  We propose a solution to the longstanding permalloy problem$-$why the
particular composition of permalloy, Fe$_{21.5}$Ni$_{78.5}$, achieves a
dramatic drop in hysteresis, while its material constants show no obvious
signal of this behavior. We use our recently developed coercivity tool to show
that a delicate balance between local instabilities and magnetic material
constants are necessary to explain the dramatic drop of hysteresis at 78.5% Ni.
Our findings are in agreement with the permalloy experiments and, more broadly,
provide theoretical guidance for the discovery of novel low hysteresis magnetic
alloys.
