Dzyaloshinskii-Moriya interaction in NaV$_2$O$_5$: a microscopic study
  We present a unified account of magnetic exchange and Raman scattering in the quasi-one-dimensional transition-metal oxide NaV$_2$O$_5$. Based on a cluster-model approach explicit expressions for the exchange integral and the Raman-operator are given. It is demonstrated that a combination of the electronic-structure and the Dzyaloshinskii-Moriya interaction, allowed by symmetry in this material, are responsible for the finite Raman cross-section giving rise to both, one- and two-magnon scattering amplitudes. 
Roser Valenti, Claudius Gros and Wolfram Brenig