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Conventional superexchange rules predict ferromagnetic exchange interactionbetween Ni(II) and M (M=Mo(V), W(V), Nb(IV)). Recent experiments show that insome systems this superexchange is antiferromagnetic. To understand thisfeature, in this paper we develop a microscopic model for Ni(II)-M systems andsolve it exactly using a valence bond approach. We identify the direct exchangecoupling, the splitting of the magnetic orbitals and the inter-orbital electronrepulsions, on the M site as the parameters which control the ground state spinof various clusters of the Ni(II)-M system. We present quantum phase diagramswhich delineate the high-spin and low-spin ground states in the parameterspace. We fit the spin gap to a spin Hamiltonian and extract the effectiveexchange constant within the experimentally observed range, for reasonableparameter values. We also find a region in the parameter space where anintermediate spin state is the ground state. These results indicate that thespin spectrum of the microscopic model cannot be reproduced by a simpleHeisenberg exchange Hamiltonian.Comment: 8 pages including 7 figure

physical review. b, condensed matter and materials physics

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Microscopic model for high-spin versus low-spin ground state in[Ni2M(CN)8](M=MoV,