The first magnetic force microscope (MFM) images of a series of epitax
ial magnetic thin films is presented. The films studied, Ni/Cu/Si(001)
capped by 2 nm of Cu, exhibit perpendicular magnetization over an exc
eptionally broad Ni thickness range 2 < h < 14 nm. The Ni domain struc
ture shows a sharp transition to a finer length scale above a finite c
ritical thickness of order 9 nm. The average force measured by the MFM
tip reflects this refinement in domain structure. Micromagnetic theor
y, combined with our measurements of K-eff(h), provides the first quan
titative description for these general but previously unexplained phen
omena.