Modulation instability of electromagnetic excitations in the nonlocal Josephson electrodynamics of thin magnetic superconducting films

The modulation instability of plane finite-amplitude nonlinear waves with the Josephson frequency is studied for a Josephson contact in thin nonmagnetic and magnetic (two-dimensional) superconducting films. Dispersion relations for the increments of small-amplitude perturbations are derived. Modulation instability is shown to develop in the finite range 0<Q<Q _b of the wavevectors of amplitude perturbations for the nonmagnetic films and for any perturbation wavevector 0<Q<∞ for the magnetic films.     

Nonlocal Josephson electrodynamics of electromagnetic excitations in a superconducting magnetic (three-dimensional) thin film

The integro-differential equation for the dynamics of the phase difference with temporal and spatial nonlocality for a Josephson junction in a superconducting three-dimensional magnetic thin film is derived. The equation is valid for any type of magnetic ordering. The magnetic subsystem is shown to significantly renormalize the spectrum of small-amplitude electromagnetic excitations, which, as a result, are damped.     

Nonlocal Josephson electrodynamics of a magnetic (two-or three-dimensional) superconductive thin film

For the Josephson junction in a two-or three-dimensional magnetic superconductive thin film, an integro-differential equation of phase-difference dynamics, including time and space nonlocality, is deduced. It is shown that the magnetic subsystem induces the substantial renormalization of the spectrum of small-amplitude electromagnetic excitations and causes them to decay.     

Modulation instability of electromagnetic excitations for a Josephson unction in a finite-thickness slab

The modulation instability of finite-amplitude uniform plane waves oscillating with a Josephson frequency and experiencing a nonlinear frequency shift in a finite-thickness slab is studied in terms of the nonlocal electrodynamics of Josephson junction. A dispersion relation for the growth rate of small amplitude perturbation is derived. The domains of modulation instability for these waves are found. Modulation instability of the waves is shown to arise when the wavevectors of long-wave amplitude perturbations fall into the finite range 0 < Q < Q _B (A, D, L). In the range Q ≥ Q _B (A, D, L), the waves are stable.     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

Electromagnetic waves in the nonlocal Josephson electrodynamics of a thin film of a magnetic superconductor

An integrodifferential equation describing the dynamics of the phase difference with spatial and temporal nonlocality is derived for a Josephson junction in a thin film of magnetic superconductor. It is shown that the magnetic subsystem renormalizes the spectrum of small-amplitude electromagnetic excitations and leads to their damping. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 2, 132–138 (25 January 1999)     

Dendritic flux avalanches and nonlocal electrodynamics in thin superconducting films

We report a mechanism of nonisothermal dendritic flux penetration in superconducting films. Our numerical and analytical analysis of coupled nonlinear Maxwell and thermal diffusion equations shows that dendritic flux pattern formation results from spontaneous branching of propagating flux filaments due to nonlocal magnetic flux diffusion and positive feedback between flux motion and Joule heating. The branching is triggered by a thermomagnetic edge instability, which causes stratification of the critical state. The resulting distribution of thermomagnetic microavalanches is not universal, because it depends on a spatial distribution of defects. Our results are in good agreement with experiments on Nb films.     

The spectrum of speeds of topological solitons in nonlocal Josephson electrodynamics

For the model [6] of nonlocal electrodynamics with nonsmooth (piecewise linear) nonlinearity, the problem of point spectrum of speeds of topological solitons with the minimal topological charge is analyzed. The variation of the spectrum of speeds under one-parameter deformation of such a nonlinearity is determined.     

Modulation instability of dispersive electromagnetic waves in a Josephson junction in a finite-thickness plate

Modulation instability of finite-amplitude dispersive electromagnetic waves is studied in the framework of nonlocal electrodynamics of a Josephson junction in a finite-thickness plate. The dispersion equation is derived for the increment of small amplitude perturbations. For this type of waves, the regions of development of modulation instability and stability of waves are determined. It is shown that modulation instability of waves develops in a finite range of wavevectors Q _B1(k, D, L) < Q < Q _B2(k, A, D, L), while waves are stable in the important long-wave region 0 ≤ Q ≤ Q _B1(k, D, L) and for Q ≥ Q _B2(k, A, D, L). The unique possibility of controlling the modulation instability region by dispersion parameter k, viz., the wave vector (or frequency ω(k)) of the modes in the linear approximation.     

