Anomalous diamagnetic transitions in Ba$_2$Cu$_3$O$_4$Cl$_2$ and Sr$_2$Cu$_3$O$_4$Cl$_2$ antiferromagnets

The magnetic properties of Ba$_2$Cu$_3$O$_4$Cl$_2$ and Sr$_2$Cu$_3$O$_4$Cl$_2$ oxychlorides have been studied. A spontaneous manifestation of diamagnetism has been found at quasi-zero and low fields. The temperature of these transitions coincides with the temperature of the antiferromagnetic ordering in Ba$_2$Cu$_3$O$_4$Cl$_2$ ($T_{\text{N}\,\text{I}}\approx337\,$K) and Sr$_2$Cu$_3$O$_4$Cl$_2$ ($T_{\text{N}\,\text{I}}\approx 386$ K). The recorded diamagnetic signal is $-10^{-4}$ emu. It is comparable with the percentage of the superconducting phase in the sample. It is supposed that the arising superconductivity is due to the formation of the superconducting clusters with the direct overlap of the copper $d$ orbitals owing to the frustration processe.