  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 manganite systems.
Motivated by the discovery in one dimension of homogeneous ``island phases'',
we consider the possibility of analogous phases in higher dimensions. We
characterize the phases present at commensurate fillings, and consider in
detail the effects of phase separation in all filling and parameter regimes. We
deduce that island and flux phases are stable for intermediate values of K/t 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 ordering observed in a wide variety
of manganite compounds.
