In this paper, we describe the unusual low-frequency magnetic resonances in
alkali vapor with oriented atomic spins regarding the framework of density
matrix formalism. The feature of the resonance is the absence of a constant
component in the external magnetic field. To explain steep increase of the spin
orientation at certain frequencies, we define special closed atomic spin
trajectories governed by periodic magnetic perturbation. Any closed trajectory
is characterized by the frequency of spin motion. The resonance effect was
numerically verified in the paper. For instance, these trajectories can be
observed in an alkali vapor via optical excitation. Surprisingly, the width of
the resonance line is found to be narrower, as one may expect