We present the results of 3D simulations, performed with the ASH code, of the nonlinear, magnetic coupling between the convective and radiative zones in the Sun, through the tachocline. Contrary to the predictions of Gough & McIntyre (1998), a fossil magnetic field, deeply buried initially in the solar interior, will penetrate into the convection zone. According to Ferraro's law of iso-rotation, the differential rotation of the convective zone will thus expand into the radiation zone, along the field lines of the poloidal field.