Magnetic Ramp Rate Research Articles

Magnetic flux instability in NbN films exposed to fast field sweep rates

Magneto-optical imaging of dendritic flux instability is reported for NbN films exposed to magnetic fields ramped at a fast rate (0.1–3.2 kT s−1). The results show that as the magnetic ramp rate increases, the temperature and field range of the instability extends significantly. In particular, the lower and upper threshold fields ( and respectively) that bound the field range for dendritic instability are affected. The upper field is found to increase linearly with the applied field sweep rate, a behavior which is discussed in terms of a recent theoretical work (Vestgarden et al 2016 Phys. Rev. B 73 174511). The extended instability range should be taken into account in applications in which the superconducting films are exposed to rapid changes in the magnetic field.

Macroscopic flux-creep magnetization of superconductors in applied magnetic field and local change peculiarities of their differential resistivity

The physical peculiarities of the flux-creep dynamics of low- and high-temperature superconductors placed in external varying magnetic field are studied. The flux-creep problem was studied for the partial penetration state. The proposed analysis was based on the macroscopic description of the flux creep by power and exponential equations of current–voltage characteristics of superconductors. It is shown that during flux creep the screening current penetrates into the superconductor at a finite velocity. Therefore, inside the superconductor a moving boundary of a magnetization region appears like in the critical state model. The time-dependent equations of screening current front have been written. However, unlike the critical state model nontrivial conditions are fulfilled at the moving boundary. They describe the smooth transition of the electromagnetic field induced by external perturbation to the undisturbed ones. A flux-creep distribution of the differential resistivity of the superconductor has been discussed. The performed analysis reveals that it monotonically decreases toward the moving boundary and depends on the magnetic ramp rate. In accordance with these flux-creep conditions the energy dissipation in the superconductors and their magnetic moment depend on the propagation law of the screening current moving boundary. The applicability of the Bean model for describing the flux-creep states is investigated.

Time scales of the flux creep in superconductors.

We have studied both theoretically and experimentally flux-creep dynamics in superconductors. A theoretical analysis of nonlinear flux diffusion shows that the relaxation of the electric field proves to be similar for different models of thermally activated flux creep, whereas the long-time decay of the magnetic moment M(t) can be essentially model dependent. A proposed scaling analysis indicates that the short-time decay of M(t) in the subcritical region j${\mathit{j}}_{\mathit{c}}$ is universal and consists of two stages. The initial nonlogarithmic stage is due to a transient redistribution of magnetic flux over the sample cross section, the duration of this stage ${\mathrm{\ensuremath{\tau}}}_{0}$ being entirely determined by macroscopic quantities, such as sample sizes, flux creep rate ${\mathit{M}}_{1}$(T,B)=dM/d lnt, and magnetic ramp rate B${\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}_{\mathit{e}}$=dB/dt. The second stage corresponds to the approximately logarithmic relaxation M(t)=${\mathit{M}}_{\mathit{c}}$-${\mathit{M}}_{1}$ln(t/${\mathit{t}}_{0}$), with ${\mathit{t}}_{0}$ being a macroscopic time constant that also depends on sample sizes, ${\mathit{M}}_{1}$(T,B), and the voltage criterion ${\mathit{E}}_{\mathit{c}}$ at which the critical current density ${\mathit{j}}_{\mathit{c}}$ is defined.We consider different models of flux dynamics with nonlinear flux-creep-activation barriers U(j) and obtain explicit formulas for ${\mathrm{\ensuremath{\tau}}}_{0}$ and ${\mathit{t}}_{0}$ for the exponential V-I curve and the vortex-glass model. We have also performed an experimental study of magnetic relaxation in grain-oriented ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ in which the time constant ${\mathrm{\ensuremath{\tau}}}_{0}$ has been measured directly at different temperatures 4.2 KT88 K, magnetic fields 0B8 T, and ramp rates 5 \ensuremath{\mu}T/sB${\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}_{\mathit{e}}$10 mT/s. We have observed the inverse dependence of ${\mathrm{\ensuremath{\tau}}}_{0}$ upon B${\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}_{\mathit{e}}$, with ${\mathrm{\ensuremath{\tau}}}_{0}$ ranging from 1 s to ${10}^{3}$ s and reaching 5000 s at B${\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}_{\mathit{e}}$=5 \ensuremath{\mu}T/s, B=6 T, and T=20 K. It is shown that, in accordance with our model, the dependences of ${\mathrm{\ensuremath{\tau}}}_{0}$ upon T and B coincide with those for the flux-creep rate ${\mathit{M}}_{1}$(T,B)=dM/d lnt measured on the logarithmic stage of the flux creep. We have also measured the dependences of the initial magnetic moment M(0) on T, B, and B${\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}_{\mathit{e}}$. Manifestations of the obtained results in magnetic and relaxation measurements on high-${\mathit{T}}_{\mathit{c}}$ superconductors are discussed.