductors modelled as Josephson coupled CuO₂ bilayers. The isothermal and temperature dependent DC and AC magnetization measurements forH‖c in a single crystal of Bi2212 have been performed. Qualitative changes are observed to occur over a narrow range of temperature values before reaching the superconducting-normal transition. The observed behaviour can be ascribed to the rapid variation in the strength of the coupling between the superconducting CuO₂ planes (i.e., bilayers in the case of Bi2212). Strongly coupled planes behave like a 3D superconductor, whereas weakly coupled planes have a two component response attributable to 2D planes and interplanar couplings. We believe that this paper is a plethora of new findings. Our observations imply that resistivity across the planes becomes zero earlier than that within the planes. A new line (designated asH _2D(T)) above which the change in the electromagnetic response is dominated by quasi 2D-planes has been determined for the first time. This paper also contains the first observation of Differential Diamagnetic Effect (DDE) in the In-phase AC susceptibility data which signals the onset (atT _2D(H)) of dominance of response from 2D-planes. In addition to a host of interesting thermomagnetic history effects which are a consequence of interplay between the diamagnetic responses from the two components, a comparison of irreversibility lines (of the 3D state) determined by different methods on the same specimen of a HTSC is also being presented for the first time. We have come across Paramagnetic Meissner Effect (PME), first recognized in ceramic samples of Bi2212, in the temperature region of dimensional crossover in our single crystal sample, whichinter-alia confirms our labelling of the two component behaviour. A schematic phase diagram summarizing the various transformations that can occur nearT _c in the electromagnetic response of an anisotropic layered system has been drawn.     

Harmonic generation in superconducting Bi(Pb)SrCaCuO thick films

We present a detailed study of harmonic generation in Bi(Pb)SrCaCuO superconducting thick film prepared by screen printing technique. A comparative study of amplitude of harmonics of two films of different J_c have been carried out. The variation of amplitudes of the harmonics are studied as a function of magnitude of ac and dc field. The temperature dependence of amplitude of third harmonic (V³) is studied with increasing amplitude as well as frequency of ac field. These results are analyzed in the frame work of critical state model. V₃ -T curve also indicates the presence of two phases in Bi(Pb)SrCaCuO film.     

Low field anomaly in magnetization curves

We present a calculation of the isothermal magnetization hysteresis curves appropriate to highT _csuperconductors. We discuss the nature of the low field anomaly as one goes from this strong pinning case to the weak pinning case. We show that the shape of the equilibrium (thermodynamic) magnetization curve is recovered in the limit ofJ _capproaching zero.     

Comparison of irreversibility temperatures determined via DC and AC magnetization techniques in conventional superconductors

A comparison has been made of irreversibility temperature determined by four different methods in few specimens of lead (type-I) and niobium (type-II). The merger ofM _ZFC(T) andM _FC(T) curves giveT _r(H) values lower than those evident from vanishing the hysteresis in isothermal DC magnetization. The identification of peak temperature inx″ _H (T) data withT _r(H) is appropriate only if the contribution from changes in the normal state electrodynamics can be isolated and the peak is narrow. The appearance of differential paramagnetic effect inx′ _H (T) data is adequate to imply reversibility, however, its efficacy to precisely locate irreversibility line remains to be established.     

Magnetic behavior of nanoscopic superconductors

The magnetic behavior of nanometer-scale superconducting grains at finite temperature is investigated using the correlated static path approximation to the partition function. In these systems, the field penetration depth is much larger than the spatial dimension and Pauli paramagnetism becomes dominant. It is shown that deviations from both the bulk behavior and the BCS results for fixed number parity become significant due to gap fluctuations, which lead to appreciable pairing effects in the spin magnetization and susceptibility beyond the BCS critical fields or sizes. Differences between even and odd systems are also discussed.     

Anomalous magnetic hysteresis loops and smallH c1 values in highT c superconductors

We have studied the hysteresis loops of RBa₂Cu₃O₇ (R=Gd, Ho and Y) and detected anomalies in some of them. The observed anomalies support a recent prediction by Ravi Kumar and Chaddah based on an extension of Bean’s model. The anomalies indicate lowH _c1 values and we have confirmed this by studying the onset of low-field hysteresis in less than 10 Oe at 77 K for these highT _c superconductors.     

