Electronic and spin structures of polyoxometalate V₁₅ from a first-principles non-collinear molecular-magnetism approach

The results of first-principles calculations of the electronic structure of a spin-frustrated V₁₅ cluster with the use of a generalized density functional scheme that allows non-collinear spin configurations are presented. By using the results of these calculations, it was possible to determine a Heisenberg-Dirac-Van Vleck (HDVV) Hamiltonian with 21 exchange coupling parameters that link the V ions with predominant spin density and the ligands that carry partially transferred spin density. The numerical procedure is based on a least-squares fit of the results obtained by deviation of the direction of the magnetic moment on each atom around the energy minimum. The energy pattern was found from the effective HDVV Hamiltonian acting in the restricted spin space of the V ions by the application of the irreducible tensor operators (ITO) technique. Comparisons of the energy pattern with that obtained with the isotropic exchange models conventionally used for the analysis of this system and with the results of non-collinear spin structure calculations show that our complex investigations provide a good description of the pattern of the spin levels and spin structures of the nanomagnetic V₁₅ cluster. The results are discussed in view of the general problem of spin frustration related to the orbital degeneracy of the antiferromagnetic ground state.