  We study the valence electron of an alkaline atom or a general charged
particle with arbitrary spin and with magnetic moment moving in a rotating
magnetic field. By using a time-dependent unitary transformation, the
Schr\"odinger equation with the time-dependent Hamiltonian can be reduced to a
Schr\"odinger-like equation with a time-independent effective Hamiltonian.
Eigenstates of the effective Hamiltonian correspond to cyclic solutions of the
original Schr\"odinger equation. The nonadiabatic geometric phase of a cyclic
solution can be expressed in terms of the expectation value of the component of
the total angular momentum along the rotating axis, regardless of whether the
solution is explicitly available. For the alkaline atomic electron and a strong
magnetic field, the eigenvalue problem of the effective Hamiltonian is
completely solved, and the geometric phase turns out to be a linear combination
of two solid angles. For a weak magnetic field, the same problem is solved
partly. For a general charged particle, the problem is solved approximately in
a slowly rotating magnetic field, and the geometric phases are also calculated.
