Existence conditions of surface spin waves in ferromagnetic nanowires and nanoparticles

A theoretical treatment of spin-wave excitations in ferromagnetic wires and particles in the presence of single-ion surface anisotropy is developed wi thin the framework of the matrix theory. Two different models of surface an isotropy are considered, one of which assumes the anisotropy axes are perpe ndicular to the surfaces (current model) and the other one with a single se lected axis for the whole system (Aharoni model). The results obtained indi cate the possibility of the existence of surface exchange spin waves in fer romagnetic nanowires and nanoparticles in both models. However, under assum ptions of the Aharoni model, this occurs only for the surface anisotropy of the proper sign (the single ion anisotropy constant at the surface of the wire or particle has to be negative, D <0), while under the assumptions of the current model, in the grains the surface states are always present, but -depending on the sign of D-they are localized at different faces. Therefor e, both models are hardly distinguishable when applied to wires, but essent ially nonequivalent when used to describe grains. It is suggested that reso nance experiments on small magnetic grains should point out which of these models can be applied. (C) 2001 American Institute of Physics.