Power-law behavior of coercivity in nanocrystalline magnetic alloys with grain-size distribution

Coercivity of nanocrystalline magnetic alloys depends on the grain size D according to a power law H_c ∝ Dⁿ with n from 2 to 6. The law H_c ∝ D⁶ is derived based on the random magnetic anisotropy model and is clearly manifested in experimental studies of some Finemet type alloys. In this letter using computer modeling it is demonstrated that a power-law behavior with the exponent n less than 6 can be due to a grain-size distribution. An increase of grain size variance results in a decrease of the exponent from 6 to the value of about 3.