Anderson-Kim Model Research Articles

Evidence of current stabilization after long-time decay in high- TC superconductors

In this work, we have studied flux creep phenomenon over a long time period viz. about 1.5 × 10 7 s (i.e. for six months) at liquid nitrogen temperature. For this purpose, a high current was induced in four high- T C superconducting rings by means of a field-cooling (one sample) or a ferromagnetic field-cooling procedure (three samples). The resulting current decay was measured using a Hall probe system and the results obtained revealed lower relaxation rates in the ferromagnetic field-cooled samples. Also, the experimental data were found to leave the prediction of the classical Anderson–Kim model after a time long enough. The slope of the logarithmic current decay plot exhibited an oscillatory phenomenon at approximately 2 × 10 5 s (about 55 h). Oscillations vanished at approximately 4–5 × 10 6 s (46–58 days), after which the induced current remained stable throughout the remainder of the experiencing period.

The Study on AC Susceptibility and Magnetization of High-TcSuperconductor Bi-2223 Using a Critical-State Model

The Anderson–Kim model for a granular superconductor was employed to calculate both temperature and magnetic field dependencies of the AC susceptibility of a Bi-2223 superconductor. Moreover, similar calculations were performed for the magnetization. The prediction of the model, including the intergranular and intragranular contribution, for susceptibilities and magnetizations was consistent with experimental data very well by considering the temperature-dependent effective volume fraction. The temperature-dependence of fitting parameters was shown to obey almost quadratic power relation (1−T/Tc)β with β ≈ 2.

Pinning Energies and Relaxation Rates in Laser Ablated Al-Doped YBCO Superconducting Thin Films

Systematic magnetization measurements were performed on laser ablated Al-doped YBCO thin films in the temperature range from 4 to 80 K and fields up to 12 T. The magnetization as a function of logarithmic time in the temperature range from 10 to 80 K generally showed a linear behavior. This type of performance allows us to determine the temperature and field dependence of the apparent pinning potential on the basis of the Kim–Anderson model for thermal activation of flux motion. The relaxation rate values are calculated from the time-dependent magnetization curves. The relaxation rate dependence on temperature, magnetic field, and doping concentrations has been investigated for different Al concentrations and applied fields up to 5 T. A strong nonlinearity was observed for the relaxation rate dependence on both temperature and applied fields. The apparent pinning potential values, Uo, are estimated from the dependence of relaxation rates temperature curves using Uo=kBT/S expression. The dependence of Uo on both temperature and fields is elaborated and discussed in detail. The pinning potential, Uo, increases with temperature up to 40 K, however, above 40 K, a rapid decrease of Uo has been observed. Besides, a noticeable decrease in Uo as the applied field increases up to 0.1 T for temperatures below 40 K, and it is almost field independent for temperatures exceeding 40 K.

Temperature dependence of critical current density and flux creep of Hg(Re)-1223 powdered specimens

Magnetic hysteresis and flux creep phenomena of grain aligned HgRe 0.18Ba 2Ca 2Cu 3O y powder samples have been measured by SQUID and PPMS. The critical current densities for two field directions of B∥ c-axis and B∥ ab-plane showed J c( B∥ c-axis)> J c( B∥ ab-plane) in low temperature region. But the J c( B∥ c-axis) began to reduce abruptly at a certain temperature and became smaller than the J c( B∥ ab-plane) in higher temperature region. Such abrupt change was also measured in the flux creep phenomena, i.e. so called flux creep rate S=| d( lnΔM/ ΔM 0)/ d ln t| reduces at temperature which is approximately the same as the J c( B∥ c-axis) anomaly arises. Such anomaly is also observed in the temperature dependence of the magnetization itself at relevant magnetic field. Temperature dependence of the S is successfully analyzed by the Kim–Anderson model and the collective creep model.