Magnetization curves of hard superconductor samples with non-zero demagnetization factor

We present exact solutions of Bean’s critical state model for some sample shapes having non-zero demagnetization factorN. Virgin and hysteresis magnetization curves are obtained for samples in the shape of (i) a sphere (ii) a spheroid (iii) a cylinder of circular cross-section with its axis perpendicular to the field and (iv) a cylinder of elliptical cross section with its axis perpendicular to the field. Some interesting features seen in these first solutions forN ≠ 0 are discussed.     

Magnetic properties of high-T c superconductors from NQR and NMR measurements

NMR and NQR spectra and spin-lattice relaxation measurements carried out in LASCO and YBCO-type crystals are presented and analyzed in order to derive insights on the correlations and spin-dynamics of the Cu²⁺ ions and on the microscopic mechanisms of high-T _c superconductivity. As an illustrative example on how the magnetic correlation length and spin dynamics properties can be extracted from the relaxation rateW, the³⁵Cl NMR data in the two-dimensional Heisenberg system Sr₂CuCl₂O₂, around the paramagnetic-antiferromagnetic (PA-AF) transition are first considered. Then the¹³⁹La NQR relaxation measurements in La_2?xSr_xCuO₄ are briefly reviewed and it is shown how a simple picture of localized Cu²⁺ magnetic moments, whose spin fluctuation times are controlled by the charge defects induced by the doping, leads in a direct way to quantitative estimates for the progressive shift, on cooling, of the spectral density of the low-frequency spin excitations towards the high frequency range. This phenomenon can be described in terms of effective spin at the Cu²⁺ ions, and its similarities with the analogous effect of progressive delocalization in Heavy Fermions systems are pointed out. Thus, the superconducting transition appears to occur in an unconventional Fermi liquid with AF correlations among itinerant pseudoparticles, possibly involving a mechanism not directly related to the magnetic correlated dynamics. In fact, a universal behavior of the relaxation rates as a function of temperature is observed, regardless of the transition temperatureT _c. The independence ofT _c from the low frequency static and dynamical spin properties is also indicated by⁸⁹Y Knight shifts and from⁶³Cu relaxation rates in systems like YBa₂Cu₄O₈ (Y124), whereT _c can be changed by atomic substitutions and by controlling the oxygen stoichiometry. The effect of an external magnetic field on the correlated spin dynamics of the AF Fermi liquid is investigated and from a comparison of Cu NQR relaxation and NMR relaxation in oriented powder of YBCO and LASCO it is shown that the external field has the small but unambiguous effect of depressing the relaxation rates aboveT _c, besides strongly enhancing them in the superconducting phase. A maximum in the ratio \({{W\left( {NQR} \right)} \mathord{\left/ {\vphantom {{W\left( {NQR} \right)} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}} \right. \kern-0em} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}\) is thus observed around 80 K, either in LASCO or in YBCO, again indicating that the transition could be driven by a mechanism not directly involving the spin dynamic properties. To study the role of the fluxions belowT _c ⁸⁹Y NMR shifts and spectra in oriented powders of YBCO are analyzed. Information on the spin susceptibility and on the structure of the vortex lattice is obtained. In addition, from the temperature behavior of the linewidth a motional narrowing related to flux melting is evidenced. The effective correlation time for the vortex motion is derived and it is discussed why μ⁺SR cannot detect it in view of the different rigid-lattice line broadening.     

Thermomagnetic history effects in niobium and its implication for H c1 in highT c superconductors

The existence of a remanent magnetization (M _rem) on switching off the field of a field cooled (FC) sample of a highT _c superconductor is often reported. It has recently been argued thatM _rem should equal the difference in FC and zero field cooled (ZFC) magnetizations (M _FC —M _ZFC) in hard superconductors and this has been demonstrated to hold in single crystals of YBCO at 4.2K over a limited range ofH values. We report the detailed magnetization measurements under various thermomagnetic histories (of whichM _rem is one special case) on two specimens of Nb, which show different extents of flux trapping. We find that there are in general three regions inH, T space, corresponding toM _rem+M _ZFC−M _FC=0,M _rem<(M _FC−M _ZFC) andM _rem>(M _FC−M _ZFC). At anyT, the equality holds forH<H _c1(T), and forH→H _c2 (M _FC−M _ZFC) asymptotically vanishes and thereM _rem>(M _FC−M _ZFC). We show that there exists an intermediate region in all hard superconductors, whereM _rem<(M _FC−M _ZFC). The range over which this situation persists, however, depends on the degree of irreversibility in a sample. We can explain qualitatively all the history dependent magnetization data in terms of the critical state model. We point out an inconsistency in an earlier analysis to determineH _c1(T) from such data in YBCO. We also propose a new criterion for putting limits onH _c1(T) in hard superconductors.     

