Frustrated Antiferromagnetic Spin Chains of Edge-Sharing Tetrahedra in Volcanic Minerals K3Cu3(Fe0.82Al0.18)O2(SO4)4 and K4Cu4O2(SO4)4MeCl

The calculation of the sign and strength of magnetic interactions in two noncentrosymmetric minerals (klyuchevskite, K\(_{3}\)Cu\(_{3}\)(Fe\(_{\mathrm {0.82}}\)Al\(_{\mathrm {0.18}})\textit {O}_{2}\)(SO\(_{4})_{4}\), and piipite, K\(_{4}\)Cu\(_{4}\textit {O}_{2}\)(SO\(_{4})_{4}\)Cu\(_{\mathrm {0.5}}\)Cl) has been performed based on the structural data. As seen from the calculation results, both minerals comprise quasi-one-dimensional frustrated antiferromagnets. They contain frustrated spin chains from edge-sharing Cu\(_{4}\) tetrahedra with strong antiferromagnetic couplings within chains and very weak ones between chains. Strong frustration of magnetic interactions is combined with the presence of the electric polarization in tetrahedral chains in piipite. The uniqueness of magnetic structures of these minerals caused by peculiarities of their crystal structures has been discussed.