Effect of the Exchange Coupling ofMn++Ions on the Magnetic Susceptibilities of ZnS: MnS Crystals

Abstract

The magnetic susceptibilities have been measured over the temperature range of 20-500°K for five ZnS single crystals doped with ${\mathrm{Mn}}^{++}$ in varying concentrations from 0.5 to 7.5%. The susceptibilities are essentially linear in $\frac{1}{T}$ for $T<\mathrm{}77\mathrm{}$°K, but above this temperature the graphs of $\chi$ show appreciable curvatures which increase with the ${\mathrm{Mn}}^{++}$ concentration. The departure from the Curie behavior can be explained by the antiferromagnetic coupling between the ${\mathrm{Mn}}^{++}$ ions situated at the nearest-neighbor sites in the ZnS lattice. By assuming that the numbers of clusters of various types are determined by statistics, the total magnetic susceptibilities of the single ions, pairs, and triples of ${\mathrm{Mn}}^{++}$ in the ZnS crystals have been calculated. The observed susceptibilities can be fitted to the theoretical values if the exchange coupling is taken as the form $-2J\left({\mathbf{s}}_1\mathbf{·}{\mathbf{s}}_2\right)$ with $J$ equal to -9±1 ${\mathrm{cm}}^{-1\mathrm{}}$.