Electron-phonon and spin-phonon coupling in NaV${}_2$O${}_5$: charge fluctuations effect

We show that the asymmetric crystal environment of the V site in the ladder compound NaV${}_2$O${}_5$ leads to a strong coupling of vanadium 3d electrons to phonons. This coupling causes fluctuations of the charge on the V ions, and favors a transition to a charge-ordered state at low temperatures. In the low temperature phase the charge fluctuations modulate the spin-spin superexchange interaction, resulting in a strong spin-phonon coupling.