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

The magnetic phase diagram of a two-dimensional generalized Hubbard model p roposed for manganites is studied within Hartree-Fock approximation. In thi s model the hopping matrix includes anisotropic diagonal hopping matrix ele ments as well as off-diagonal elements. The antiferromagnetic (AF), ferroma gnetic (F), canted (C), and paramagnetic (P) states are included in the ana lysis as possible phases. It is found that away from half-filling only the canted and F states may exist and AF and P states which are possible for th e usual Hubbard model do not appear. This is because the F order has alread y developed for on-site repulsion U=0 due to the hopping matrix of the gene ralized model. When applied for manganites the orbital degree is described by a pseudospin. Thus our "magnetic" phase diagram obtained physically desc ribes how orbital order changes with U and with doping for manganites. Part of our results are consistent with other numerical calculations and some e xperiments.