Magneto–rotational and Thermal Evolution of Magnetars with Crustal Magnetic Fields

The interpretation of Soft–Gamma–Repeaters (SGRs) and Anomalous X–Ray Pulsars (AXPs) as Magnetars (Thompson & Duncan 1996) raises again the issue of the generation of the ultra–strong magnetic fields (MFs) in neutron stars (NSs) and the related question of where these fields are anchored: in the core, penetrating the whole star, or confined to the crust. Recently, Heyl & Kulkarni (1998) considered the magneto–thermal evolution of magnetars with a core field. Since the assumption of a crustal field is at least not in disagreement with the observations of isolated pulsars (Urpin & Konenkov 1997) and of NSs in binary systems (Urpin, Geppert & Konenkov 1998, Urpin, Konenkov & Geppert 1998), here we would like to address the question whether the observations of SGRs and AXPs can be interpreted as magnetars having a crustal MF. Given the strength of the MF in magnetars we take into account, in an approximate manner, the strongly non–linear Hall effect on its decay. We intend to provide a contribution to an unified picture of NS MF evolution based on the crustal field hypothesis.