Magnetization of underdoped YBa$_2$Cu$_3$O$_{y}$ above the irreversibility field

Torque magnetization measurements on YBa$_2$Cu$_3$O$_{y}$ (YBCO) at doping $y=6.67$($p=0.12$), in DC fields ($B$) up to 33 T and temperatures down to 4.5 K, show that weak diamagnetism persists above the extrapolated irreversibility field $H_{\rm irr} (T=0) \approx 24$ T. The differential susceptibility $dM/dB$, however, is more rapidly suppressed for $B\gtrsim 16$ T than expected from the properties of the low field superconducting state, and saturates at a low value for fields $B \gtrsim 24$ T. In addition, torque measurements on a $p=0.11$ YBCO crystal in pulsed field up to 65 T and temperatures down to 8 K show similar behaviour, with no additional features at higher fields. We discuss several candidate scenarios to explain these observations: (a) superconductivity survives but is heavily suppressed at high field by competition with CDW order; (b) static superconductivity disappears near 24 T and is followed by a region of fluctuating superconductivity, which causes $dM/dB$ to saturate at high field; (c) the stronger 3D ordered CDW that sets in above 15 T may suppress the normal state spin susceptibility sufficiently to give an apparent diamagnetism of the magnitude observed.