Jahn-Teller distortion and magnetic structures inLaMnO3

Structural optimization is performed for LaMnO${}_3$ with the first-principles pseudopotential method based on the local density approximation (LDA), the generalized gradient approximation, and the LDA+U approximation. The Jahn-Teller distortion is reproduced even by LDA but the magnitude of the distortion for all three approximations is not quite large enough compared with the experimental value. The same analysis is performed also for the hypothetical ferromagnetic state. The Jahn-Teller distortion still exists but the magnitude is much reduced. The unit-cell shape becomes nearly cubic. These features are qualitatively consistent with the related experimental observations. If the crystal structure is optimized for each magnetic state, the present band calculation predicts the ferromagnetic state to be lower in energy than the $A$-type antiferromagnetic state, which is inconsistent with the experimental observation. The origin of the failure in the prediction of the ground state is discussed.