Practically useful form of Kim model from hysteresis loop of a superconductor

TL;DR

This paper introduces a hysteretic Kim model derived from the hysteresis loop of superconductors, providing a practical expression for the Kim constant and demonstrating its application to various high-temperature superconductors.

Contribution

It develops a hysteretic Kim model with an empirical relation for the Kim constant, improving understanding of superconductor hysteresis behavior beyond the original Kim model.

Findings

The hysteretic Kim model fits experimental data for high-temperature superconductors.

The dependence of penetration field on sample width is approximately proportional to the square root of width.

The model offers better insights into the intergranular matrix of YBa2Cu3O7−δ superconductors.

Abstract

Considering a theoretical hysteresis loop within the Kim model for the Kim constant $H_0$ = 0 it has been found that the expression of $H_0$ obtained in Lal [R. Lal, Physica C 470 (2010) 281] provides a nonzero value 0.3424$H_p$ for this constant. ($H_p$ is full penetration field.) This different value of the Kim constant for the same hysteresis loop has been made a base for a different version of the Kim model, the hysteretic Kim model, such that the value zero of $H_0$ corresponds to the original Kim model and the value 0.3424$H_p$, denoted by a different notation $H_{0,hys}$, corresponds to the hysteretic Kim model. The two versions of the Kim model are interrelated so that $H_{0,hys}$ is a function of $H_0$. An empirical relation, $H_{0,hys}$=0.3424$H_p$exp(1.4$^{0.5}$($H_0$/$H_p$)), has been worked out on the basis of the theoretical $H_0$>0 hysteresis loops. The hysteretic Kim model has been cast in a practically useful form by obtaining an expression of $H_p$ in terms of the hysteretic magnetization. The importance of the hysteretic Kim model has been illustrated by applying it to the YBa$-2$Cu$_3$O$_7$, Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ and Ba$_0.72$K$_0.28$Fe$_2$As$_2$ superconductors by taking hysteresis loops of these systems from literature. It has been found that in these superconductors the dependence of $H_p$ on the sample width is mainly like $^{0.5}$(2$a$), and not like 2$a$ (Bean model). (2$a$ is the sample width.) The empirical relation of $H_{0,hys}$ and $H_0$ has been found to provide a reasonably good understanding of the intergranular matrix of the YBa$_2$Cu$_3$O$_{7-\delta}$ superconductor, where Kim model has not been found successful earlier.