Theory of Higher Order Spin Noise Spectrum and Its Measurement

Optical spin noise spectroscopy is a perturbation-free technique that enables one to characterize spin dynamics by detecting thermodynamic spin fluctuations via the Faraday or Kerr effect. However, most of the research has concentrated on the second-order spin noise correlator, i.e., the power spectrum, whereas higher-order correlators can also be measured and analyzed. Here, we theoretically show that the measurement of higher-order spin noise correlators can tell us more information about the physical system, such as the correlation effect, time-reversal symmetry breaking processes, and higher-order fluctuation dissipation theorems. These would be difficult to detect with other experimental techniques. We illustrate these ideas with experimental data on magnetization fluctuations in a ferromagnetic Pt/Co/Pt trilayer.