  Elucidating the emergence of long-range magnetic ordering from its precursor
short-range magnetic ordering (SRMO) in two-dimensional van der Waals materials
holds profound implications for fundamental research and technological
advancements. However, directly observing the intricate stages of this magnetic
dimensional crossover (MDC) remains a significant experimental challenge. While
magneto-elastic coupling offers a promising avenue, detecting the minute
lattice response to SRMO proves challenging. Recent investigations utilizing
second harmonic generation have unveiled a two-step MDC in a van der Waals
ferromagnetic insulator. However, an unambiguous detection of MDC through the
time-resolved techniques remains elusive. To meet this goal, we have executed
an alternative approach by employing picosecond acoustic strain pulses
generated by femtosecond lasers to probe the various stages of MDC through the
magneto-elastic coupling for the first time. By analyzing the shape of the
strain pulse in both the time and frequency domains as a function of
temperature, we clearly demonstrate the detection of the subtle influence of
spin fluctuations on the lattice. Additionally, the ultrafast carrier dynamics
also show signatures of MDC. Our measurements pave the way towards
characterizing magnetic materials in time-resolved experiments that are crucial
in designing a new generation of spin-based optoelectronic devices.
