  We obtained the magnetic field configurations, including both poloidal and
toroidal components, throughout the interior and exterior of magnetars using a
realistic equation of state. We divided the magnetized star into the
hydromagnetic equilibrium core, Hall equilibrium crust and twisted force-free
magnetosphere. We systematically and simultaneously calculated these regions
under various boundary conditions using the Green function relaxation method,
and noted the following interesting characteristics of these numerical results.
First, the strength and structure of core magnetic fields affect the crustal
magnetic fields. Second, the current sheet on the core-crust interface affects
both internal and external magnetic field configurations. Third, the twisted
magnetosphere makes a cross-point of magnetic field lines, such as X-point
geometry, in the magnetosphere. The X-point geometry appears and disappears
according to the strength of the twisted field in the magnetosphere or the
core-crust boundary conditions. Our results mean that both Hall
magnetohydrodynamics secular evolution and magnetospheric dynamical evolution
are deeply affected by conditions of another region and the core-crust stress
of magnetars.
