  We have succeeded in obtaining magnetized equilibrium states with
differential rotation and differential toroidal magnetic fields. If an internal
toroidal field of a proto-neutron star is wound up from the initial poloidal
magnetic field by differential rotation, the distribution of the toroidal
magnetic field is determined by the profile of this differential rotation.
However, the distributions of the toroidal fields in all previous magnetized
equilibrium studies do not represent the magnetic winding by the differential
rotation of the star. In this paper, we investigate a formulation of a
differential toroidal magnetic field that represents the magnetic field wound
up by differential rotation. We have developed two functional forms of
differential toroidal fields which correspond to a v-constant and a j-constant
field in analogy to differential rotations. As the degree of the differential
becomes very high, the toroidal magnetic field becomes highly localized and
concentrated near the rotational axis. Such a differential toroidal magnetic
field would suppress the low-T/|W| instability more efficiently even if the
total magnetic field energy is much smaller than that of a non-differential
toroidal magnetic field.
