Magneto-optical spectra were observed for the dilute gas phase of the Cs metal. The non-linear Faraday effect was investigated with a frequency tunable laser diode of weak intensity. Theoretical spectral profiles were obtained via optical coherence derived from the density matrix formalism. As a result of the analysis, it was ascertained that the coherent Larmor precession of atoms induces a broadening and a phase shift in the optical coherence in opposite directions for sigma + and for sigma - light. This effect originates from off-diagonal elements of the Hamiltonian.