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The magnetic phase diagram of a two-dimensional generalized Hubbard modelproposed for manganites is studied within Hartree-Fock approximation. In thismodel the hopping matrix includes anisotropic diagonal hopping matrix elementsas well as off-diagonal elements. The antiferromagnetic (AF), ferromagnetic(F), canted (C) and paramagnetic (P) states are included in the analysis aspossible phases. It is found that away from half-filling only the canted and Fstates may exist and AF and P states which are possible for the usual Hubbardmodel do not appear. This is because the F order has already developed foron-site repulsion U=0 due to the hopping matrix of the generalized model. Whenapplied for manganites the orbital degree is described by a pseudospin. Thusour ``magnetic'' phase diagram obtained physically describes how orbital orderchanges with $U$ and with doping for manganites. Part of our results areconsistent with other numerical calculations and some experiments.Comment: 5 eps figures; a note added, to appear in Phys. Rev.

Phase diagram of a generalized Hubbard model applied to orbital order in manganites