Response of glass and liquid phases in the vortex lattice to an external AC magnetic field at different frequencies

We individuated a method to distinguish a glass phase from a highly viscous liquid phase in a lattice of vortices, established in type-two superconductors. Our analysis is based on the study of the temperature dependence of numerically obtained 1st and 3rd harmonics curves of the AC magnetic susceptibility, by changing the frequency of the applied AC magnetic field. The harmonics are obtained by integrating the non-linear diffusion equation for the magnetic field, with different voltage–current characteristics, corresponding to the two different phases. This method could be applied to the analysis of experimental curves in order to determine if the detected magnetic response of superconducting samples may be interpreted in terms of vortex glass or Kim–Anderson model.

Harmonics of the AC susceptibility as probes to differentiate the various creep models

We measured the temperature dependence of the first and the third harmonics of the AC magnetic susceptibility on some type II superconducting samples at different AC field amplitudes, h AC. In order to interpret the measurements, we computed the harmonics of the AC susceptibility as function of the temperature T, by integrating the non-linear diffusion equation for the magnetic field with different creep models, namely the vortex glass-collective creep (single-vortex, small bundle and large bundle) and Kim–Anderson model. We also computed them by using a non-linear phenomenological I– V characteristics, including a power law dependence of the pinning potential on h AC. Our experimental results were compared with the numerically computed ones, by the analysis of the Cole–Cole plots. This method results more sensitive than the separate component analysis, giving the possibility to obtain detailed information about the contribution of the flux dynamic regimes in the magnetic response of the analysed samples.

An ultrasonic study of magnetic flux pinning and the determination of the flux pinning energy inY Ba2Cu3O7−δ **This paper is dedicated to a dear friend, colleague and researcher, Professor GraemeRussell, who passed away during its preparation. He is sadly missed.

Ultrasonic studies at 85 kHz on polycrystallineY Ba2Cu3O7−δ (Y123)below Tc, with an applied magnetic field, have yielded details of the interaction of the magnetic fieldwith the superconductor. When the magnetic field is applied to the sample there is animmediate increase in acoustic damping, which then decreases logarithmically over anextended period of time to a trapped flux value. When the field is turned off a similarprocess is observed. The results are interpreted in terms of the Anderson–Kim model forthermally assisted flux creep, and they allow the determination of the apparentmagnetic flux pinning energy. The results indicate two distinct pinning energies, onefor the normal long term flux creep observed over minutes, and another lowervalue, which predominates during the first 5 s after a magnetic field is applied.

Measurement of magnetization curve and magnetic relaxation for 2H−NbSe2 crystals

The characteristics of electronic transport properties: behaviors of magnetization curve and magnetic relaxation of a typical normal superconductor 2H−NbSe2 are investigated. The results show thatTc and ΔTc of the samples are 7. 2, 0. 18 K, indicating that superconducting energy gap at zero temperature is 1. 1. meV. No fish tail shape is found in the magnetization curves at several temperatures. The relationship between remnant magnetic moment and time reveals that the magnetic flux creep of the sample agrees with the Kim-Anderson thermal activation model with the relaxation rateS=0.00036 atT=6 K.

Ac magnetic response of MgB 2 bulk superconductor based on the Anderson–Kim model

Magnetic response of an intermetallic bulk superconductor MgB 2 was carried out by use of ac susceptibility and ac magnetization measurements. The theoretical model calculations corresponding to the measurements were obtained employing the Anderson–Kim model. The measured susceptibilities, χ n = χ n ′+i χ n ′′ ( n=1, 3, 5, 7), as a function of temperature with various H m fields agree well with model calculations. The comparisons of ac magnetization measurement at different temperatures with corresponding model calculations also show satisfactory agreements. In addition, the temperature-dependent of critical current density was predicted from experimental data. This relation was shown to obey the almost quadratic power relation.

