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This study was focused on the investigation of a magnetic field penetratingfrom the core of a neutron star to its surface. The range of possible fieldconfigurations in the intermediate solid crust is less limited owing to theelastic force acting on the force balance. When the Lorentz force isexcessively strong, the magnetoelastic equilibrium does not hold, and thus, themagnetic field becomes constrained. By numerically solving for themagnetoelastic equilibrium in a thin crust, the range of the magnetic field atthe core-crust interface was determined, while assuming the exterior to befixed as a dipole in vacuum. The results revealed that the toroidal componentshould be smaller than the poloidal component at the core-crust interface forthe surface dipole, $B_{0} > 2.1 \times 10^{14}$G. Consequently, a strongtoroidal field, for example, $B \sim 10^{16}$G, as suggested by free precessionof magnetars should be confined to a deep interior core and should be reducedto $B \sim 10^{14}$G at the bottom of the crust. The findings of this studyprovide insights into the interior field structure of magnetars. Furtherinvestigations on more complicated geometries with higher multipoles andexterior magnetosphere are necessary.

How different is the magnetic field at the core-crust interface from  that at the neutron star surface? -- the range allowed in magnetoelastic  equilibrium