Nonlinear localized magnetization wave in a ferromagnet as a bound state of a large number of magnons

A new type of exact solution is found for the one-dimensional nonlinear equations describing magnetization dynamics in anisotropic ferromagnets. The two-parameter solution has the shape of a localized wave moving with a constant velocity V, in which the magnetization vector precesses with a fixed frequency ω'. The long-wave approximation does not impose any restrictions on the magnitude of the velocity V. The quantum analogue of such a wave is shown to be a bound state of a large number of magnons. The wave parameters, V and ω, are expressed through the integrals of motion P, the magnetization wave momentum, and N, the total number of spin deviations in the wave. The wave energy E is calculated as a periodic function of P. The quasiclassical solution is compared with the result obtained for the exactly solvable quantum problem. It is concluded that the localized waves in a ferromagnet can be observed experimentally.

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