Derivation of Magnetostriction and Anisotropic Energies for Hexagonal, Tetragonal, and Orthorhombic Crystals

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Abstract
In order to determine the measurements necessary to characterize the anisotropic energy and the saturation magnetostriction in hexagonal cobalt, a phenomenological derivation has been given for the equations which characterize the effects. Out to fourth rank tensors, the results are the same as those for circular symmetry and it requires two constants to specify the anisotropic energy and four to specify the magnetostriction. When sixth rank tensors are evaluated, a characteristic hexagonal symmetry appears. It requires four constants to characterize the anisotropic energy and nine to characterize the magnetostriction. These constants can be measured by using two oriented slabs. Four of the constants can be determined by measurements parallel to the saturation magnetization, four when the magnetostriction is perpendicular to the magnetization and one when they are 45° apart.

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