Two-stage evolution of magnetic correlations in spiral spin liquid material, Ca$_{10}$Cr$_{7}$O$_{28}$

We present an X-band and tunable high-frequency/high-field electron spin resonance (HF-ESR) study of single-crystalline Ca$_{10}$Cr$_{7}$O$_{28}$, which constitutes alternating antiferromagnetic and ferromagnetic kagome bilayers. At high temperatures, a phonon-assisted relaxation process is evoked to account for the pronounced increase of the linewidth in an exchange-narrowing regime ($k_{\rm B}T\gg J$). In contrast, at low temperatures ($k_{\rm B}T\lesssim J$), a power-law behavior in line narrowing is observed. Our data reveal two distinct power-law regimes for the linewidth which crossover at $T^*\approx 7.5$~K. Notably, the intriguing evolution of the ESR linewidth in this alternating kagome bilayer system with opposite sign of exchange interactions highlights distinct spin dynamics compared to those in a uniform kagome antiferromagnet.