A theoretical model for tellurite-sulfates Na₂Cu₅(TeO₃)(SO₄)₃(OH)₄ and K₂Cu₅(TeO₃)(SO₄)₃(OH)₄

A theoretical model for two new tellurite-sulfates, namely Na$_2$Cu$_5$(TeO$_3$)(SO$_4$)$_3$(OH)$_4$ and K$_2$Cu$_5$(TeO$_3$)(SO$_4$)$_3$ (OH)$_4$ is determined to be compatible with ab-initio calculations. The results obtained in this work show that some previous speculations in the literature about the couplings are correct, obtaining a model with a mixture of ferromagnetic and antiferromagnetic couplings. We use a combination of numerical techniques to study the magnetic properties of the model. Our numerical calculations based on the density-matrix renormalization group method reveal that the system presents Ising-like magnetization plateaux at rational values of the saturation magnetization.