  We investigate new solutions for magnetized neutron stars with a barotropic
core in magnetohydrodynamic (MHD) equilibrium and a magneto-elastic crust,
which was neglected by previous studies concerning stars in MHD equilibrium.
The Lorentz force of the barotropic star is purely irrotational and the
structures of magnetic fields are constrained. By contrast, a solenoidal
component of the Lorentz force exists in the elastic crust and the structures
of the magnetic fields are less restricted. We find that the minor solenoidal
component in the elastic crust is important for sustaining the strong magnetic
field in the core. Unlike previous studies, the toroidal magnetic field exists
in the entire region of the core, and we obtain equilibrium states with large
toroidal magnetic fields, where the toroidal magnetic energy is larger than the
poloidal magnetic energy. The elastic force of the crust sustains an order of
$10^{15}~\mathrm{G}$ toroidal magnetic field in the core, and the maximum
strength of the toroidal magnetic field is approximately proportional to the
crust thickness.
