Following the recent discussion on the puzzling nature of the interactions in the nanotubular system ${\mathrm{Na}}_2{\mathrm{V}}_3{\mathrm{O}}_7$, we present a detailed ab initio microscopic analysis of its electronic and magnetic properties. By means of a nontrivial downfolding study we propose an effective model in terms of tubes of nine-site rings with the geometry of a spin-diamond necklace with frustrated inter-ring interactions. We show that this model provides a quantitative account of the observed magnetic behavior.

• Received 23 September 2004

DOI:https://doi.org/10.1103/PhysRevLett.95.107201