  Timing observations of rapidly rotating neutron stars revealed a great number
of glitches, observed both from canonical radio pulsars and magnetars. Among
them, 76 glitches have shown exponential relaxation(s) with characteristic
decay times ranging from several days to a few months, followed by a more
gradual recovery. Glitches displaying exponential relaxation with single or
multiple decay time constants are analysed in terms of a model based on the
interaction of the vortex lines with the toroidal arrangement of flux tubes in
the outer core of the neutron star. Model results agree with the observed
timescales in general. Thus, the glitch phenomenon can be used to deduce
valuable information about neutron star structure, in particular on the
interior magnetic field configuration which is unaccessible from surface
observations. One immediate conclusion is that the magnetar glitch data are
best explained with a much cooler core and therefore require that direct Urca
type fast cooling mechanisms should be effective for magnetars.
