  Recent data reported on the magneto-electric coupling,{\alpha}, of
hexaferrite materials is very high, and they have the potential to impact
future technologies in a major way. The fundamental question addressed in this
paper is what does {\alpha} depend on and, therefore, to what extent can
{\alpha} increase in future experiments. Mathematical formulation of a
microscopic theory would be rather complex, especially for a complex crystal
structure as the Z-type hexaferrite, for example. We have opted for a
thermodynamic argument in which a functional relationship between {\alpha} and
material parameters was derived. We find that {\alpha} is best described as a
tensor property proportional to the product of the magnetostriction and
piezoelectric strain tensors. Quantitative estimates of {\alpha} are given for
hexaferrites and composites.
