Abnormal Critical Fluctuations Revealed by Magnetic Resonance in the Two-Dimensional Ferromagnetic Insulators

Abstract

Phase transitions and critical phenomena, which are dominated by fluctuations and correlations, are one of the fields replete with physical paradigms and unexpected discoveries. Especially for two-dimensional magnetism, the limitation of the Ginzburg criterion leads to enhanced fluctuations breaking down the mean-field theory near a critical point. Here, by means of magnetic resonance, we investigate the behavior of critical fluctuations in the two-dimensional ferromagnetic insulators $\rm CrXTe_3 (X=Si, Ge)$. After deriving the classical and quantum models of magnetic resonance, we deem the dramatic anisotropic shift of the measured $g$ factor to originate from fluctuations with anisotropic interactions. The deduction of the $g$ factor behind the fluctuations is consistent with the spin-only state (${g\approx}$ 2.050(10) for $\rm CrSiTe_3$ and 2.039(10) for $\rm CrGeTe_3$). Furthermore, the abnormal enhancement of $g$ shift, supplemented by specific heat and magnetometry measurements, suggests that $\rm CrSiTe_3$ exhibits a more typical two-dimensional nature than $\rm CrGeTe_3$ and may be closer to the quantum critical point.