Orbital ordering in the ferromagnetic insulator Cs2AgF4 from first principles

We found, using density-functional theory calculations within the generalized gradient approximation, that Cs2AgF4 is stabilized in the insulating orthorhombic phase rather than in the metallic tetragonal phase. The lattice distortion present in the orthorhombic phase corresponds to the x(2)-z(2)/y(2)-z(2) hole-orbital ordering of the Ag2+ 4d(9) ions, and this orbital ordering leads to the observed ferromagnetism, as confirmed by the present total-energy calculations. This picture holds in the presence of moderate 4d-electron correlation. The results are compared with the picture of ferromagnetism based on the metallic tetragonal phase.