We investigate the bulk magnetic, electron paramagnetic resonance, and magneto-optical properties of {Ni4Mo12}, a magnetic molecule with antiferromagnetically coupled tetrahedral Ni II in a diamagnetic molybdenum matrix. The low-temperature magnetization exhibits steps at irregular field intervals, a result that cannot be explained using a Heisenberg model even if it is augmented by magnetic anisotropy and biquadratic terms. Allowing the exchange and anisotropy parameters to depend on the magnetic field provides the best fit to our data, suggesting that the molecular structure (and thus the interactions between spins) may be changing with applied magnetic field.

The tetrameric Ni(II) spin cluster Ni4Mo12 has been studied by INS. The data were analyzed extensively in terms of a very general spin Hamiltonian, which includes antiferromagnetic Heisenberg interactions, biquadratic 2-spin and 3-spin interactions, a single-ion magnetic anisotropy, and Dzyaloshinsky-Moriya interactions. Some of the experimentally observed features in the INS spectra could be reproduced, however, one feature at 1.65 meV resisted all efforts. This supports the conclusion that the spin Hamiltonian approach is not adequate to describe the magnetism in Ni4Mo12. The isotropic terms in the spin Hamiltonian can be obtained in a strong-coupling expansion of the Hubbard model at half-filling. Therefore detailed theoretical studies of the Hubbard model were undertaken, using analytical as well as numerical techniques. We carefully analyzed its abilities and restrictions in applications to molecular spin clusters. As a main result it was found that the Hubbard model is also unable to appropriately explain the magnetism in Ni4Mo12. Extensions of the model are also discussed.PACS. 75.50.Xx Molecular magnets -75.10.Dg Crystal-field theory and spin Hamiltonians -33.15.Kr Electric and magnetic moments (and derivatives), polarizability, and magnetic susceptibility

The magnetic properties of the tetrahedral 'Ni 4 ' molecule are discussed in terms of the Heisenberg model, with magnetic anisotropy terms included, and on the basis of first-principle calculations within the density functional theory. It is shown that the isotropic Heisenberg model does not provide an adequate description of magnetization at low temperatures, and the inclusion of single-site anisotropy terms does not help to improve the situation. We assume that the magnetostriction of the molecule and, hence, the dependence of the interatomic coupling parameters on the magnetization may be important for an adequate description of the magnetic properties. The first-principle calculations confirm the system's general preference for antiferromagnetic coupling, as well as the failure of the isotropic Heisenberg model. A conjugated-gradient search for the relaxed structure of the 'Ni 4 ' molecule in ferromagnetic and antiferromagnetic configurations did not show any clear tendency to diversification of the interatomic distances. These calculations, however, have not yet included the spin-orbit coupling, which can be essential for analysing the effects of magnetostriction.