A leading candidate for the origin of magnetars has involved the presence of a very strong magnetic field in a rapidly rotating neutron star. Magnetar formation and magnetic fields have traditionally been attributed to the effects of the differential rotation in the newly born neutron star. However, recent 3D magnetohydrodynamic simulations of differentially rotating neutron stars have generally led to the formation of a magnetic dipole, in contradiction with the observed field geometry of magnetars. These findings point to the necessity to revisit the standard mechanisms of magnetic field generation in these sources, and have led to the consideration of different scenarios for the formation of magnetars.

A very strong seed magnetic field (of the order of \( 10^{15} \) G) is required for the magnetic field amplification mechanism by differential rotation to work. Different sources of such a seed field have been proposed, e.g., fields created by dynamo processes during the evolution of the progenitor star, or fields amplified during the core-collapse event leading to the formation of the neutron star. In either case, the initial magnetic field must be axisymmetric and strong enough to avoid Ohmic dissipation of the magnetic field through the turbulent fluid motions that develop during the evolution of the neutron star. It has been suggested that convection occurring in the outer layers of the newborn magnetar might contribute to the confinement and amplification of this field.

One interesting possibility is that the seed magnetic field results from the magnetic flux that is advected inward by the accreting gas during the supernova fallback. The magnetohydrodynamic interaction of this infalling matter with the magnetic field of the neutron star could explain several key properties observed in magnetars. In particular, it has been suggested that it could give rise to a toroidal component of the magnetic field, the observed field multipolarity, and possibly also explain the origin of the ultra-long period magnetars.