  A parametrized spin model was recently introduced and intended for
one-dimensional ferromagnets with a deformable Zeeman energy. This model is
revisited and given more realistic interpretation in terms of a model for
ferromagnetic systems with nonconvex anisotropies. A main virtue of the
improved form is its exact reduction to the discrete Remoissenet-Peyrard model,
i.e. a parametrized version of the Takeno-Homma's discrete sine-Gordon model.
The spin-wave phase of the improved parametrized spin model is investigated
assuming both harmonic and anharmonic excitations. Intrinsic-self-localized
modes, regarded as zone-boundary breather spin waves, are pointed out by
simulating the nonlinear difference equations describing the spin equilibrium
positions in the chain, and are shown to exist irrespective of values of the
model parameter. Domain-wall textures of the model are also numerically
examined in terms of kink solitons and with regard to the parametrization.
