The ferromagnetic Kondo lattice model with an antiferromagnetic interaction
between localized spins is a minimal description of the competing kinetic
(t) and magnetic (K) energy terms which generate the rich physics of mangan
ite systems. Motivated by the discovery in one dimension of homogeneous "is
land phases." we consider the possibility of analogous phases in higher dim
ensions. We characterize the phases present at commensurate fillings, and c
onsider in detail the effects of phase separation in all filling and parame
ter regimes. We deduce that island and flux phases are stable for intermedi
ate values of Kit at the commensurate fillings n=1/4, 1/3, 3/8, and 1/2. We
discuss the connection of these results to the charge and magnetic orderin
g observed in a wide variety of manganite compounds.