We present a novel formulation for SQUID operation, which enables us to evaluate and compare the sensitivity and applicability of different devices. SQUID magnetometers for low-frequency applications are analyzed, taking into account the coupling circuits and electronics. We discuss nonhysteretic and hysteretic single-junction rf SQUIDs, but the main emphasis is on the dynamics, sensitivity, and coupling considerations of dc-SQUID magnetometers. A short review of current ideas on thin-film, dc-SQUID design presents the problems in coupling and the basic limits of sensitivity. The fabrication technology of tunnel-junction devices is discussed with emphasis on how it limits critical current densities, specific capacitances of junctions, minimum linewidths, conductor separations, etc. Properties of high-temperature superconductors are evaluated on the basis of recently published results on increased flux creep, low density of current carriers, and problems in fabricating reliable junctions. The optimization of electronics for different types of SQUIDs is presented. Finally, the most important low-frequency applications of SQUIDs in biomagnetism, metrology, geomagnetism, and some physics experiments demonstrate the various possibilities that state-of-the-art SQUIDs can provide.

SQUID magnetometers for low-frequency applications

Raman and IR-measurements on the high- T c material series La 2 CuO 4 and YBa 2 Cu 3 O 7 are reviewed. This summary focuses on lattice vibrations in these superconducting systems, on impurity phases, the influence of oxygen stoichiometry and element substitution. The determination of the superconducting gap, the phonon renormalization in the superconducting state, and the isotope effect with its implications on the theory of superconductivity in these materials are discussed. In addition, the measured lattice vibrations are compared with the results of lattice dynamics calculations.

Lattice vibrations in high-Tc superconductors: Optical spectroscopy and lattice dynamics☆

A number of the important issues in the processing of dense, superconducting ceramics are addressed and illustrated with examples drawn from our studies of the processing of yttrium barium cuprate. Among the phenomena affecting the attainment of dense, fully superconducting materials are those common to the processing of other ceramics, namely, control of composition, prevention of microcracking, adequate time for the decomposition, and escape of intermediaries prior to surface densification (the so-called “binder burn-off” problem). Additional requirements include the necessity to ensure complete oxygenation throughout the microstructure for full volume superconductivity and the control of texture development for maximizing the attainable transport critical current density. On the basis of the processing issues described, it is concluded that the optimum microstructure is one having finescale, interconnected porosity (to ensure escape of carbonate-like species and subsequent, rapid oxygenation) with a fine grain size (∼1 μm) to avoid microcracking.

Issues in the Processing of Cuprate Ceramic Superconductors

Measurements of the dependence of the magnetic hysteresis loop amplitude in a superconductor on the magnetic field sweep rate dHe/dt are shown to provide essentially the same information as magnetic relaxation experiments (flux-creep) at fixed external field He. For practical reasons, however, magnetic hysteresis loop measurements are better suited to investigate fast flux-line movements than conventional flux-creep measurements. From the general flux movement differential equation it is shown that each magnetic hysteresis loop recorded at a given dHe/dt can be labelled by an effective time t M 0 so that this experimental information can be used to extend the time window of flux-creep measurements to short times. This method is applied to the experimental data obtained on a YBa2Cu3O7 single crystal. In this way the time window is extended to less than 10-2 s which is valuable for a more precise check of existing theoretical models for the activation energy of flux motion. It is found that the experimental data are well described by using an activation energy U(j)=(Uc/μ)[(jc/j)μ-1] with μ=0.74 at 16 K and 1.8 T.

Extension of the time window for investigation of relaxation effects in high-Tc superconductors

The dependence of the magnetic momentm obtained from the hysteresis loops on the speed of the magnetic field sweep
 
$$\dot H$$

 =dH
ext/dt is explained on the basis of Anderson's interpretation of the magnetic flux creep. In addition, a phenomenological model is suggested which predicts a linear dependence ofm on ln ‖
 
$$\dot H$$

 ‖ with the slope ∂m/∂ ln ‖
 
$$\dot H$$

 ‖, numerically equal to the relaxation rate ∂m/∂ ln(t) from the usual magnetic relaxation. Such linear relations betweenm and ln ‖
 
$$\dot H$$

 ‖ were observed experimentally in single crystals of YBaCuO. Preliminary experiments on the complementary time dependent relaxation ofm after a simulated step change ofH
ext gave mostly relaxation rates close to the predicted values. The model here presented also enables one to compare the critical state in the superconductor at a field sweep rate
 
$$\dot H$$

 with the critical state at some timet
eff after a step change ofH
ext. The values of
 
$$\dot H$$

 analyzed in our experiments actually correspond to the critical state at timest
eff between0.04 and4 sec after an imaginary large step change ofH
ext.

Correlation between magnetic hysteresis and magnetic relaxation in YBaCuO single crystals

A new method for the determination of melt equilibria has been developed to clear some aspects of the phase relationships in the Y-Ba-Cu-(O) system at 950°C in air and at 975°C in oxygen. The procedure is based on the separation of the melt from an equilibrium sample and the consequent analysis of its solid residue. Approximative liquidus curves were suggested and boundaries of four primary crystallization fields were estimated.

On the melt equilibria in the Y-Ba-Cu-(O) system

Quantum interference at liquid nitrogen temperature in a bulk sample of high-Tc superconductor YBa2Cu3O9−y is described. The SQUID quantization loop is formed at random inside the sintered sample as an internal percolation loop with a Josephson weak link. The estimated values of this multiply connected quantization loop are: the inductance of the loopLSQ≈4×10−10 H, the critical currentIc≈1×10−6 A, the area of the loopA≈1×10−8 m2, and the hysteresis parameter β L ≈1. In the flux-locked loop regime the field sensitivity of this liquid nitrogen SQUID with a random loop is 10−9 T/Hz1/2 and the resolution is 5×10−3 Φ0/Hz1/2.

SQUID behavior at liquid nitrogen temperature in high-Tc superconductors of the type Y−Ba−Cu−O

Charge distribution, pressure and composition effects of CuOx based superconductors

The study of phase relationships in a part of the Bi-Sr-Cu-(O) system was carried out in order to determine approximate boundaries of liquid, liquid+solid and two solids+liquid regions at 800°C and for 850°C, respectively, in an area where Bi2Sr2CuO6 and Bi2+xSr2-yCuO6+y phases occur. In particular, attention was paid to the delimitation of the primary crystallization field of the latter phase with regard to its importance for the crystal growth.

E. Pollert

Papers

On the melt equilibria in the Y-Ba-Cu-(O) system

SQUID behavior at liquid nitrogen temperature in high-Tc superconductors of the type Y−Ba−Cu−O

Charge distribution, pressure and composition effects of CuOx based superconductors

Solid-liquid equilibria and crystallization in the Bi-Sr-Cu-(O) system

On phases and characterisation of quenched YBa2Cu3Ox