Origin of the spin gap in sodium vanadium bronze Na 9V 14O 35

The cause for the spin gap of Na ₉V ₁₄O ₃₅ was examined by identifying its spin dimers, calculating their spin orbital interaction energies and then finding a model spin Hamiltonian appropriate for Na ₉V ₁₄O ₃₅. In essence, the spin exchange interactions in the V ₁₀O ₃₀ chains of Na ₉V ₁₄O ₃₅ are equivalent to those of the fused chain of 10-node rings, where each node represents a spin site and nearest-neighbor spin exchange interactions are antiferromagnetic. To a first approximation, the energy gap between the ground and first excited states of this fused chain is the same as that of a 10-node ring. In general, the fused chain of n-node rings with even n is expected to have a spin gap.