  $La_xCa_{1-x}MnO_3$ (LCMO) has been studied in the framework of density
functional theory (DFT) using Hubbard-U correction. We show that the formation
of spin-polarons of different configurations is possible in the G-type
antiferromagentic phase. We also show that the spin-polaron (SP) solutions are
stabilized due to an interplay of magnetic and lattice effects at lower La
concentrations and mostly due to the lattice contribution at larger
concentrations. Our results indicate that the development of SPs is unfavorable
in the C- and A-type antiferromagnetic phases. The theoretically obtained
magnetic state diagram is in good agreement with previously reported
experimental results
