We have determined the magnetic phase diagram of Dy as a function of e
xpitaxial strain epsilon, applied field H, and temperature T. YxLu1-x
alloys were employed as templates to clamp the films at selected strai
ns. The separate roles of epitaxial clamping and strain are identified
for the first time. There is a clearly defined transition as the stra
in is changed at low temperature from the clamped helical phase to the
ferromagnetic phase. The transition is modeled by a linear coupling t
reatment of the magnetoelastic strains.