Chapter 1 - Centered System Magnons

Abstract

This chapter presents two simple models of magnons in centered systems. The first model represents N, with N ≥ 2, electron spins pointing in the same space direction and situated at different space positions. The first of these spins is in the center of a circle. The others are on this circle and are the surface of this system. This model uses the Heisenberg interaction Hamiltonian. The second model uses the long-wavelength approximation of this Hamiltonian. These models present degenerate resonant subsystem states, localized each on two of the N − 1 system constituents. They show also trapping, isolation effects, degenerate surface mode behaviors, and so on. A transposition of magnons to phonons is presented then, as an example of how these excitation models are similar. Such transpositions are one of the aim of this interface transmission book series. Some general perspectives are finally given: bound in continuum states, model tuning, breaking symmetry effects, possible transpositions to other waves: plasmons, electrons, photons, polaritons, and so on.