A generalized phenomenological model for the critical state of type-II superconductors with magnetic field parallel to the superconducting plate is proposed. This model considers the global magnetization including both the equilibrium magnetization from surface screening current and the non-equilibrium magnetization from bulk pinning in a self-consistent way. Our model can be used to simulate the magnetization-hysteresis-loops (MHLs) and flux penetrating process of different type-II superconductors, from low- to high-kappa values. Here we take an optimally doped Ba0.6K0.4Fe2As2 single crystal as a testing example. The model can fit the data quite well and several important parameters can be extracted from the fitting. Thus, the model can be extended to a general case for studying the magnetization and flux penetration in other type-II superconductors.
Polarized neutron reflectometry (PNR) provides evidence that nonlocal electrodynamics governs the magnetic field penetration in an extreme low-k superconductor. The sample is an indium film with a large elastic mean free path (11 mkm) deposited on a silicon oxide wafer. It is shown that PNR can resolve the difference between the reflected neutron spin asymmetries predicted by the local and nonlocal theories of superconductivity. The experimental data support the nonlocal theory, which predicts a nonmonotonic decay of the magnetic field.
We measured the specific heat, the magnetization, and the magnetoresistance of a single crystal of ZrB12, which is superconducting below Tc ~ 6 K. The specific heat in zero field shows a BCS-type superconducting transition. The normal- to superconducting-state transition changes from first order (with a latent heat) to second order (without latent heat) with increasing magnetic field, indicating that the pure compound is a low-kappa, type-II/1 superconductor in the classification of Auer and Ullmaier [J. Auer and H. Ullmaier, Phys. Rev.B 7, 136 (1973)]. This behavior is confirmed by magnetization measurements. The H-T phase diagram based on specific-heat and magnetization data yields Hc2(0) =550 G for the bulk upper critical field, whereas the critical field defined by vanishing resistance is a surface critical field Hc3(0) ~ 1000 G.
The magnetization of a planar heterostructure of periodically alternating type-II superconductor and soft-magnet strips exposed to a transverse external magnetic field is studied. An integral equation governing the sheet current distribution in the Meissner state of the superconductor constituents is derived. The field of complete penetration of magnetic flux in the critical state of the superconductor constituents is calculated for different widths of the superconductor and the soft-magnet constituents and a range of values of the relative permeability of the soft-magnet constituents.
Numerical calculations on a mesoscopic ring of a type II superconductor in the London limit suggest that an Abrikosov vortex can be trapped in such a structure above a critical magnetic field and generate a phase shift in the magnetoresistance oscillations. We prepared submicron-sized superconducting loops of single-crystal, type II superconductor NbSe$_2$ and measured magnetoresistance oscillations resulting from vortices crossing the loops. The free energy barrier for vortex crossing determines the crossing rate and is periodically modulated by the external magnetic flux threading the loop. We demonstrated experimentally that the crossing of vortices can be directed at a pair of constrictions in the loop, leading to more pronounced magnetoresistance oscillations than those in a uniform ring. The vortex trapping in both a simple ring and a ring featuring two constrictions was found to result in a phase shift in the magnetoresistance oscillations as predicted in the numerical calculations. The controlled crossing and trapping of vortices demonstrated in our NbSe$_2$ devices provide a starting point for the manipulation of individual Abrikosov vortices, which is useful for future technologies.
We review the magnetic form factor deduced by Delrieu from the Gorkovs equation for a Bardeen-Cooper-Schrieffer (BCS) type-II superconductor near its Bc2 phase boundary, i.e. when its magnetization is small. A numerical study of the form factor, field map, and field distribution follows. The characteristics of the transition from the low-temperature BCS to the high-temperature Ginzburg-Landau vortex lattices is studied. The exotic shape of the component field distribution and the form factor at low temperature and as a function of the external field intensity are discussed. Our numerical work should be helpful for the analysing of small angle neutron scattering and muon spin rotation vortex-lattice data recorded for BCS superconductors and maybe other superconductors in the clean limit.
Wei Xie
,Yu-Hao Liu
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(2021)
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"A generalized phenomenological model for the magnetic field penetration and magnetization hysteresis loops of a type-II superconductor"
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Wei Xie
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