Nonuniversal temperature dependencies of the low-frequency ac magnetic susceptibility in high-Tcsuperconductors

Abstract

The complex ac magnetic susceptibilities $({\ensuremath{\chi}}_{n}={\ensuremath{\chi}}_{n}^{\ensuremath{'}}+i{\ensuremath{\chi}}_{n}^{\ensuremath{''}})$ of high-${T}_{c}$ superconductors in absence of dc fields have been studied by numerically solving the nonlinear diffusion equation for the magnetic flux, where the diffusivity is determined by the resistivity. In our approach the parallel resistor model between the creep and flux flow resistivities is used, so that the crossover between different flux dynamic processes (thermally activated flux flow, flux creep, flux flow) can naturally arise. For this reason we remark that, as the frequency increases, the presence of a different nonlinearity in different regions of the $I\ensuremath{-}V$ characteristic determines nonuniversal temperature dependencies of the ${\ensuremath{\chi}}_{n},$ i.e., the ${\ensuremath{\chi}}_{n}$ are found to be not universal functions of a frequency- and temperature-dependent single parameter. Moreover, the actual frequency-dependent behavior is also shown to be strictly related to the particular pinning model chosen for the simulations. Indeed, for large values of the reduced pinning potential $(U/KT>~220)$ and for increasing frequency, a transition has been observed between dynamic regimes dominated by creep and flux flow processes. On the other hand, for smaller reduced pinning potentials, a transition from the thermally activated flux flow (Taff) to the flow regime occurs. In qualitative agreement with available experimental data but in contrast with previously used simpler models, the amplitude of the peak of the imaginary part of the first harmonic is shown to be frequency dependent. Moreover the frequency dependence of its peak temperature shows large discrepancies with approximated analytical predictions. Finally, the shapes of the temperature dependencies of the higher harmonics are found to be strongly affected by the frequency.