  Magnetic coercivity is often viewed to be lower in alloys with negligible (or
zero) values of the anisotropy constant. However, this explains little about
the dramatic drop in coercivity in FeNi alloys at a non-zero anisotropy value.
Here, we develop a theoretical and computational tool to investigate the
fundamental interplay between material constants that govern coercivity in bulk
magnetic alloys. The two distinguishing features of our coercivity tool are
that: (a) we introduce a large localized disturbance, such as a spike-like
magnetic domain, that provides a nucleation barrier for magnetization reversal;
and (b) we account for magneto-elastic energy -- however small -- in addition
to the anisotropy and magnetostatic energy terms. We apply this coercivity tool
to show that the interactions between local instabilities and material
constants, such as anisotropy and magnetostriction constants, are key factors
that govern magnetic coercivity in bulk alloys. Using our model, we show that
coercivity is minimum at the permalloy composition (Fe-21.5Ni-78.5) at which
the alloy's anisotropy constant is not zero. We systematically vary the values
of the anisotropy and magnetostriction constants, around the permalloy
composition, and identify new combinations of material constants at which
coercivity is small. More broadly, our coercivity tool provides a theoretical
framework to potentially discover novel magnetic materials with low coercivity.
