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In spin noise spectroscopy, the magnetic susceptibility spectrum is known to be provided by the spin-system untouched by any external perturbation, or, better to say, disturbed only by its thermal bath. We propose a new version of spin noise spectroscopy, with the detected magnetization (Faraday-rotation) noise being "stimulated" by an external fluctuating magnetic field with a quasiwhite spectrum. An experimental study of the stimulated spin noise performed on a BaF 2 : U 3 + crystal in a longitudinal magnetic field has revealed specific features of this approach and allowed us to identify the Van-Vleck and population-related contributions to the AC susceptibility of the system and to discover unusual magnetic-field dependence of the longitudinal spin relaxation rate in low magnetic fields. It is shown that spectra of the stimulated and spontaneous spin noise, being both closely related to the spin-system magnetic susceptibility, are still essentially different. Distinctions between the two types of the spin-noise spectra and two approaches to spin noise spectroscopy are discussed. [ABSTRACT FROM AUTHOR]