We study the elementary excitations for a multilayer of spins represented by a Heisenberg ferromagnet with nearest-neighbor and next-nearest-neighbor exchange. In addition to the bulk modes, and the usual monotonic surface ones characterized by an exponential decay of the amplitude of the spin fluctuations, we find for opportune conditions other localized modes that present a π phase variation when passing from a layer to the adjacent one. Furthermore we show that the surface-plane magnetization is much more affected by the surface modes in a film than in a semi-infinite system. Also the effects of surface single-ion anisotropies and of dipolar interactions are investigated using the Green’s-function method. Some analytical expressions are obtained for the energy of the lowest mode of the multilayer, which makes it possible to find the dependence on the number of layers N. Finally, we derive a formal expression for the magnetization profile which is valid for systems with a nondiagonal quadratic boson Hamiltonian.

• Received 15 June 1992

DOI:https://doi.org/10.1103/PhysRevB.46.8312