He.*

We experimentally study the metastability of the A phase of superfluid ³He, as either temperature (T) or pressure (P) is varied. We find significant supercooling, with the A-B transition occurring well below the temperature of the thermodynamic phase boundary in bulk. The observed transition in two chambers (separated by a 1.1 μm tall channel) shadows the thermodynamic A-B line in the T-P plane but extends below the polycritical point and terminates in the B phase (and not at T_c). We find significant path dependence (memory effect) in the metastability: When we sweep pressure at fixed temperature, the region of metastable A is larger than when we sweep temperature at fixed pressure. We find U-shaped depressurizing-cooling-pressurizing paths in the T-P plane which enable the metastable A phase to exist well below the polycritical point at 21.2 bar that cannot be reached by a temperature sweep. While cooling at constant pressure, we observe A-B transitions down to 20.85 bar, wheras while depressurizing, A-B transitions are seen down to 19.5 bar. Ongoing experiments in a 50 G field show unexpected behavior. The measurements highlight the role of surfaces in nucleation and the memory effect.