We have measured the magnetization of the ferromagnetic second layer o
f pure He-3 films adsorbed on Grafoil down to 0.075 mK. The zero-tempe
rature magnetization is linear in second layer density (rho2) and rise
s by a factor of approximately 7 with a 6% increase in rho2 and less t
han a factor of 2 increase in the apparent exchange energy, indicating
that the ferromagnetic phase coexists with a lower density phase. Thi
s is the first experiment to measure the low-temperature limiting magn
etization of a 2D Heisenberg ferromagnet. Our data may also support El
ser's model of a registered antiferromagnetic phase at lower rho2.