The effect of the spontaneous magnetization in the grain boundary region on the magnetic softness of nanocrystalline materials

The relationship between the mean hyperfine field of the residual intergranular amorphous phase 〈B_hf〉 and the coercivity H_c in various nanocrystalline soft magnetic samples has been investigated in order to clarify the effect of the spontaneous magnetization in the grain boundary region on their magnetic softness. Nanocrystalline samples with various 〈b_hf〉 values were prepared by annealing an amorphous Fe₉₁Zr₇B₂ precursor for periods of 60 s-108 ks, at temperatures of 823-973 K. H_c shows a clear tendency to decrease with increasing 〈B_hf〉 or decreasing volume fraction of the residual amorphous phase. These effects of the residual amorphous phase on H_c are well understood within the framework of our extended two-phase random anisotropy model where both the exchange stiffness constant and volume fraction of the grain boundary phase are relevant to the exchange correlation length. Our results indicate that the exchange stiffness constant of the intergranular region varies as the square of the spontaneous magnetization of the residual amorphous phase. A small exchange stiffness constant on the order of 10^-13 J/m is predicted for the residual amorphous phase in the Fe-Zr-B alloy.