Magnetisation and the Irreversibility Line in Strongly Underdoped YBa$_2$Cu$_3$O$_{7-\delta}$

Torque magnetometry experiments were made on a high purity single crystal of YBa$_2$Cu$_3$O$_{6.354}$. The irreversibility line $H_{irr}(T)$ was measured and found to lie very low in field, with a high temperature end-point at 5~K, far below the superconducting $T_c$ of 12~K, and a steep upturn at the lowest temperatures. Considerable suppression of $H_{irr}(T)$ in the presence of a small AC magnetic field indicates that the irreversibilty line is distinct from a flux-lattice melting transition in this material. A second feature $H^*(T)$, observed in the magnetisation data at fields above $H_{irr}(T)$, was unaffected by a similar AC field. Torque measurements as a function of crystal orientation revealed a sharp lock-in transition at angles of field close to the $ab$-plane, and illustrate the high degree of anisotropy in this system at very low doping levels.