Elastic constants and charge ordering inα′−NaV2O5

Abstract

We present the temperature dependence of shear and longitudinal elastic constants in ${\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{-}{\mathrm{NaV}}_{2}{\mathrm{O}}_{5}.$ For the longitudinal ${c}_{22}$ and ${c}_{33}$ modes we find anomalies at ${T}_{c}$ in contrast to the spin-Peierls substance ${\mathrm{CuGeO}}_{3}$ where only the longitudinal mode along the chain shows a pronounced anomaly at ${T}_{\mathrm{SP}}.$ The ${c}_{66}$ shear mode (propagation along the chain in b direction, polarization in a direction) shows strong softening of 12%. Such a large effect is absent for all shear modes in ${\mathrm{CuGeO}}_{3}.$ We can interpret this softening with a coupling of the ${\ensuremath{\varepsilon}}_{\mathrm{xy}}$ symmetry strain to the charge fluctuation of ${B}_{1g}$ symmetry. We give the possible low-temperature charge distribution.