The dissipation of toroidal magnetic fields and spin-down evolution of young and strongly magnetized pulsars

Magnetars are a kind of pulsars powered mainly by superhigh magnetic fields. They are popular sources with many unsolved issues in themselves, but also linked to various high energy phenomena, such as QPOs, giant flares, fast radio bursts and super-luminous supernovae. In this work, we first review our recent works on the dissipation of toroidal magnetic fields in magnetars and rotationally powered pulsars, then review the spin-down evolution of young and strongly magnetized pulsars, especially of magnetars. We present an interesting and important relation between the magnetization parameter, and magnetic field in the magnetar crust. Finally, we introduce our two works in progress: to explain the magnetar "anti-gltich" events in the thermal plastic flow model and to revisit the expression of braking index $n$, which is independent of the second derivative of spin frequency of a pulsar and give some proposals for our future work.