Ferromagnetic polarons in ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ and ${\mathrm{La}}_{0.33}{\mathrm{Ca}}_{0.67}{\mathrm{MnO}}_3$

Unrestricted Hartree-Fock calculations on ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ $(x=0.5\mathrm{}$ and $x=0.67)$ in the full magnetic unit cell show that the magnetic ground states of these compounds consist of “ferromagnetic molecules” or polarons ordered in herring-bone patterns. Each polaron consists of either two or three Mn ions separated by ${\mathrm{O}}^{-}$ ions with a magnetic moment opposite to those of the Mn ions. Ferromagnetic coupling within the polarons is strong, while coupling between them is relatively weak. Magnetic moments on the Mn ions range between $3.8{\mu }_{\mathrm{b}}$ and 3.9 ${\mu }_B$ in the $x=0.5\mathrm{}$ compound and moments on the ${\mathrm{O}}^{-}$ ions are $-0.7{\mu }_B.$ Each polaron has a net magnetic moment of $7.0{\mu }_B,$ in a good agreement with recently reported magnetization measurements from electron microscopy. The polaronic nature of the electronic structure reported here is obviously related to the Zener polaron model recently proposed for ${\mathrm{Pr}}_{0.60}{\mathrm{Ca}}_{0.40}{\mathrm{MnO}}_3$ on the basis of neutron-scattering data.