  Several new and interesting aspects of neutrino oscillations in a magnetic
field are considered: 1) We develop a standard usually used approach to the
neutrino spin oscillations in the neutrino mass basis and obtain the effective
neutrino spin (and "spin-mass") oscillation Hamiltonian that can be used for
description of the neutrino oscillations between different pairs of neutrino
states with different masses and helicities; 2) We derive the exact solution of
the Dirac equation for a massive neutrino with nonzero magnetic moment in the
presence of a constant transversal magnetic field that is rotating along the
direction of the neutrino propagation (the twisting magnetic field) and on the
basis of the obtained energy spectrum the neutrino spin oscillation effective
Hamiltonian is derive; 3) We develop a new approach to neutrino spin
oscillations that is based on the description of the neutrino spin states with
the corresponding spin operator that commutes with the neutrino dynamics
Hamiltonian in the magnetic field. The obtained new results can have important
phenomenological applications.
