The earth abundant oxides with fidelity to form novel quasi-particles are extraordinary features for energy storage applications, batteries, supercapacitors to magnetoresistance and spintronics. The present theoretical study has provided a systematic description of Mn(3d)-O(2p) electronic-correlation treatment in two bulk oxides of La-manganites, \({\text{LaMnO}}_{3}\) (LMO) with orthorhombic (o-) and rhombohedral (r-) bulk crystal symmetry. Herein, we have determined an accurate on-site Hubbard U from first-principles density functional perturbation theory (i.e., self-consistent Hubbard U, say Uself) in both of these pristine LMOs and applied on partially reduced manganites model, \({\text{LaMnO}}_{3-\text{x}}(0.0\le x\le 0.04\) ). The strong correlation treatments within the density functional theory with on-site Hubbard U (DFT + U) not only on metal sites but also on the non-metals, are found to be quite crucial while searching for correct magnetic ground states and metal–insulator transitions pertaining to the reductions of Mn3+ ions in LMOs with/out intrinsic Jahn–Teller (JT). Thus, we decouple the point-defects induced transport and broken magnetic symmetry magnetic-exchange (ME) to unravel the mesmerizing magnetic ground states search of LMOs as debated in the last several decades. The Uself is also applied for determining the geometries, structural descriptors, ME interactions and corroborated with electronics structures of LMOs in close comparison to other known on-site Ueff calculations. The present Uself helps not only to get better visualize the strong-correlations and non-local itinerant character of Mn(3d) occupancies in LMOs, but also correct valence and conduction bands compositions and transport character vs. known exp. data. Our study provides that a weaker and positive sign of ME interactions (say, J⊥, J||) from the native Mn3+(3d4)—O—Mn3+(3d4) skeletons of the o-LMO with JT-distortions is viable, while these are an order larger and also strongly positive in other non-JT La-manganite, r-LMO. However, in the reduced format, we predict more negative out-of-plane ME interactions (J⊥) in o-LMO3-x made out of the Mn2+(3d5)— • —Mn2+(3d5) skeletons (• = Oxygen vacancy) immersed inside Mn3+(3d4)—O—Mn3+(3d4) skeletons due to low defect concentration. We discussed the formation of A-type anti-ferromagnetic (AFM) polarons and ferromagnetic (FM) doublons type magnetic quasi-particles in these manganites in variation of the JT-distortions, super-exchange and double exchange mechanism. This has essentially shed light on decades old enigma of the AFM ground state search in o-LMO and opens future scope of study on FM insulating r-LMO – a milestone that reshuffles the scope of the first-principles calculations with DFT + U formulation. With enhanced O-vacancy concentrations, the o- \({\text{LMO}}_{3-\text{x}}\) results better charge-transfer insulating type transport due to AFM ordered mono-polarons formations. But, Nagaoka-type FM polarons (doublons) in r- \({\text{LMO}}_{3-\text{x}}\) showcase orbital selective Mott-insulating nature in contrast to the FM ordered metallic types in the pristine one. These observations are also consistent with recent model studies from Samajdar and Bhatt, 2024 and would enlighten further scope of applications of JT-type perovskites in catalysis to spintronics and towards the orbitronics, as guided by magnetic quasi-particles.
