We perform charge density functional theory plus $U$ calculation of LaMnO$_3$. While all the previous calculations were based on spin density functionals, our result and analysis show that the use of spin-unpolarized charge-only density is crucial to correctly describe the phase diagram, electronic structure and magnetic property. Using magnetic force linear response calculation, a long-standing issue is clarified regarding the second neighbor out-of-plane interaction strength. We also estimate the orbital-resolved magnetic couplings. Remarkably, the inter-orbital $e_g$-$t_{ 2g}$ interaction is quite significant due to the Jahn-Teller distortion and orbital ordering.
Categories: cond-mat.str-el cond-mat.mtrl-sci