Two-Magnon Bound States in the Heisenberg Ferromagnet with Anisotropic Exchange and Uniaxial Anisotropy Energies

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Abstract
An exact theory for the two-magnon bound state problem in the Heisenberg ferromagnet with arbitary spin S and arbitrary dimensionality is developed at absolute zero temperature. The Hamiltonian which describes the system is assumed to include a nearest neighboring anisotropic exchange interaction and a one-ion type anisotropy energy of the form of -DS2z (D > 0). We are interested in the S ≧ 1 cases where, besides the previous BHWF(Bethe-Hanus-Wortis-Fukud)-type two-magnon bound state, there exists another type of two-magnon bound state in which the amplitude for finding two spin-deviations at the same site is maximum. In the case of a spin-1 ferromagnet this new single-ion type two-magnon bound state may be called the Ising-type two-magnon bound state. It is found that, when the value of D is sufficiently large, the single-ion type two-magnon bound state exists for each value of K (the total momentum of the magnon pair) inside the first Brillouin zone. In the S = 1 case the Ising-type two-magnon bound state becomes the first excited state of the system for much laarger values of D. A brief discussion concerning the ground state of the system described by our Hamiltonian is also given. It is shown that for the S ≧ 1 cases, even when the minimum excitation energy of the single magnon state is positive, there exists the case where the state in which all spins point in the positive (or negative) z direction is unstable. Furthermore, an application of the present theory is made to anhydrous ferrous chloride with the assumption that this substance is a two-dimensional triangular spin-1 ferromagnet.

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