Giant magnonic band gaps and defect modes in serial stub structures: application to the tunneling between two wires

In the frame of the long-wavelength Heisenberg model, we investigate the existence of giant gaps in the band structure of a comblike geometry composed of a one-dimensional magnonic waveguide along which N′ dangling side branches are grafted at N equidistant sites. These gaps originate not only from the periodicity of the system but also from the resonance states of the grafted branches (which play the role of resonators). The width of these gaps is sensitive to the length of the side branches as well as to the numbers N and N′. The presence of defect branches in the comblike structure can give rise to localized states inside the gaps. These states may have useful applications in the band structure engineering of nanostructure materials. second part of this work, we consider the tunneling between two monomode quantum wires through a coupling device. We give the conditions for selective transfer of a single propagating magnon from one wire to the other, leaving all the neighbor states unaffected. The magnon channel drop tunneling in this system is due to one localized state situated within a gap of the coupling device.