The nature of the ferromagnetic ground state in the Mn4 molecular magnet

Using ab initio band structure and model calculations we studied magnetic properties of one of the Mn$_4$ molecular magnets (Mn4(hmp)6), where two types of the Mn ions exist: Mn3+ and Mn2+. The direct calculation of the exchange constants in the GGA+U approximation shows that in contrast to a common belief the strongest exchange coupling is not between two Mn3+ ions (J_{bb}), but along two out of four exchange paths connecting Mn3+ and Mn2+ ions (J_{wb}). The microscopic analysis performed within the perturbation theory allowed to establish the mechanism for this largest ferromagnetic exchange constant. The charge ordering of the Mn ions results in the situation when the energy of the excited state in the exchange process is defined not by the large on-site Coulomb repulsion U, but by much smaller energy V, which stabilizes the charge ordered state. Together with strong Hund's rule coupling and specific orbital order this leads to a large ferromagnetic exchange interaction for two out of four Mn2+ --Mn3+ pairs.