Spin noise spectroscopy, as a sort of magnetic resonance technique, uses, for detection of spin precession, spontaneous fluctuations of magnetization revealed as a peak in the Faraday-rotation (FR) noise spectrum at Larmor frequency. In the model of precessing magnetization, the FR noise signal should be the greatest in the Voigt geometry (with magnetic field aligned across the light propagation), and should vanish in the Faraday geometry (with the field along the probe beam). This reasoning employs, implicitly or explicitly, the so-called Van Vleck theorem that establishes, within the limits of certain assumptions, a direct relation between the FR and magnetization of the spin system. We show that violation of these assumptions in crystals with anisotropic paramagnetic centers may qualitatively change the conventional laws of spin noise detection, making, in particular, the FR noise detectable in the Faraday geometry. These conclusions are confirmed by experimental studies of spin-noise spectra of ${\mathrm{CaF}}_2$ crystals with tetragonal centers of ${\mathrm{Nd}}^{3+}$ ions.

• Received 17 October 2022
• Revised 13 January 2023
• Accepted 15 February 2023

DOI:https://doi.org/10.1103/PhysRevB.107.064427