A resonant parametric mechanism of generation of the zeroth and second harmonics of acoustic pulses propagating in a crystal involving resonance Zeeman transitions is proposed. The analysis performed has made it possible to determine the conditions for the effective acoustic rectification and excitation of the second harmonics in the resonant parametric soliton regime. The advantage of the proposed mechanism of acoustic harmonic generation over the conventional mechanism associated with the acoustic anharmonicity is that the degree of conversion is controlled by a change in the external magnetic field strength and the direction of propagation of the input pulse.