  Spin noise spectroscopy is a method of magnetic resonance widely used,
nowadays, in atomic and semiconductor research. Classical objects of the EPR
spectroscopy - dielectrics with paramagnetic impurities - seemed to be
unsuitable for this technique because of large widths of allowed optical
transitions and, therefore, low specific Faraday rotation (FR). We show,
however, that the FR noise detected at the wavelength of a weak optical
transition (with low regular FR) may increase by many orders of magnitude as
its homogeneous width decreases. This spin-noise gain effect, numerically
described by the ratio of the inhomogeneous linewidth to homogeneous, relates
primarily to forbidden intraconfigurational transitions of impurity ions with
unfilled inner electronic shells. Specifically, for the f-f transitions of
rare-earth ions in crystals, this factor may reach 10$^8$. In this paper, we
report on the first successful application of spin noise spectroscopy for
detecting magnetic resonance of rare-earth ions in crystals.
