Discrete breathers (nonlinear localised 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 Heisenberg exchange on spatial $d$-dimensional lattices (with and without the presence of single-ion anisotropy). We show that discrete breathers exist for 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 localised excitations using the implicit function theorem and obtain necessary conditions for their existence. The most interesting case is the easy-plane one which yields excitations with locally tilted magnetisation. There is no continuum analogue for such a solution and there exists an energy threshold for it, which we have estimated analytically. We support our analytical results with numerical high-precision computations, including also a stability analysis for the excitations.

15 pages, 12 figures