Studies of the Superfluid Phases of Helium Three and the Magnetization of Thin Solid Films of Helium Three

We have studied the transition between the A and B phases in superfluid ^3He, which is inhibited by the large surface energy between the two phases. The two phases share a common transition temperature (T_{rm c}) from the normal phase, but at low magnetic fields the A phase is preferred only in a narrow temperature region just below T_{rm c}. The transition was studied in A phase samples which were confined by the smooth surfaces of fused silica tubes and isolated from rough surfaces by a region of high magnetic field. In this sample cell, the transition in low magnetic fields exhibited dramatic supercooling down to 0.15T_ {rm c}. The lifetime, tau, of the metastable deeply supercooled A phase showed a temperature and magnetic field dependence consistent with Leggett's baked Alaska model based on nucleation of the B phase by ionizing radiation. Furthermore, a flux of gamma radiation or of thermal neutrons incident on the samples strongly reduced tau. Monte Carlo simulations also showed reasonable agreement with the observed decrease in tau in the presence of the gamma source. We also measured the A phase NMR frequency shift in the low temperature limit, confirming the theoretically predicted low temperature behavior of the A phase. Combined with new measurements of the shift near T_ {rm c}, these data allowed us to make the first experimental estimates of the BCS cutoff energy in ^3He and of the zero temperature A phase energy gap. We have also made NMR studies of thin films of ^3He. Such films were cooled to {~}75muK, an order of magnitude colder than previous measurements. The magnetization (M_2) of the solid second atomic layer displays ferromagnetic behavior at high densities. At such densities, M_2(T = 0) is linear in second layer density (rho_2) and rises by a factor of ~7 with a 6% increase in rho_2 suggesting that the ferromagnetic phase coexists with a lower density phase. The high temperature magnetization and the NMR frequency are also consistent with this model of two phase coexistence. We also find that M_2 follows the temperature dependence for a 2 dimensional Heisenberg ferromagnet down to T << J.