“…On the other hand, the static and dynamic magnetic properties of magnetic nanotubes, such as the magnetic equilibrium states [ 34 , 35 , 36 , 37 , 38 ], magnetization reversal mechanisms [ 16 , 17 , 21 , 23 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ] and magnetostatic interaction [ 44 , 45 , 46 , 47 ], have also been investigated theoretically. González et al [ 48 ] went further and calculated the spin wave spectra associated with the vortex domain wall confined within a nanotube, which encouraged the synthesis of Fe 3 O 4 nanotubes with this type of domain wall [ 49 ].…”