Inhomogeneous magnetic state in the system of solid solutions $(1-x)$Cu$_{0,5}$Al$_{0,5}$Cr$_2$S$_4$-$x$CuCr$_2$S$_4$

The magnetic and electrical properties of the system of solid solutions $(1-x)$Cu$_{0,5}$Al$_{0,5}$Cr$_2$S$_4$-$x$CuCr$_2$S$_4$ are studied. All the compositions studied have semiconductor conductivity of $p$ type. The dependence of the magnetization on the field strength is a superposition of the magnetization characteristic for an antiferromagnet and the small spontaneous magnetization. The spontaneous moment corresponding to one impurity ion Cu$^{2+}$ is close to the magnetization of the ferromagnetic cluster Cr$^{3+}$ formed by Cr ions, the nearest neighbors of Cu$^{2+}$. It is suggested that these clusters (ferrons) are created by localization of holes around the acceptor copper ion because of the energy gain of $s$-$d$ exchange. The presence of ferrons in these materials is also confirmed by the sharp rise in paramagnetic susceptibility in the region of the Curie point. Estimates of the magnitude of $s$-$d$ exchange in these materials are given.