Magneto-elastic couplings in the distorted diamond-chain compound azurite

We present results of ultrasonic measurements on a single crystal of the distorted diamond-chain compound azurite Cu${}_3$(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 quantitative analysis of the magnetic contribution to $c_{22}$ the magneto-elastic coupling $G$ = $\mathrm{\partial }{J}_2$/$\partial \epsilon_b$canbedetermined,where$J_2$ is the intra-dimer coupling constant and ${ϵ}_b$ the strain along the intra-chain $b$ axis. We find an exceptionally large coupling constant of $\mathrm{\mid }G\mathrm{\mid }\sim ($3650 $\pm$ 150) 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 Cu${}_2$O${}_6$ dimer units are incorporated in an unusually stretched manner, is responsible for the anomalously large magneto-elastic coupling.