Tensor Properties of the Magneto-electric Coupling in Hexaferrites
Recent data reported on the magneto-electric coupling,α, 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 α depend on and, therefore, to what extent can α 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 α and material parameters was derived. We find that α is best described as a tensor property proportional to the product of the magnetostriction and piezoelectric strain tensors. Quantitative estimates of α are given for hexaferrites and composites.