Quadruple perovskites $A{\text{Cu}}_3{\mathrm{Fe}}_2{\mathrm{Re}}_2{\mathrm{O}}_{12}$ attract considerable interest due to their high Curie temperatures (up to 710 K), which strongly depend on the $A$-site cation. In this work, we employ first-principles calculations to investigate their electronic structure and magnetic exchange interactions. A band mechanism of magnetism that explains the antiferromagnetic character of the exchange interactions and their strong dependence on the filling of the Re $t_{2g}$ states is proposed. These antiferromagnetic interactions stabilize the ferrimagnetic ground state. The calculated Curie temperatures, obtained within the Onsager reaction field theory, are in good agreement with the experimental data.

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• Density of states
• Ferrimagnetism
• First-principles calculations
• Frustrated magnetism
• Transition temperature
• Half-metals
• Perovskites
• Strongly correlated systems
• DFT+U
• Density functional theory
• Heisenberg model
• Mean field theory