Exchange Parameters in the TCNE-based Magnets as Estimated with use of the Effective Hamiltonian Crystal Field Method

Estimates of the exchange interaction parameter (J) between electronic magnetic momenta residing in the d-shells of several divalent first row transition metal ions, and those residing on the [TCNE]$^-$. anion-radicals (TCNE = tetracyanoethylene) that are bonded to the metal ion are obtained by the use of the EHCF method in the cluster approximation. The clusters geometry was set according to that observed for Mn$^{II}$(TCNE)$_{1/2}$(I$_3$)$_{1/2}$ and M$^{II}$(TCNE)(C$_4$(CN)$_8$)$_{1/2}$ (M = Fe, Mn) with the [TCNE]$^{-.}$. For the Mn$^{II}$(TCNE)$_{1/2}$(I$_3$)$_{1/2}$ two cluster types are considered: one with the geometry corresponding to [TCNE]$^{-.}$ in the two-dimensional layer, and another connecting the layers. For M$^{II}$(TCNE)(C$_4$(CN)$_8$)$_{1/2}$ only the layer position of the [TCNE]$^{-.}$ is considered. In all cases the LUMO (singly filled in the material) is predominantly concentrated on the ethylenic C-C bond and is antibonding. The J value for the Mn$^{II}$(TCNE)$_{1/2}$(I$_3$)$_{1/2}$ layer is at least as twice as strong as one for the similar geometry for M$^{II}$(TCNE)(C$_4$(CN)$_8$)$_{1/2}$. The correct order of magnitude of the calculated exchange parameters, as compared with those extracted from experimentsindicates the general validity of this approach. However, the direct comparison of these J values with the critical temperatures is not possible since these latter heavily depend on details of the interlayer coupling not available through the EHCF procedure. In order to get more information on the geometry dependence of the exchange parameters, the dependence on the tilt angle of the TCNE with respect to the plane formed by the metal ions and four equatorial NCMe groups was investigated. In all cases, a remarkably strong dependence, having different trends depending on the number of electrons in the d-shells of respective transition metal ions was observed.