Critical fluctuation and noise spectra in two-dimensional Fe₃GeTe₂ magnets

Critical fluctuations play a fundamental role in determining the spin orders for low-dimensional quantum materials, especially for recently discovered two-dimensional (2D) magnets. Here we employ the quantum decoherence imaging technique utilizing nitrogen-vacancy centers in diamond to explore the critical magnetic fluctuations and the associated temporal spin noise in van der Waals magnet rm{Fe₃GeTe₂}. We show that the critical fluctuation contributes to a random magnetic field characterized by the noise spectra, which can be changed dramatically near the critical temperature T_c. A theoretical model to describe this phenomenon is developed, showing that the spectral density is characterized by a 1/f noise near the T_c, while away from this point it behaves like a white noise. The crossover at a certain temperature between these two situations is determined by changing of the distance between the sample and the diamond. This work provides a new way to study critical fluctuation and to extract some of the critical exponents, which may greatly deepen our understanding of criticality in a wide range of physical systems.