Origin of the spin gap in sodium vanadium bronze Na9V14O35

The cause for the spin gap of Na9V14O35 was examined by identifying its spin dimers, calculating their spin orbital interaction energies and then finding a model spin Hamiltonian appropriate for Na9V14O35. In essence, the spin exchange interactions in the V10O30 chains of Na9V14O35 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.