Mixing zones in magnetized differentially rotating stars

We study the secular instability of magnetized differentially rotating radiative zones taking account of viscosity and magnetic and thermal diffusivities. The considered instability generalizes the well-known Goldreich-Schubert-Fricke instability for the case of a sufficiently strong magnetic field. In magnetized stars, instability can lead to a formation of non-spherical unstable zones where weak turbulence mixes the material between the surface and interiors. Such unstable zones can manifest themselves by a non-spherical distribution of abundance anormalies on the stellar surface.