A solution to the permalloy problem—A micromagnetic analysis with magnetostriction

A long-standing puzzle in the understanding of magnetic materials is the “Permalloy problem,” i.e., why the particular composition of Permalloy, Fe 21.5 Ni 78.5, achieves a dramatic drop in hysteresis and concomitant increase in initial permeability, while its material constants show no obvious signal of this behavior. In fact, the anisotropy constant κ1 and the magnetostriction constants λ 100 , λ 111 all vanish at various nearby, but distinctly different, compositions than Fe 21.5 Ni 78.5. These compositions are in fact outside the compositional region where the main drop in hysteresis occurs. We use our newly developed coercivity tool [A. Renuka Balakrishna and R. D. James, Acta Mater. 208, 116697 (2021)] to identify a delicate balance between local instabilities and magnetic material constants that lead to a dramatic decrease in coercivity at the Permalloy composition Fe 21.5 Ni 78.5. Our results demonstrate that specific values of magnetostriction constants and anisotropy constants are necessary for the dramatic drop of hysteresis at 78.5% Ni. Our findings are in agreement with the Permalloy experiments and provide theoretical guidance for the development of other low hysteresis magnetic alloys.