Temperature dependence of the upper critical field of type-II superconductors from isothermal magnetization data: Application to high-temperature superconductors

Abstract

Using the Ginzburg-Landau theory in very general terms, we develop a simple scaling procedure which allows to establish the temperature dependence of the upper critical field H c2 and the value of the superconducting critical temperature T c of type-II superconductors from measurements of the reversible isothermal magnetization. An analysis of existing experimental data shows that the normalized dependencies of H c2 on T/T c are practically identical for all families of high-T c superconductors at all temperatures for which the magnetization data are available.

Comparison of the scaling analysis of mixed-state magnetization data with direct measurements of the upper critical field for YBa2Cu3O7−x

“…At the same time, H c2 represents one of the main parameters of a superconductor and knowledge of it is of primary importance. This is why several indirect approaches have been proposed and used in order to evaluate H c2 (T ) from equilibrium magnetization data collected in fields H H c2 [6][7][8][9][10][11][12]. However all these approaches are based on certain assumptions, which are not necessarily satisfied in experiments.…”

“…We shall not consider all theoretical methods for the analysis of magnetization data. Our goal is to discuss a scaling procedure proposed in [12] in order to compare the normalized temperature dependences of H c2 obtained by employing this procedure with direct measurements of the upper critical field. As we demonstrate below, good agreement between the results provides convincing evidence of the validity of this scaling analysis and allows us to draw some conclusions about the temperature dependence of the Ginzburg-Landau parameter κ for HTSCs.…”

“…In this case, equilibrium mixed-state magnetizations measured at different temperatures but in the same normalized fields H /H c2 (T ) are proportional to H c2 (T ). According to [12], this leads to the following relation between magnetizations of a sample at two different temperatures:…”

“…and [4], respectively. The solid line is obtained in [12] by scaling of magnetization data for the case κ = const and fitted to data points. The dashed line was obtained in [19] in an analogous way, but assuming κ(T ) as shown in the inset.…”

“…By a suitable choice of h c2 and c 0 (T ), individual M(H ) curves measured at different temperatures may be merged into a single master curve M eff (H, T 0 ). In this way the temperature dependence of the normalized upper critical field is obtained [12]. The temperature dependence of the upper critical field may be written as…”