Spin dynamics and surface magnons in antiferromagnetic monoxide lattices along  and  directions
A theoretical model to study the localized surface spin states, along two different directions  and 
is presented. The model is mainly used to analyze the antiferromagnetic monoxide network of spins, using
the matching method theory. The magnon spectrum is determined by numerical calculations based on the
Landauer-B¨ uttiker formalism of the scattering matrix. Our simulation results show the interference effects
between magnon states of the monoxide continuum and the localized magnon modes created by the surface
region with Fano resonance characteristics.
Additionally, the results are obtained by computing different possibilities of the magnetic parameters, characterizing
the antiferromagnetic and the ferromagnetic couplings between spin sites on the monoxide structures. The
interactions between the refection and the propagating spin modes describe several types of oscillations. We
notice that the magnetic spectra at the surface of monoxide lattices are proportional to the magnetic coupling
and the spin intensity of the antiferromagnetic lattices.
Simulations and numerical calculations relating to spin excitations in monoxide lattices make it possible to extract
useful information for the elaboration of sensors for specific applications.