Thermoelectric power of high-T c superconductors using extended Hubbard model

The thermoelectric power (TEP) for a one dimensional lattice has been studied by using the extended Hubbard model in the limitU≠∞, whereU is the on-site Coulomb interaction. A new expression for TEP, derived in this study, has been found to successfully reproduce the experimental results of the insulating samples of different hole- and electron-doped high temperature superconducting systems.     

Squeezing and sub-Poissonian effects up-to fourth order in fifth harmonic generation

The concept of squeezing of the electromagnetic field is investigated in fundamental mode in fifth harmonic generation with the approximation |gt|²?1, where g is coupling constant and t, the interaction time between waves during the process. It has been found that squeezing occurs in amplitude, amplitude-squared, amplitude-cubed and fourth-order amplitude states of the field for selective phase values of field amplitude of fundamental mode. The dependence of squeezing on the photon number has also been investigated and found to be sub-Poissonian in nature. The signal to noise ratio has been studied in different order. It is found that the signal to noise ratio is higher in lower order.     

Studies of irreversible magnetization in superconductors—a review

Magnetic measurements in the superconducting state of the high temperature superconductors have been characterized by the feature of irreversibility. Similar effects have been known in the conventional type II superconductors for about three decades now, and have been studied in great detail during the last few years. Recent studies of magnetic irreversibilities, in both conventional and high temperature superconductors, will be reviewed here. Thermally-activated relaxation accompanies such irreversibilities, and studies on flux-creep will also be reviewed. This review shall cover the measurement of isothermal magnetization curves, of ac susceptibility, of thermo-magnetic history effects in the magnetization at a particular field and temperature, and of flux creep. An understanding of these in terms of Bean’s celebrated macroscopic model shall be discussed. We shall also cover measurements that confirm the existence of weak links in ceramic high-temperature, as well as in conventional multifilamentary, superconductors.     

Higher-order squeezing and photon statistics in fourth harmonic generation

Squeezing of the electromagnetic field is investigated in fundamental mode in fourth harmonic generation under a short time approximation based on quantum mechanical approach. The occurrence of squeezing in field amplitude and in higher power amplitude (up to fourth-order) in fundamental mode has been studied. It is found to be dependent on phase of field amplitude of the fundamental mode. The dependence of squeezing on the photon number has also been investigated. It is found that squeezing increases non-linearly. It has also been found that the photon statistics of the field in fundamental mode is sub-Poissonian. The signal to noise ratio has been studied in different order. It is found that signal to noise ratio is higher in lower order.     

Second harmonic generation in deposited clusters

We analyse theoretically the generation of second and higher harmonics for sodium clusters deposited on an insulating surface. To this end, we use the time-dependent local-density approximation solved on a three-dimensional grid. We explore the impact of the various laser parameters (intensity, frequency, polarisation) on the efficiency of second harmonic generation. The success sensitively depends on a proper tuning of these parameters. We find optimum conditions for which the laser frequency is half the resonance frequency of the system, if the polarisation is directed orthogonal to the surface of the substrate, and if the intensity is large but safely below the critical value for destruction of the electron cloud. Received 22 October 1999 and Received in final form 14 December 1999     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

Quadripartite entanglement from coupled type I second harmonic generation

We present a feasible protocol of continuous variable quadripartite entanglement from the coupled type I second harmonic generation (SHG) below threshold. According to the sufficient inseparability criteria for multipartite continuous variable (CV) entanglement, the four output fields are proved to be multicolored entangled beams in separable locations with four‐mode amplitude quadratures correlation and relative phase quadratures correlation. It shows that the coupled system can produce a compact tunable multimode entangled source that can be applied into the quantum communication.