Magnetic behavior and Coulomb-lattice-gas ordering of ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Sn}}^{4+}$ ions in ${\mathrm{K}}_2$${\mathrm{MnSnS}}_4$

A quaternary chalcogenide ${\mathrm{K}}_2$ ${\mathrm{MnSnS}}_4$, which consists of [${\mathrm{M}}_4$ ${\mathrm{S}}_{10}$ ${]}^{8\mathrm{-}}$ tetrameric clusters linked by sharing their terminal sulfur atoms to form a quasi-two-dimensional structure, exhibits magnetic properties which can be explained by a model containing no exchange coupling between neighboring clusters. To explain this result we calculated the Coulomb energy of different configurations of ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Sn}}^{4+}$ ions. These calculations clearly showed that the lowest energy configurations occurred when the distribution of ${\mathrm{Mn}}^{2+}$/${\mathrm{Sn}}^{4+}$ ions in each cluster was such that no ${\mathrm{Mn}}^{2+}$ was magnetically coupled to a ${\mathrm{Mn}}^{2+}$ in an adjacent cluster through a sulfur bond, in agreement with the magnetic analysis.