  We present a strategy for the design of ferromagnetic materials with
exceptionally low magnetic hysteresis, quantified by coercivity. In this
strategy, we use a micromagnetic algorithm that we have developed in previous
research and which has been validated by its success in solving the "Permalloy
Problem" -- the well-known difficulty of predicting the composition 78.5% Ni of
lowest coercivity in the Fe-Ni system -- and by the insight, it provides into
the "Coercivity Paradox" of W. F. Brown. Unexpectedly, the design strategy
predicts that cubic materials with large saturation magnetization $m_s$ and
large magnetocrystalline anisotropy constant $\kappa_1$ will have low
coercivity on the order of that of Permalloy, as long as the magnetostriction
constants $\lambda_{100}, \lambda_{111}$ are tuned to special values. The
explicit prediction for a cubic material with low coercivity is the
dimensionless number $(c_{11}-c_{12}) \lambda_{100}^2/\kappa_1 = 81$ for
$\langle 100 \rangle$ easy axes. The results would seem to have a broad
potential application, especially to magnetic materials of interest in energy
research.
