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.
Special features of the crystal field splitting of $d-$levels in the transition metal compounds with the small or negative charge-transfer gap $Delta_{CT}$ are considered. We show that in this case the Coulomb term and the covalent contribution to th
e $t_{2g} - e_g$ splitting have different signs. In order to check the theoretical predictions we carried out the ab-initio band structure calculations for Cs$_2$Au$_2$Cl$_6$, in which the charge-transfer gap is negative, so that the $d-$electrons predominantly occupy low-lying bonding states. For these states the $e_g$-levels lie below $t_{2g}$ ones, which demonstrates that at least in this case the influence of the $p-d$ covalency on the total value of the crystal field splitting is stronger than the Coulomb interaction (which would lead to the opposite level order). We also show that the states in conduction band are made predominantly of $p-$states of ligands (Cl), with small admixture of $d-$states of Au.
The experimental data available up to date in literature corresponding to the paramagnetic - spin density wave transition in nonsuperconducting LaOFeAs are discussed. In particular, we pay attention that upon spin density wave transition there is a r
elative decrease of the density of states on the Fermi level and a pseudogap formation. The values of these quantities are not properly described in frames of the density functional theory. The agreement of them with experimental estimations becomes more accurate with the use of fixed spin moment procedure when iron spin moment is set to experimental value. Strong electron correlations which are not included into the present calculation scheme may lead both to the decrease of spin moment and renormalization of energy spectrum in the vicinity of the Fermi level for correct description of discussed characteristics.
Effects of Coulomb correlation on LaOFeAs electronic structure have been investigated by LDA+DMFT(QMC) method. The calculation results show that LaOFeAs is in the regime of intermediate correlation strength with significant part of the spectral densi
ty moved from the Fermi energy to Hubbard bands. However the system is not on the edge of metal insulator-transition because increase of the Coulomb interaction parameter value from $U$=4.0 eV to $U$=5.0 eV did not result in insulator state. Correlations affect different d-orbitals not in the same way. $t_{2g}$ states ($xz,yz$ and $x^2-y^2$ orbitals) have higher energy due to crystal filed splitting and are nearly half-filled. Their spectral functions have pseudogap with Fermi energy position on the higher sub-band slope. Lower energy $e_g$ set of d-orbitals ($3z^2-r^2$ and $xy$) have significantly larger occupancy values with typically metallic spectral functions.
Combining infrared reflectivity, transport, susceptibility and several diffraction techniques, we find compelling evidence that CaCrO3 is a rare case of a metallic and antiferromagnetic transition-metal oxide with a three-dimensional electronic struc
ture. LSDA calculations correctly describe the metallic behavior as well as the anisotropic magnetic ordering pattern of C type: The high Cr valence state induces via sizeable pd hybridization remarkably strong next-nearest neighbor interactions stabilizing this ordering. The subtle balance of magnetic interactions gives rise to magneto-elastic coupling, explaining pronounced structural anomalies observed at the magnetic ordering transition.
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-ga
p 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.