Rigid vortices in MgB2

Magnetic relaxation of high-pressure synthesized MgB2 bulks with different thickness is investigated. It is found that the superconducting diamagnetic moment depends on time in a logarithmic way: the flux-creep activation energy decreases linearly with the current density (as expected by Kim–Anderson model) and the activation energy increases linearly with the thickness of sample when it is thinner than about 1 mm. These features suggest that the vortices in the MgB2 are rather rigid, and the pinning and creep can be well described by Kim–Anderson model.

Magnetic susceptibility studies of grains in HgPb1223 ceramic superconductors

AC susceptibilities and DC magnetizations of Hg (1− x) Pb x Ba 2Ca 2Cu 3O y ( x=0.1 denoted as Hg-01 and x=0.2 as Hg-02) synthesized directly from the metal oxides were measured using a SQUID magnetometer and a PPMS susceptometer. The superconducting volume fractions were estimated from the temperature dependence of Meissner magnetization. Pb substitution of Hg site showed to enhance the volume fraction without sacrificing the critical temperatures of 134 K in both samples. Critical current densities J c were estimated from the magnetization width. Pinning potentials U p were evaluated from the relaxation rate of magnetic flux creep characteristics by using the Anderson–Kim model. Both samples show rapid decreases of the J c at high temperature. Hg-01 sample showed slightly higher J c and U p. Second peaks χ ″ p2 in the imaginary part of the AC susceptibilities χ″ appeared at low magnetic fields in both samples. The peak χ ″ p2 of Hg-01 disappears gradually at high magnetic field and the χ ″ p2 of Hg-02 sample dominates at low temperatures. Dependence of the χ ″ p2 on the temperature, DC magnetic field and AC field is extensively examined. Grain characteristics in HgPb1223 ceramic superconductors are discussed by taking into account of weak-coupling effect between grains and existence of second phases in both samples.

Role of the field dependence of the heat capacity for the flux jump process in HTSC materials

Magnetization and magnetostriction loops were calculated in terms of the Kim–Anderson model incorporating the flux jump instability criterion and taking into account magnetic field and temperature dependencies of the heat capacity of YBaCuO. Regions in the H– T diagram where flux jumps occur were determined. The stabilizing role of the specific heat for the critical state of the material was observed.

AC susceptibility of high Tc superconductor Tl 0.8Pb 0.2Bi 0.2Sr 1.6Ba 0.4Ca 2Cu 3O x using a critical state model

The Anderson–Kim model is employed to calculate the temperature and AC magnetic field dependence of the complex susceptibility, χ= χ ′+i χ ′′, of high T c superconductor Tl 0.8Pb 0.2Bi 0.2Sr 1.6Ba 0.4Ca 2Cu 3O x . Intergranular Josephson vortices sweep in and out of the weak-link network, while intragranular Abrikosov vortices move in and out of the superconducting grains, both causing bulk pinning hysteresis loss. The calculated χ ′ and χ ′′ are consistent with experimental data very well by considering the proper volume fraction of superconducting grains and intergranular region. Using field dependence of critical current density obtained from fitting parameter, the property of intergranular region is discussed and the intergranular lower critical field H c1J is determined.

Magnetothermal instabilities in type II superconductors: The influence of magnetic irreversibility

Complete magnetization and magnetostriction loops for type II superconductors were calculated in terms of the following pinned critical state models which incorporate the flux jump instability criterion: the Kim–Anderson model, the exponential model, the linear model, and the model with peak effect. These results were used for constructing magnetic field–temperature (H–T) diagrams of instability of these critical state models. Magnetothermal instabilities of superconductors with peak effect were investigated experimentally and theoretically. Regions in the H–T diagram where flux jumps occur were built and compared with experimental M(H) hysteresis loops. We have explained the phenomenon of “island” jumps. The influence of flux trapping on the flux jump regions of magnetic fields was studied.

Analysis of H-T flux jump diagrams from different critical state models

The magnetic field - temperature ranges where the critical state for type II superconductors is unstable were calculated in terms of the following pinned critical state models: the Kim-Anderson model, the exponential model and the linear model. Comparative discussion of H-T diagrams of flux instabilities is presented.

