HOW PECULIAR CAN THE TEMPERATURE-VARIATION OF MAGNETIC-ANISOTROPY BE - LIMITATIONS BY A GENERAL THEOREM

The variation of anisotropy constants is studied within the three-cons tant approximation to the anisotropy free energy. The anisotropy-flow concept for tracing the evolution of the system in the anisotropy spac e of the system is introduced. Unexpected features of the variation of anisotropy are uncovered for realistic values of the intrinsic parame ters e.g., two zero points for the first anisotropy con stants and, co rrespondingly, two successive reorientation transitions between phases with different easy axes of magnetization. The question of the ultima te possible peculiarity of variation of anisotropy and magnetostrictio n is addressed by formulating and proving a far-reaching theorem by vi rtue of which the superposition of p different functions with certain widely met properties may not have more than p - 1 zeroes or internal extrema.