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A ferromagnetic, ferroelectric, or ferroelastic crystal is called full or partial, according to whether all or not all but some of its orientation states are different in spontaneous magnetization vector, spontaneous polarization vector, or spontaneous strain tensor. In previous theories --- for nonmagnetic crystals --- the concept of "species" was introduced, a determination was made of all possible species of full ferroelectrics and of full ferroelastics, and those species were found in which ferroelectricity and ferroelasticity coexist and completely couple with each other. These theories are now extended to cover magnetic crystals in addition to nonmagnetic crystals and to cover the partial in addition to the full. A determination is made of all possible species of full ferromagnetics, partial ferromagnetics, full ferroelectrics, partial ferroelectrics, full ferroelastics, and partial ferroelastics, and it is found out in which of these species two or all of ferromagnetism, ferroelectricity, and ferroelasticity should couple completely or incompletely with each other.
Kêitsirô Aizu (Sat,) studied this question.