Magnetoelastic couplings in the distorted diamond-chain compound azurite

Abstract

We present results of ultrasonic measurements on a single crystal of the distorted diamond-chain compound azurite ${\mathrm{Cu}}_{3}$(${\mathrm{CO}}_{3}$)${}_{2}$(OH)${}_{2}$. Pronounced elastic anomalies are observed in the temperature dependence of the longitudinal elastic mode ${c}_{22}$ which can be assigned to the relevant magnetic interactions in the system and their couplings to the lattice degrees of freedom. From a semiquantitative analysis of the magnetic contribution to ${c}_{22}$ the magnetoelastic coupling $G=\ensuremath{\partial}{J}_{2}$/$\ensuremath{\partial}{\ensuremath{\epsilon}}_{b}$ can be estimated, where ${J}_{2}$ is the intradimer coupling constant and ${\ensuremath{\epsilon}}_{b}$ the strain along the intrachain $b$ axis. We find an exceptionally large coupling constant of $|G|\ensuremath{\sim}$ 3650 K highlighting an extraordinarily strong sensitivity of ${J}_{2}$ against changes of the $b$-axis lattice parameter. These results are complemented by measurements of the hydrostatic pressure dependence of ${J}_{2}$ by means of thermal expansion and magnetic susceptibility measurements performed both at ambient and finite hydrostatic pressure. We propose that a structural peculiarity of this compound, in which ${\mathrm{Cu}}_{2}$${\mathrm{O}}_{6}$ dimer units are incorporated in an unusually stretched manner, is responsible for the anomalously large magnetoelastic coupling.