Solitary waves in elastic ferromagnets

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Abstract
It is shown, on the basis of the continuum equations of the magnetoelasticity of ferromagnetic crystals, that Bloch walls in an infinite crystal and Néel walls in a thin elastic film can be represented by ‘‘magnetoelastic’’ solitary waves. In the first case the solitary waves are solutions of a simple sine-Gordon equation in which the only alteration as compared to Enz’s case is a change in the reference length as a result of the presence of magnetostrictive internal strains. These solitary waves may therefore be true solitons. In the second case, in addition to the same effect resulting both from magnetostrictive internal strains and demagnetizing effects, the magnetic-spin orientation remains nonlinearly coupled to the elastic displacement polarized in the plane of the film. One therefore has to deal with a nonlinearly coupled system of a sine-Gordon or a double–sine-Gordon equation and two wave equations. Solitary-wave solutions are obtained in closed form for this system. These solitary waves, however, are not true solitons in that radiations always accompany the interactions of such two waves, as already shown in a parallel study concerning ferroelectric crystals.

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