POLDER TENSOR GENERALIZATIONS
Evtikhov Mikhail G.
Kotel’nikov Institute of Radio Engineering and Electronics, Branch in Fryazino, Russian Academy of Ssience, http://fire.relarn.ru
141120 Fryazino, Moscow region, Russian Federation
Polder tensor describes the linear approximation in the high-frequency permeability of isotropic ferromagnets, magnetized to saturation by a field, directed along one of the axes. This tensor is used to describe the magnetic oscillations and waves (including spin waves) in ferromagnets and the films based on them [1-4]. As a mathematical tool that allows to record generalizations Polder tensor in a coordinate-independent form used dyadic (Kronecker product of vectors). Previously, this technique has been successfully used in the theory gyrotropy . There have been attempts to use his spin waves . Effectiveness of modern algebraic methods in physics can be increased by using an theorem proving in symbolic computation systems. In this paper isotropic ferromagnet Polder tensor generalized to arbitrary magnetization direction and written in a coordinate-independent form. On the basis of the results of , a more general coordinate- independent record high magnetic permeability tensor, taking into account the magnetic damping, inhomogeneous exchange and uniaxial anisotropy uniformly magnetized to saturation ferromagnets. Generalizations derived tensor Polder extend the capabilities of constructing models of magnetic oscillations and waves in ferromagnets and study them both numerical, and analytical methods. Discussed generalizations derived from the same principles, the same methods, so built with the help of their comparable model not only qualitatively but also quantitatively.
Keywords: spin waves Polder tensor, high magnetic permeability tensor, isotropic ferromagnets, uniaxial ferromagnets, dyadic, covariant method.
PACS: 02.10., 76.50.+g
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