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.
We report experimental results for nickel films which examine finite-size nanoscaling of the magnetic-order exponent β with temperature as a function of thickness. The data confirm the trends predicted by Monte Carlo calculations of an Ising spin lattice for thicknesses L much less than in-plane dimensions. A crossover in dimensionality D is seen in the magnetization M(T) at a rescaled reduced temperature txo, which delineates a change in the order parameter from three dimensional to two dimensional. This crossover temperature is a feature of ultrathin films over a wide range of thicknesses L.
We report an analysis of data on the thickness-dependent Curie temperatures TC of itinerant ferromagnetic thin films with variable range of spin interactions “tuned” by alloying transition metals. We observe that TC decreases with decreasing film thickness according to the finite-size effect power law for two-dimensional Ising thin films, down to a critical thickness R0, beyond which point TC reduces linearly with further decreasing thickness. The demarcation point scales with the range of spin interactions R0. The parameter R0 scales with the evolution of the magnetic moment on the Slater-Pauling curve. This analysis of ultrathin film data provides a measure of the effective range of spin interactions in ferromagnets and demonstrates that, when the dimension L reduces below the intrinsic interaction length R0, TC no longer follows the finite-size effect power law behavior.
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