Charge Ordering and Spin Dynamics in ${\mathrm{NaV}}_2{O}_5$

We report high-resolution neutron inelastic scattering experiments on the spin excitations of ${\mathrm{NaV}}_2{\mathrm{O}}_5$. Below $T_c$, two branches with distinct energy gaps are identified. From the dispersion and intensity of the spin excitation modes, we deduce the precise zigzag charge distribution on the ladder rungs and the corresponding charge order: ${\Delta }_c\approx 0.6$. We argue that the spin gaps observed in the low- $T$ phase of this compound are primarily due to the charge transfer.