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Crystal and electronic structure of the room temperature organometallic ferrimagnet V(TCNE)$_2$. Analysis of numerical DoS and magnetic properties as related to orbital and spin-Hamiltonian models

We present a detailed analysis of the results of our numerical study of the crystal and electronic structure of the room temperature organometallic ferrimagnet of general composition V(TCNE)$_{x}$ with $% x\approx 2$. The results of the LSDA+$U$ study show that the experimentally determined structure complies with the magnetic measurements and thus can serve as a prototype structure for the entire family of the M(TCNE)$_{2}$ organometallic magnets. The results of the numerical study and of the magnetic experiments are interpreted using model Hamiltonians proposed here. This allowed us to obtain estimates of the critical temperature in three- and two-dimensional regimes and to give an explanation of the differences in behavior of probably isostructural V(TCNE)$_{2}$ and Fe(TCNE)$_{2}$ species.