Juan M. Clemente-Juan, Hanspeter Andres, Juan J. Borras-Almenar, Eugenio Coronado, Hans U. Güdel, Michael Aebersold, Gordon Kearly, Herma Büttner and Markus Zolliker
Magnetic Excitations in Polyoxometalate Clusters observed by Inelastic Neutron Scattering: Evidence for Ferromagnetic Exchange Interactions and Spin Anisotropy in the Tetrameric Nickel(II) Cluster [Ni₄(H₂O)₂(PW₉O₃₄)₂]^10- and Comparison with the Magnetic Properties.
J. Am. Chem. Soc. 121, 10021-10027 (1999)                 

Abstract: The ground-state properties of the tetranuclear Ni²⁺ cluster [Ni₄(H₂O)₂(PW₉O₃₄)₂]^10– were investigated by combining magnetic susceptibility and magnetization measurements with a detailed inelastic neutron scattering (INS) study on a fully deuterated sample of K₆Na₄[Ni₄(H₂O)₂(PW₉O₃₄)₂]·24H₂O. The temperature dependence of the magnetic susceptibility indicates a ferromagnetic coupling of the four constituent Ni²⁺ ions (s = 1), and a low-temperature magnetization study provides the magnitude of the S = 4 ground-multiplet splitting due to the single-ion anisotropy of the Ni²⁺ ions. Besides a more direct and precise determination of the anisotropic S = 4 ground-multiplet splitting, INS enabled the determination of excited spin multiplets. The best fit to the experimental energy level diagram was obtained by an isotropic Spin Hamiltonian with the inclusion of axial single-ion anisotropy: H=-2J(S₁S₃ + S₁S₄ + S₂S₃ + S₂S₄)-2J' S₁S₂ + D(S_z1² + S_z2²), where J = 0.83 meV, J' = 0.39 meV, D = 0.47 meV, and D' = 0.60 meV. Within this model the experimental intensities of the magnetic cluster excitations, their characteristic dependence on the scattering vector , as well as the temperature dependence of the magnetic susceptibility and the magnetization properties are reproduced.