Magnetic equation of state for 3He in thin 3He-4He superfluid films

We examine the thermodynamics of a two-dimensional Fermi gas model describing adsorbed 3He in a thin superfluid 4He film. We show that the magnetic steps seen in experiment are a simple manifestation of the T=0 K equation of state and that the thermal stability of the steps is determined by the larger of Δε/2, one-half of the level spacing, and μmH0, the magnetic energy. We derive the conditions under which there exist points in the phase space (termed invariant points) through which all low-temperature isotherms pass exponentially close. The calculated invariant points for the magnetic susceptibility versus coverage are in good agreement with experiment. We calculate the magnetic susceptibility and show that it should exhibit a step-like structure versus 3He coverage similar to that of the magnetization