Elastic constants and charge ordering inα′−NaV2O5

Abstract

We present the temperature dependence of shear and longitudinal elastic constants in ${\alpha }^{\prime }-{\mathrm{NaV}}_2{\mathrm{O}}_5.$ 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 ${\varepsilon }_{\mathrm{xy}}$ symmetry strain to the charge fluctuation of $B_{1g}$ symmetry. We give the possible low-temperature charge distribution.