Proving the curvature-induced frequency asymmetry of spin-wave modes in magnetic nanotubes with coplanar wave guides

We calculate the optimal conditions to quantify curvature-induced nonreciprocity in the dispersion relation of a magnetic nanotube by calculating the coupling impedance between spin waves modes of the nanotube and Coplanar Wave Guides (CPWs). We calculate the system parameters to quantify the curvature-induced frequency asymmetry up to GHz orders, and the changes on the asymmetry up to the same GHz range when a magnetic field {mu}0|Hz| u003c 60 mT is applied along the large nanotube axis. Moreover, we show the feasibility of the CPWs to excite higher order SW modes with wavelengths down to few hundred of nanometers, which could be used to encode information not only in the longitudinal SW phase but also in the azimuthal one, therefore paving the way towards technologies that increases the density and fidelity of information transfer, as well as for encouraging technological development of 3D magnonic devices.