Reversible and irreversible magnetostriction of untwinned YBa$_2$Cu$_3$O$_{6.999}$ single crystals

We present anisotropic magnetostriction measurements of untwinned $YBa_2 Cu_3 O_{6.999} $ single crystals between 40 K and 150 K and in fields up to 10 T applied along the c-axis. The isothermal magnetostriction, which probes the pressure dependence of the magnetization, is nearly reversible above 55 K, which allows a thermodynamic analysis of the data. These data are used to derive the uniaxial pressure dependences of $T_c $, the thermodynamical critical field $H_c^o $and the electronic specific heat coefficient$\gamma _{electronic} $. The data also provide a unambiguous measure of the broadened$H_{c2} $, which shows excellent 3D-XY scaling. Below 55 K and above 6-8 T, the magnetostriction becomes irreversible due to increased flux pinning at the Bose-glass to vortex-glass transition of the vortex matter. In contrast to the magnetization, which shows the typical monotonic peak effect, the irreversible magnetostriction exhibits reproducible fine structure within the transition region. This may be due to nucleation of large vortex domains in the crystal and points to a first-order phase transition.