Discrete breathers in classical spin lattices

Discrete breathers (nonlinear localized modes) have been shown to exist in various nonlinear Hamiltonian lattice systems. In the present paper, we study the dynamics of classical spins interacting via the Heisenberg exchange on spatial d-dimensional lattices (with and without presence of single-ion anisotropy). We show that discrete breathers exist for the cases when the continuum theory does not allow for their presence (easy-axis ferromagnets with anisotropic exchange and easy-plane ferromagnets). We prove the existence of localized excitations, using the implicit function theorem, and obtain necessary conditions for this existence. The most interesting case is the easy-plane one, which yields excitations with locally tilted magnetization. There is no continuum analog for such a solution and there exists an energy threshold for it, which is estimated analytically. We support our analytical results with numerical high-precision computations, including also a stability analysis for the excitations.