Random magnetocrystalline anisotropy in two-phase nanocrystalline systems

In order to clarify the effect of the exchange stiffness in the intergranular phase on the exchange correlation length ${(L}_{\mathrm{ex}})$ and the random magnetocrystalline anisotropy $\left(〈K_1〉\right)$ of two-phase nanocrystalline soft magnetic materials, the hyperfine fields ${(}^{57}\mathrm{Fe}),$ coercivity and remanence to saturation ratio of nanocrystalline ${\mathrm{Fe}}_{91}{\mathrm{Zr}}_7{\mathrm{B}}_2$ have been studied in the temperature range from 77 to 473 K. We observe that the coercivity of the nanocrystalline ${\mathrm{Fe}}_{91}{\mathrm{Zr}}_7{\mathrm{B}}_2$ in the temperature range near the Curie temperature of the intergranular amorphous phase ${(T}_C^{\mathrm{am}})$ varies as approximately the $-6\mathrm{th}$ power of the mean hyperfine field of the intergranular phase. This indicates that $L_{\mathrm{ex}}$ near $T\sim T_C^{\mathrm{am}}$ is mostly governed by the exchange stiffness of the intergranular amorphous phase and $〈K_1〉$ of the Fe-Zr-B sample should vary as the $-3\mathrm{rd}$ power of the exchange stiffness constant in the intergranular region. These results are explained well by our extended two-phase random anisotropy model in which two local exchange stiffness constants are considered for the spin-spin correlation within $L_{\mathrm{ex}}.$