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In real paramagnets, there is always a subtle many-body contribution to the system's energy, which can be regarded as a small effective local magnetic field $B_{loc}$. Usually, it is neglected, since it is very small when compared with thermal fluctuations and/or external magnetic fields $B$. Nevertheless, as both the temperature $T \rightarrow$ 0K and $B \rightarrow$ 0T, such many-body contributions become ubiquitous. Here, employing the magnetic Gr\"uneisen parameter $\Gamma_{mag}$ and entropy arguments, we report on the pivotal role played by the mutual interactions in the regime of ultra-low-$T$ and vanishing $B$. Our key results are: $i$) absence of a genuine zero-field quantum phase transition due to the presence of $B_{loc}$; $ii$) connection between the canonical definition of temperature and $\Gamma_{mag}$; and $iii$) possibility of performing adiabatic magnetization by only manipulating the mutual interactions. Our findings unveil unprecedented aspects emerging from the mutual interactions., Comment: 21 pages, 8 figures

In this paper we use spontaneous flux production in annular superconductors to shed light on the Kibble-Zurek scenario. In particular, we examine the effects of finite size and external fields, neither of which is directly amenable to the KZ analysis. Supported by 1D and 3D simulations, the properties of a superconducting ring are seen to be well represented by analytic Gaussian approximations which encode the KZ scales indirectly. Experimental results for annuli in the presence of external fields corroborate these findings., Comment: 20 pages, 10 figures; submitted to J. Phys: Condens. Matter for the special issue 'Condensed Matter Analogues of Cosmology'; v2: considerably reduced length, incorporation of experimental details into main text, discussion improved, references added, version accepted for publication

Consistent with the predictions of Kibble and Zurek, scaling behaviour has been seen in the production of fluxoids during temperature quenches of superconducting rings. However, deviations from the canonical behaviour arise because of finite-size effects and stray external fields. Technical developments, including laser heating and the use of long Josephson tunnel junctions, have improved the quality of data that can be obtained. With new experiments in mind we perform large-scale 3D simulations of quenches of small, thin rings of various geometries with fully dynamical electromagnetic fields, at nonzero externally applied magnetic flux. We find that the outcomes are, in practice, indistinguishable from those of much simpler Gaussian analytical approximations in which the rings are treated as one-dimensional systems and the magnetic field fluctuation-free., Comment: 10 pages, 3 figures, presentation at QFS2012, to appear in JLTP

We analyze the consequences resulting from the asymmetric boundary conditions imposed by a non-uniform external magnetic field at the extremities of a planar Josephson tunnel junction and predict a number of testable signatures. When the junction length $L$ is smaller than its Josephson penetration depth $\lambda_j$, static analytical calculations lead to a Fresnel-like magnetic diffraction pattern, rather than a Fraunhofer-like one typical of a uniform field. Numerical simulations allow to investigate intermediate length ($L\approx \lambda_j$) and long ($L>\lambda_j$) junctions. We consider both uniform and $\delta$-shaped bias distributions. We also speculate on the possibility of exploiting the unique static properties of this system for basic experiments and devices., Comment: 9 pages, 3 figures

The behavior of a long Josephson tunnel junction drastically depends on the distribution of the dc bias current. We investigate the case in which the bias current is fed in the central point of a one-dimensional junction. Such junction configuration has been recently used to detect the persistent currents circulating in a superconducting loop. Analytical and numerical results indicate that the presence of fractional vortices leads to remarkable differences from the conventional case of uniformly distributed dc bias current. The theoretical findings are supported by detailed measurements on a number of $\delta$-biased samples having different electrical and geometrical parameters., Comment: 14 pages, 10 figures

We report on the first experimental verification of the Zurek-Kibble scenario in an isolated superconducting ring over a wide parameter range. The probability of creating a single flux quantum spontaneously during the fast normal-superconducting phase transition of a wide Nb loop clearly follows an allometric dependence on the quenching time $\tau_{Q}$, as one would expect if the transition took place as fast as causality permits. However, the observed Zurek-Kibble scaling exponent $\sigma = 0.62\pm0.15$ is two times larger than anticipated for large loops. Assuming Gaussian winding number densities we show that this doubling is well-founded for small annuli., Comment: 10 pages, 2 figures, submitted to Phys. Rev. Letts

Superconducting shields are commonly used to suppress external magnetic interference. We show, that an error of almost an order of magnitude can occur in the coil-factor in realistic configurations of the solenoid and the shield. The reason is that the coil-factor is determined by not only the geometry of the solenoid, but also the nearby magnetic environment. This has important consequences for many cryogenic experiments involving magnetic fields such as the determination of the parameters of Josephson junctions, as well as other superconducting devices. It is proposed to solve the problem by inserting a thin sheet of high-permeability material, and the result numerically tested., Comment: 3 pages, 4 figures, submitted to APL

We have carried out a detailed experimental investigation of the static properties of planar Josephson tunnel junctions in presence of a uniform external magnetic field applied in an arbitrary orientation with respect to the barrier plane. We considered annular junctions, as well as rectangular junctions (having both overlap and cross-type geometries) with different barrier aspect ratios. It is shown how most of the experimental findings in an oblique field can be reproduced invoking the superposition principle to combine the classical behavior of electrically small junctions in an in-plane field together with the small junction behavior in a transverse field that we recently published [R. Monaco et al., J. Appl. Phys. vol 104, 023906 (2008)]. We explore the implications of these results in supposing systematic errors in previous experiments and in proposing new possible applications. We show that the presence of a transverse field may have important consequences, which could be either voluntarily exploited in applications or present an unwanted perturbation., Comment: 16 pages, 10 figures, with a note

