Quantum and classical descriptions of weakly-bound magnon states in a ferromagnetic chain

We study the spatially localized excited states of a Heisenberg chain with the “easy plane” type of anisotropy. A classical description of this system is given in terms of the magnetization density. Magnetic solitons are shown to exist in the system, and can be quantized quasiclassically. Although the number of spin deviations in the system is not conserved, the quasiclassical expression for the soliton energy reduces to the expression for the energy of a bound state of a large number of magnons. Consequently, the well known result that from a quantum-mechanical point of view classical-field solitons are the bound state of a large number of magnons of this field can be generalized to systems where the number or particles is not conserved.

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