Three-magnon bound states in the two-dimensional isotropic and anisotropic Heisenberg ferromagnet

The existence is shown of bound complexes of three magnons in a two-dimensional simple cubic Heisenberg ferromagnet. The Heisenberg spin hamiltonian is replaced by Dyson's boson hamiltonian. The spurious features of this hamiltonian are treated explicitly. Using Faddeev's formalism, detailed calculations of the three-magnon bound state energy curves have been performed both for the isotropic and the longitudinally anisotropic ferromagnet. Attention is paid to the possibility of observing these three-magnon bound states experimentally.