Grain size dependence of coercivity and permeability innanocrystalline ferromagnets

Amorphous ribbons of composition Fe_74.5-xCu_xNb₃Si_13.5B₉ (x=0, 1 at.%) have been annealed between about 500°C and 900°C. This produced a series of crystallized samples with grain sizes between about 10 nm and 300 nm and with coercivities H _c and initial permeabilities μ_i varying over several orders of magnitude. The best soft magnetic properties (H _c≈0.01 A/cm and μ_i≈80×10³ ) were observed for the smallest grain sized of about 10 nm. With increasing grain size D, coercivity steeply increases following a D⁶-power law (up to D≈50 nm). H_c then runs through a maximum of H_c≈30 A/cm and decreases again for grain sizes above 150 nm according to the well-known 1/D law for polycrystalline magnets. The initial permeability was found to vary in a similar manner, essentially being inversely proportional to coercivity. The variation of the soft magnetic properties with the average grain size is discussed and compared with the predictions of the random anisotropy model and other theories for the magnetization reversal