The magnetic field distribution in the barrier of small planar Josephson tunnel junctions is numerically simulated in the case when an external magnetic field is applied perpendicular to the barrier plane. The simulations allow for heuristic analytical solutions for the Josephson static phase profile from which the dependence of the maximum Josephson current on the applied field amplitude is derived. The most common geometrical configurations are considered and, when possible, the theoretical findings are compared with the experimental data., Comment: Submitted to JAP with 24 pages and 14 figures

We report on the spontaneous production of fluxons in the presence of a symmetry-breaking magnetic field for annular Josephson tunnel junctions during a thermal quench. The dependence on field intensity $B$ of the probability $\bar{f_1}$ to trap a single defect during the N-S phase transition drastically depends on the sample circumferences. We show that the data can be understood in the framework of the Kibble-Zurek picture of spontaneous defect formation controlled by causal bounds., Comment: Submitted to Phys. Rev. B with 5 figures on Nov. 15, 2007

Traditionally, since the discovery of the Josephson effect in 1962, the magnetic diffraction pattern of planar Josephson tunnel junctions has been recorded with the field applied in the plane of the junction. Here we discuss the static junction properties in a transverse magnetic field where demagnetization effects imposed by the junction geometry and configuration of the electrodes are important. Measurements of the critical current versus magnetic field in planar Nb-based high-quality junctions with different geometry, size and critical current density show that it is advantageous to use a transverse magnetic field rather than an in-plane field to suppress the Josephson tunnel current and Fiske resonances in practical applications., Comment: 5 pages, 2 figures, submitted to Journal of Applied Physics

It has been argued by Zurek and Kibble that the likelihood of producing defects in a continuous phase transition depends in a characteristic way on the quench rate. In this paper we discuss an improved experiment for measuring the Zurek-Kibble scaling exponent $\sigma $ for the production of fluxons in annular symmetric Josephson Tunnel Junctions. We find $\sigma \simeq 0.5$. Further, we report accurate measurements of the junction gap voltage temperature dependence which allow for precise monitoring of the fast temperature variations during the quench., Comment: 12 pages, 5 figures, submitted to Phys. Rev. B

New scaling behavior has been both predicted and observed in the spontaneous production of fluxons in quenched $Nb-Al/Al_{ox}/Nb$ annular Josephson tunnel junctions as a function of the quench time, $\tau_{Q}$. The probability $f_{1}$ to trap a single defect during the N-S phase transition clearly follows an allometric dependence on $\tau_{Q}$ with a scaling exponent $\sigma = 0.5$, as predicted from the Zurek-Kibble mechanism for {\it realistic} JTJs formed by strongly coupled superconductors. This definitive experiment replaces one reported by us earlier, in which an idealised model was used that predicted $\sigma = 0.25$, commensurate with the then much poorer data. Our experiment remains the only condensed matter experiment to date to have measured a scaling exponent with any reliability., Comment: Four pages, one figure

If systems change as fast as possible as they pass through a phase transition then the initial domain structure is constrained by causality. We shall show how we can trace these causal horizons by measuring the spontaneous production of flux in annular Josephson Tunnel Junctions as a function of the quench time $\tau_{Q}$ into the superconducting phase. A specific test of our analysis is that the probability P$_{1}$ to trap a single fluxon at the N-S transition clearly follows an allometric dependence on $\tau_{Q}$ as $P_1 = a \tau_Q^{-\sigma}$, with a scaling exponent $\sigma = 0.25$, in agreement with the data., Comment: Based on talks presented at the COSLAB meeting at Ambleside, 2004, to be published in 'Progress in Josephson Junction Research, ed. F. Columbus (Nova Science Publishers, Inc., USA), 2005

It has been argued by Zurek and Kibble that the likelihood of producing defects in a continuous phase transition depends in a characteristic way on the quench rate. In this paper we discuss our experiment for measuring the Zurek-Kibble scaling exponent $\sigma $ for the production of fluxons in annular symmetric Josephson Tunnel Junctions. The predicted exponent is $% \sigma =0.25$, and we find $\sigma =0.27\pm 0.05$. Further, there is agreement with the ZK prediction for the overall normalisation., Comment: 10 pages, 5 figures: To be published in Patterns of Symmetry Breaking (Ed. Jacek Dziarmaga), Proceedings of the NATO Advanced Study Institute & COSLAB School, Krakow, Poland (September 2002) Proceedings of The Nato Advanced Study Institute and COSLAB School, September 2002, Krakow, Poland

Phase transitions executed in a finite time show a domain structure with defects, that has been argued by Zurek and Kibble to depend in a characteristic way on the quench rate. In this letter we present an experiment to measure the Zurek-Kibble scaling exponent sigma. Using symmetric and long Josephson Tunnel Junctions, for which the predicted index is sigma = 0.25, we find sigma = 0.27 +/- 0.05. Further, there is agreement with the ZK prediction for the overall normalisation., Comment: To be published in Phys. Rev. Letts

In parallel with Kibble's description of the onset of phase transitions in the early universe, Zurek has provided a simple picture for the onset of phase transitions in condensed matter systems, strongly supported by agreement with experiments in He3. In this letter we show how experiments with annular Josephson tunnel Junctions can and do provide further support for this scenario., Comment: Revised version with correct formula for the Swihart velocity. The results are qualitatively the same as with the previous version but differ quantitatively. 4 pages, RevTex