  We study spin effects in the neutrino gravitational scattering by a
supermassive black hole with a magnetized accretion disk having a finite
thickness. We exactly describe the propagation of ultrarelativistic neutrinos
on null geodesics and solve the spin precession equation along each neutrino
trajectory. The interaction of neutrinos with the magnetic field is owing to
the nonzero diagonal magnetic moment. Additionally, neutrinos interact with
plasma of the accretion disk electroweakly within the Fermi approximation.
These interactions are obtained to change the polarization of incoming
neutrinos, which are left particles. The fluxes of scattered neutrinos,
proportional to the survival probability of spin oscillations, are derived for
various parameters of the system. In particular, we are focused on the matter
influence on the outgoing neutrinos flux. The possibility to observe the
predicted effects for astrophysical neutrinos is briefly discussed.
