First-principles study of the electronic and magnetic structures of the tetragonal and orthorhombic phases ofCa3Mn2O7

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On the basis of density functional theory electronic band structure calculations using the augmented spherical wave method, the electronic and magnetic properties of the orthorhombic and tetragonal phases of ${\mathrm{Ca}}_{3}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ were investigated and the spin exchange interactions of the orthorhombic phase were analyzed. Our calculations show that the magnetic insulating states are more stable than the nonmagnetic metallic state for both polymorphs of ${\mathrm{Ca}}_{3}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$, the orthorhombic phase is more stable than the tetragonal phase, and the ground state of the orthorhombic phase is antiferromagnetic. The total energies calculated for the three spin states of the orthorhombic phase of ${\mathrm{Ca}}_{3}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ led to estimates of the spin exchange interactions ${J}_{\mathit{nn}}=\ensuremath{-}3.36\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ and ${J}_{\mathit{nnn}}=\ensuremath{-}0.06\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. The accuracy of these estimates was tested by calculating the Curie-Weiss temperature within the mean-field approximation.