Abrupt dimensionality crossover in thin-film ferromagnets: Quantum size effect

We report experimental results which show that the order parameter β, which determines the long-range (spin) ordering in magnetic thin films [M∝(1−T/TC)β], changes abruptly due to a crossover in dimensionality at different thicknesses in Ni(100), Ni(110), and Ni(111) films. We argue that the different critical thicknesses arise from finite-size quantization energies of the (spin) excitations, which are dependent on the magnitudes of associated wave vectors spanning the different crystallographic directions of the fcc Fermi surface. Experimental data on Ni alloys support this view.