Spiral Spin Liquid Noise

An emerging concept for identification of different types of spin liquids is through the use of spontaneous spin noise. Here we develop spin noise spectroscopy for spin liquid studies by considering Ca$_{10}$Cr$_7$O$_{28}$, a material hypothesized to be either a quantum or a spiral spin liquid. By enhancing techniques introduced for magnetic monopole noise studies we measure the time and temperature dependence of spontaneous flux $\varPhi(t, T)$ and thus magnetization $M(t, T)$ of Ca$_{10}$Cr$_7$O$_{28}$ samples. The resulting power spectral density of magnetization noise $S_M(\omega,T)$ reveals intense spin fluctuations with $S_M(\omega,T) \propto \omega^{-\alpha(T)}$ and 0.84 < $\alpha (T)$ < 1.04 . Both the variance $\sigma_M^2(T)$ and the correlation function $C_M(t,T)$ of this spin noise undergo crossovers at a temperature $T^* \approx$ 450 mK. While predictions for quantum spin liquids are inconsistent with this phenomenology, those from Monte-Carlo simulations of a 2D spiral spin liquid state in Ca$_{10}$Cr$_7$O$_{28}$ yield overall quantitative correspondence with the measured frequency and temperature dependences of $S_M(\omega,T), C_M(t,T)$ and $\sigma _M^2(T)$, thus indicating that Ca$_{10}$Cr$_7$O$_{28}$ is a spiral spin liquid.