2002A&A...392.1015G

There exists both theoretical and observational evidence that the magnetic field decay in neutron stars may proceed in a pronounced non-linear way during a certain episode of the neutron star's life. In the presence of a strong magnetic field the Hall-drift dominates the field evolution in the crust and/or the superfluid core of neutron stars. Analysing observations of P and {dot}(P) for sufficiently old isolated pulsars we gain strong hints for a significantly non-linear magnetic field decay. Under certain conditions with respect to the geometry and strength of a large-scale magnetic background field an instability is shown to occur which rapidly raises small-scale magnetic field modes. Their growth rates increase with the background field strength and may reach ∼10⁴ times the ohmic decay rate. Consequences for the rotational and thermal evolution as well as for the cracking of the crust of neutron stars are discussed.