Field sweep rate effect on the flux creep in HTSC

We report the effect of the magnetic field sweep rate on the relaxation of the magnetization as a function of temperature and magnetic field H parallel to the c-axis in an aligned powder, thin film and melt textured YBaCuO superconductors. The real M vs. In t relationship can be deduced from the experimental one by scaling the time t to t+ τ+ t 0. The resulting curves collapse all into a single one. The correlation time τ is calculated and it obeys to the relation (dH/dt) −1 for small T and H. The behavior of the M(In t) curves cannot be described by the Kim-Anderson model for all the explored temperatures and fields.

Analysis of the magnetic relaxation in BiPbSrCaCuO high-TC superconductors by means of an interaction model

The magnetic relaxation of cylindrical polycrystalline samples of BiPbSrCaCuO high-TC superconductors has been measured using an inductive technique near the transition temperature. The relaxation data are analyzed by means of an interaction model based on the general theory of magnetic relaxation. This model assumes the existence of an effective energy barrier (Ueff) and considers thermal activation of the vortices over it. The pinning energy (U0) is reduced to the effective barrier Ueff=U0−Uint by the energy associated to the force of repulsion between vortices (Uint). In this work a linear dependence between the interaction energy and the susceptibility has been used, but other dependencies can easily be introduced to account for the observed nonlinearities of the U(J) curve. The model has been used to extract information of the relaxation of BiPbSrCaCuO samples at several magnetic fields and temperatures after switching off the field. A comparison with the results obtained by the Anderson–Kim model is also provided.

The range of giant flux instabilities in the plane in hard superconductors: calculations and experiment

We have studied magnetothermal instabilities, giant flux jumps, both theoretically and experimentally. Magnetostriction and magnetization hysteresis loops with flux jumps were calculated over a wide range of experimental parameters employing two critical-state models: the Kim-Anderson model and the exponential model. The influence of the magnetic history on the flux jumps' magnetostriction and magnetization were investigated for the LaSrCuO single crystal. The shape of the unstable region of the critical state in the temperature-magnetic field plane was constructed from calculations and experimental results. In the Kim-Anderson model H-T diagrams of flux instabilities agree well with experimental results on HTSC single-crystal LaSrCuO and experimental results on LTSC niobium.

Magnetoresistance in underdoped HgBa 2Ca 2Cu 3O 8 films in high magnetic fields

Magnetoresistance in underdoped ( T c=120 K) HgBa 2Ca 2Cu 3O 8 films prepared by a sol–gel method on Y 0.15Zr 0.85O 1.93 substrates was measured as function of field and temperature. In the temperature range 25–50 K, the resistivity is linearly dependent on the magnetic field and is dominated by thermally activated flux creep. The average activation energy required for flux depinning was estimated for several fields using the Anderson–Kim model. The depinning potential U and the critical resistivity ρ c are field dependent and decrease with external magnetic field. For fields of up to 17 T, U varies from 0.026–0.016 eV. The magnetoresistance was studied for H‖c and H‖ab configurations to reveal the anisotropy. Steps in ρ vs. H were observed at low temperatures at the resistance onset. These steps are probably due to inhomogeneous distribution of the field inside the film.

H–T phase diagram for the giant magnetic flux jumps in low temperature superconductors and high temperature superconductors

We have studied magnetothermal instabilities both theoretically and experimentally. Magnetostriction and magnetization hysteresis loops with flux jumps were calculated over a wide range of experimental parameters employing three critical state models: the original Bean model, the Kim–Anderson model, and the exponential model. The influence of the magnetic prehistory on the flux jumps, magnetostriction, and the magnetization was investigated for the LaSrCuO crystal. H–T diagrams of flux instabilities were constructed from calculation and from experimental results. One can see good qualitative agreement between these two diagrams.