It is commonly believed that the magnetic field threading a neutron star provides the ultimate mechanism (on top of fluid viscosity) for enforcing long-term corotation between the slowly spun down solid crust and the liquid core. We show that this argument fails for axisymmetric magnetic fields with closed field lines in the core, the commonly used `twisted torus field being the most prominent example. The failure of such magnetic fields to enforce global crust-core corotation leads to the development of a persistent spin lag between the core region occupied by the closed field lines and the rest of the crust and core. We discuss the repercussions of this spin lag for the evolution of the magnetic field, suggesting that, in order for a neutron star to settle to a stable state of crust-core corotation, the bulk of the toroidal field component should be deposited into the crust soon after the neutron stars birth.
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