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We perform charge density functional theory plus $U$ calculation ofLaMnO$_3$. While all the previous calculations were based on spin densityfunctionals, our result and analysis show that the use of spin-unpolarizedcharge-only density is crucial to correctly describe the phase diagram,electronic structure and magnetic property. Using magnetic force linearresponse calculation, a long-standing issue is clarified regarding the secondneighbor out-of-plane interaction strength. We also estimate theorbital-resolved magnetic couplings. Remarkably, the inter-orbital$e_g$-$t_{2g}$ interaction is quite significant due to the Jahn-Tellerdistortion and orbital ordering.

Charge density functional plus $U$ theory of LaMnO$_3$: Phase diagram, electronic structure, and magnetic interaction