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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.
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