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  1. When electron spin and momentum couple in a solid, one generally obtains intriguing and unexpected phenomena. Metallic ferromagnetic nanotubes of cobalt with circular magnetization, which have been prepared by us and others, are a particularly interesting system. Here the spins of the conduction electrons are frustrated. They would like to align parallel to the magnetic field of the magnetization, but as the electrons move quickly around the tube the spins cannot follow the magnetization direction. In a previous short theoretical paper we solved the spin dynamics using a classical model. Here we generalize our work to a quantum mechanical model. The surprising result is that the spin of most conduction electrons is not parallel or anti-parallel to the circumferential magnetization but mostly parallel or anti-parallel to the axis of the nanotube. This result means that such a cobalt nanotube is a different ferromagnet from a cobalt film or bulk cobalt.
  2. In cobalt nanotubes with a curling magnetization, the orbital motion of the conduction electrons interacts with their spin. As the spin goes around the nanotube it cannot follow the magnetization, since with the Fermi velocity it moves too fast. Instead, we predict that the spin precesses about an axis that is almost parallel to the axis of the nanotube and that rotates with the angular velocity of the electron. Therefore, the (absolute) value of the magnetic energy of the spin |μ⋅B| is strongly reduced. The physics of the ferromagnet is considerably modified.