Anomalous transport properties of a paramagnetic NiTiO$_3$ + HTSC two-phase system representing a random Josephson junction network

Composites representing a network of random Josephson junctions and characterized by the compositions 92.5 at.% ${\rm Y_{3/4}Lu_{1/4}Ba_2Cu_3O_7+7.5}$ at.% NiTiO$_3$ and 92.5 at.% ${\rm Y_{3/4}Lu_{1/4}Ba_2Cu_3O_7+7.5}$ at.% MgTiO$_3$ are synthesized, and their magnetoresistance properties are studied. The temperature dependence of the resistance $R(T)$ measured for the composite that contains the paramagnetic NiTiO$_3$ compound exhibits a characteristic feature below the superconducting transition temperature $T_c$ of the high-$T_c$ superconductor, namely, a region where $R$ is independent of the current $j$ and weakly depends on the magnetic field $H$. Below a certain temperature $T_m$, a strong dependence of $R$ on $j$ and $H$ is observed, which is peculiar to a network of Josephson junctions. The dependences $R(T, j, H)$ obtained for the «reference» samples with the nonmagnetic MgTiO$_3$ compound exhibit no such features. The anomalous behavior of the HTSC + NiTiO$_3$ composite is explained by the effect produced by the magnetic moments of Ni atoms in the insulating barriers on the transport current.