Phase-field Study Of Abrikosov Vortices Under Magnetic Coupling In Type-? Superconductors

Time-Dependent Ginzburg-Landau equations were solved by finite difference and finite element methods to study the vortex dynamics and other physical properties of type-II superconductors in various types of magnetic field situations.First,a cubic type-? superconducting sample was simulated for vortex dynamics in oscillating and steady magnetic fields,in three-dimensional geometry using finite difference scheme.Dynamic behavior of penetrating and leaving magnetic vortices in a superconductor with the oscillating magnetic field was simulated.Carrier concentration density and the average magnetization of the sample were studied as a function of an external oscillating magnetic field.Anomalies in carrier concentration at certain magnetic field values were observed and discussed.It was also observed that area swept by magnetization vs external magnetic field is magnetic oscillation frequency dependent which increases with increasing frequencies.It was suggested that this effect might cause instability in superconducting characteristics of the sample over a number of cycles.Calculated energy patterns showed consistency with vortex patterns in the steady magnetic field.Magnetic oscillations initiated oscillations in energy components,ripples in superconducting energy are subjected to the entrance and leaving of vortices,while instability observed in interaction energy is referred to vortex relaxation time.Furthermore,cubic superconducting sample was simulated under oscillating magnetic field with and without additional background static magnetic field using same technique used above.Vortex dynamics including entrance and exit from the sample was simulated.Magnetization and carrier concentration densities of the sample were studied as a function of external magnetic field variations.Anomalies in carrier concentration density were observed at certain values of the magnetic field which were correlated with the entrance and exit processes of vortices.Area swept by superconductor magnetization with magnetic field was observed to have a hysteresis-like behavior where area representing energy dissipated per cycle.This energy accumulation was suggested to cause instability in superconductor over the number of cycles and may result in thermal quenching.Temporal distribution of energy components showed consistency with the pattern observed for carrier concentration and magnetization under oscillating magnetic field.Rapid phase changes with magnetic oscillations resulted in oscillations in energy components,irregular peaks,and ripples in superconducting energy represent the situation of exit and entry of vortices.While the rise in interaction energy with cycles is referred to vortex relaxation time in a cycle,this energy is expected to accumulate and take other forms(e.g.,heat)and is predicted to cause thermal quenching.In the presence of background static magnetic field,this energy dissipation was calculated to increase significantly,while superconductor is subjected to oscillating magnetic field.Additionally,time-dependent Ginzburg-Landau equations were solved by finite element method in two-dimensional space for order parameter and energy components of the annular superconducting sample in steady magnetic fields.Vortices preferred to penetrate from the inner surface of the annulus due to lesser energy required at the concave surface.A transition magnetic field strength was observed in spatial averages of carrier concentration and energy components,showing small bumps and abrupt variations,indicating phase transition from a non-vortex to vortex state.These effects were observed to repeat with every subsequent entry of a set of vortices into the sample.Transition magnetic field strength was found to depend inversely on the annular width of the sample.Present work gives a better understanding of energy variations during phase transition from non-vortex to vortex state and predicts that vortex state can be avoided by tuning the wire thickness in practical applications e.g.superconducting electromagnets.Superconductivity and ferromagnetism are two very useful phenomena but rarely coexist in bulk materials.Bringing them together in artificial hybrid bilayer produces some unusual results.A system of superconductor-ferromagnet bilayer with a thin insulating buffer layer was designed and studied.Such superconductor-ferromagnet bilayer with magnetostatic coupling is proposed to be used as a multibit superconductor memory device and a potential candidate for memristor.Numerical simulations were performed by using Ginzburg-Landau and Landau-Lifshitz-Gilbert models for superconductor and ferromagnet materials,which highlighted some interesting resistive memory effects in superconducting layer.Vortex pattern in superconductor was observed to be strongly coupled with ferromagnet domain structure,while their dynamics controlled by the current flowing through the superconductor.Carrier concentration,energy components and magnetization in the superconductor layer were studied as a function of applied current pulses in the superconductor layer,indicating the information storage of current pulses.Multiple resistive states were observed,pointing towards the possibility of such a device to be used as multi-bit data storage device.