Theory of the Role of Covalence in the Perovskite-Type Manganites<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo>[</mml:mo><mml:mi mathvariant="normal">La</mml:mi><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mi>M</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">II</mml:mi><mml:mo>)</mml:mo><mml:mo>]</mml:mo><mml:mi mathvariant="normal">Mn</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

The theory of semicovalent exchange is reviewed and applied to the perovskite-type manganites $[\mathrm{La}, M(\mathrm{II})]\mathrm{Mn}{\mathrm{O}}_{3}$. With the hypothesis of covalent and semicovalent bonding between the oxygen and manganese ions plus the mechanism of double exchange, detailed qualitative predictions are made about the magnetic lattice, the crystallographic lattice, the electrical resistivity, and the Curie temperature as functions of the fraction of ${\mathrm{Mn}}^{4+}$ present. These predictions are found to be in accord with recent findings from neutron-diffraction and x-ray data as well as with the earlier experiments on this system by Jonker and van Santen.