The Hamiltonian of the V₁₅ Spin System from first-principles Density-Functional Calculations

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We report first-principles all-electron density-functional based studies of the electronic structure, magnetic ordering and anisotropy for the V₁₅ molecular magnet. From these calculations, we determine a Heisenberg Hamiltonian with four antiferromagnetic and one ferromagnetic coupling. We perform direct diagonalization to determine the temperature dependence of the susceptibility. This Hamiltonian reproduces the experimentally observed spin S=1/2 ground state and low-lying S=3/2 excited state. A small anisotropy term is necessary to account for the temperature independent part of the magnetization curve.