External and internal demanetizing fields as one of the main fundamental reasons for the low density of critical current in twinned YBa$_2$Cu$_3$O$_{7-x}$ high-temperature superconductors

An oscillatory differential method of local approximation is applied to study the effect of local internal and external demagnetizing fields on the density of the critical current $J_{\mathrm{c}}$ of intertwin Josephson weak links in YBCO HTSC samples. Demagnetizing fields YBa$_2$Cu$_3$O$_{7-x}$ of samples with different $J_{\mathrm{c}}$ and twin size $J_{\mathrm{c}}$ are measured in the $d$ and $H_{\mathrm{D}}$ modes. The following parameters are determined: the twin size $d$, the thermodynamic first critical magnetic fields of twins $H_{\mathrm{ic1}}$, the demagnetizing fields of twins $H_{\mathrm{ic1}}$, the densities of intertwin effective critical currents $H_{\mathrm{Dtr}}$, the critical pinning currents $J_{\mathrm{ceff}}$ , and the Meissner screening critical currents $J_{\mathrm{cp}}$. It is shown that, at the fields $H_{\mathrm{ic1}}$, large twins are stepwise decomposed into a group of smaller twins with close demagnetizing factors. It is found that an increase in $J_{\mathrm{cg}}$ and $J_{\mathrm{ceff}}$ and a decrease in $d$ lead, on the one hand, to a decrease in $H_{\mathrm{c}}$ due to an increase in $H_{\mathrm{D}}$ and $H_{\mathrm{Dtr}}$ produced by $J_{\mathrm{ceff}}$ and $J_{\mathrm{cg}}$, on the other hand, to an increase in $J_{\mathrm{ceff}}$ and $J_{\mathrm{cg}}$ due to a decrease in $d$. For samples with large $J_{\mathrm{c}}$ and $d$, as well as for samples with low values of $J_{\mathrm{c}}$ and $d$ in a field of about $\sim$ 8 $\cdot$ 10$^{-2}$ T, $H_{\mathrm{D}}$, $H_{\mathrm{Dtr}}$ and $J_{\mathrm{c}}$ suppress by $\sim$ 70 about $\sim$ 60%, respectively. According to the results obtained in the present study and the known literature data, $d$ decreases with increasing $d$; in this case, a decrease in $d$ leads to a decrease, rather than an increase, in $J_{\mathrm{c}}$. Since the weak links and low values of $J_{\mathrm{c}}$ are fundamental properties of HTSCs, the literature data should be corrected with regard to the important facts on the effect of $H_{\mathrm{D}}$ and $H_{\mathrm{Dtr}}$ on $J_{\mathrm{c}}$.