Spectroscopy of magnetic excitations in magnetic superconductors using vortex motion

In magnetic superconductors a moving vortex lattice is accompanied by an ac magnetic field which leads to the generation of spin waves. At resonance conditions the dynamics of vortices in magnetic superconductors changes drastically, resulting in strong peaks in the dc I-V characteristics at voltages at which the washboard frequency of the vortex lattice matches the spin wave frequency omegaS(g), where g are the reciprocal vortex lattice vectors. We show that if the washboard frequency lies above the magnetic gap, measurement of the I-V characteristics provides a new method to obtain information on the spectrum of magnetic excitations in borocarbides and cuprate layered magnetic superconductors.     

Electromagnetic waves in the nonlocal electrodynamics of an oblique Josephson junction of finite thickness

The new geometry for an oblique Josephson junction of finite thickness along the magnetic field is considered and a nonlocal integro-differential equation describing the dynamics of the phase difference is derived. The spectrum of low-amplitude electromagnetic excitations for lap-joint junctions is also studied. Zh. éksp. Teor. Fiz. 113, 2256–2262 (June 1998)     

Evanescent wave intensification in surface spin-wave acoustics and magnetic/nonmagnetic interface electrodynamics

A relation is found between the maximum intensification of an evanescent elastic shear wave excited in a magnetic field and the enhancement of the Schoch effect. The conditions necessary for the electromagnetic analog of this relation for the Goos-Hänchen effect in the case of a TM (TE) body wave beam incident from without are determined.     

Leggett mode in cuprate superconductors and the electromagnetic properties of Josephson junctions

The effect of multiple Andreev reflections in YBa₂Cu₃O_{7 ? x} and Tl₂Ba₂Ca₂Cu₃O_{10 ? ??} has been studied. Several independent subharmonic gap structures associated with the multigap character of these superconductors have been revealed on the I(V) and dI/dV characteristics of Andreev contacts. An additional fine structure has been observed, which can be attributed to the emission of Leggett plasmons. The electromagnetic properties of Josephson junctions at a microcrack in Tl₂Ba₂Ca₂Cu₃O_{10 ? ??} have been examined. The magnetic-field dependences of the critical current, as well as Fiske geometric resonances, have been studied in the Josephson regime (SIS type). The fundamental frequency of resonances and the Swihart velocity have been determined.     

Coupled modulational instability of copropagating spin waves in magnetic thin films

This letter reports the first results on the coupled modulational instability of copropagating spin waves in a magnetic film. Strong instability was observed for the two waves with either attractive or repulsive nonlinearity. If the two waves have attractive nonlinearity, the instability leads to the formation of bright solitons. If the two waves have repulsive nonlinearity, the process results in the formation of black solitons. The instability was also observed for the two waves in separated attractive-repulsive nonlinearity regimes.     

Resonances of thermally stimulated electromagnetic excitations of thin films on a substrate in a near field

The spectral features of thermally stimulated electromagnetic excitations generated by films of wide band gap semiconductors on metals in vacuum at different distances from a sample surface were investigated. Special attention was given to the interaction of characteristic resonances in the excitation spectrum of these fields with local vibrations of Cd impurity atoms inside ZnTe films on metal substrates.     

Josephson (001) tilt grain boundary junctions of high-temperature superconductors

We calculate the Josephson critical current I_c across in-plane (001) tilt grain boundary junctions of high-temperature superconductors. We solve for the electronic states corresponding to the electron-doped cuprates, two slightly different hole-doped cuprates, and an extremely underdoped hole-doped cuprate in each half-space, and weakly connect the two half-spaces by either specular or random Josephson tunnelling. We treat symmetric, straight, and fully asymmetric junctions with s-, extended-s, or d _{x ²?y ²} -wave order parameters. For symmetric junctions with random grain boundary tunnelling, our results are generally in agreement with the Sigrist–Rice form for ideal junctions that has been used to interpret ‘phase-sensitive’ experiments consisting of such in-plane grain boundary junctions. For specular grain boundary tunnelling across symmetric junctions, our results depend upon the Fermi surface topology, but are usually rather consistent with the random facet model of Tsuei et al. Our results for asymmetric junctions of electron-doped cuprates are in agreement with the Sigrist–Rice form. However, our results for asymmetric junctions of hole-doped cuprates show that the details of the Fermi surface topology and of the tunnelling processes are both very important, so that the ‘phase-sensitive’ experiments based upon in-plane Josephson junctions are less definitive than has generally been thought.