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 Hunds rule coupling and specific orbital order this leads to a large ferromagnetic exchange interaction for two out of four Mn2+ --Mn3+ pairs.

Electronic structure and magnetic properties of pyroxenes (Li,Na)TM(Si,Ge)2O6: novel low-dimensional magnets with 90 bonds

The results of the LSDA+U calculations for pyroxenes with diverse magnetic properties (Li,Na)TM(Si,Ge)$_2$O$_6$, where TM is the transition metal ion (Ti,V,Cr,Mn,Fe), are presented. We show that the anisotropic orbital ordering results in the spin-gap formation in NaTiSi$_2$O$_6$. The detailed analysis of different contributions to the intrachain exchange interactions for pyroxenes is performed both analytically using perturbation theory and basing on the results of the band structure calculations. The antiferromagnetic $t_{2g}-t_{2g}$ exchange is found to decrease gradually in going from Ti to Fe. It turns out to be nearly compensated by ferromagnetic interaction between half-filled $t_{2g}$ and empty $e_g$ orbitals in Cr-based pyroxenes. The fine-tuning of the interaction parameters by the crystal structure results in the ferromagnetism for NaCrGe$_2$O$_6$. Further increase of the total number of electrons and occupation of $e_g$ sub-shell makes the $t_{2g}-e_g$ contribution and total exchange interaction antiferromagnetic for Mn- and Fe-based pyroxenes. Strong oxygen polarization was found in Fe-based pyroxenes. It is shown that this effect leads to a considerable reduction of antiferromagnetic intrachain exchange. The obtained results may serve as a basis for the analysis of diverse magnetic properties of pyroxenes, including those with recently discovered multiferroic behavior.