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The evolution of the magnetic field in neutron star crusts because of theHall effect has received significant attention over the last two decades, whichis strongly justified because of the dominance of this effect in highlymagnetised neutron stars. However, the applicability of the Hall effect isbased on the assumption that the crust does not fail and sustains its rigidity.This assumption can be violated for substantially strong magnetic fields. Ifthis is the case, the evolution of the magnetic field is described by adifferent set of equations, which include the effects of a non-rigid crust. Inthis talk, after a brief review of the main characteristic of the Hallevolution, I will discuss the impact a plastic flow of the crust has on themagnetic field, studying axisymmetric models. Moreover, the way the crust failsimpacts the overall evolution, with major differences appearing if the failureis local, intermediate or global. Quite remarkably, crustal failure andplasticity do not annul the Hall effect, and under certain circumstances theymay even lead to a more dramatic evolution. I will discuss the impact of theseeffects in the context of neutron star timing behaviour, with special focus ontiming noise, outbursts and glitches.

Magnetic Field Evolution in the Crust of Neutron Stars: Crust Failure and Plastic Flow