We have made NMR studies of thin films of pure He-3 adsorbed on Grafoi
l. Such films were cooled to approximately 75 muK, an order of magnitu
de colder than previous workers could attain. In particular, we measur
ed the magnetization of the solid second atomic layer, (M2), which dis
plays antiferromagnetic (AFM) behavior at low densities and ferromagne
tic (FM) behavior at high densities. At both AFM and FM densities, we
could measure M2 at temperatures well below the exchange energy (J). O
ur data at the AFM densities may support a proposed model of that phas
e. At the FM densities, we have found that M2 (T = 0) is linear in sec
ond layer density (rho2) and rises by a factor of approximately 7 with
a 6 % increase in rho2 and less than a factor of 2 increase in the ap
parent value of J, suggesting that the FM phase coexists with a lower
density AFM phase. Our high temperature (T > J) data also support such
a two phase model. We find that M2 follows the expected behavior for
a 2 dimensional Heisenberg ferromagnet down to T much less than J, the
first experimental observation of such behavior. We also confirmed th
e importance of k = 0 spin waves in determining the low temperature be
havior of such a system. The NMR lineshape in the FM phase also displa
yed shifts and broadening due to demagnetization effects which support
the model of two phase coexistence.