Short-range magnetic order and multi-stage phase transitions in the easy-plane van der Waals magnet CrCl$_3$

We investigate the evolution of spin correlations and the nature of the multi-stage magnetic transition in the quasi-two-dimensional easy-plane van der Waals magnet $\rm CrCl_3$. By combining broadband ferromagnetic resonance (FMR) spectroscopy and DC SQUID magnetometry on mechanically exfoliated micro-flakes with non-local dynamical mean-field theory (DFT+DMFT) calculations, we analyze both long- and short range magnetic order in CrCl$_3$. Experimentally, SQUID and FMR measurements confirm the presence of the crossover to a spin polarized phase with the subsequent transition into an antiferromagnetic ground state upon cooling, but show robust short-range correlations at temperatures far above the magnetic ordering temperatures. Theoretically, we show the existence of highly stable local magnetic moments at room temperature, with a giant room temperature lifetime $\tau$ of 130--300 ps due to a wide Mott bandgap. Below room temperature, a rapid growth of the in-plane correlation length $\xi$ signals the formation of strong short range magnetic order consistent with the experimental observations. We also obtain a temperature-driven crossover of the interlayer exchange interaction, which changes from positive (ferromagnetic) at high temperatures to negative (antiferromagnetic) in the low-temperature ordered phase.