Metastable films of fcc Fe epitaxed to Cu(001) show unusual ferromagnetic properties(1). Changes in the lattice volume occur with film thickness in the 1 to 5 monolayer range, reflecting changes in the magnitude of the spin moments and the magnetic exchange coupling. The associated uniaxial strain is manifest in strong magnetic anisotropy, layer by layer lattice expansion, phonon softening, and surface layer atomic reconstructions. We present LEED results of a detailed structural investigation, neutron reflectance measurements of the spin moments, surface magneto-optic Kerr effect studies of the magnetic anisotropy, and angle resolved photoemission of the electronic states. The observed effects are due to the strain-related kinetic energy associated with the formation of the atomic spin moments, predicted by spin-density-functional calculations of bulk fcc Fe(2).