  Thermal expansion offers deep insights into phase transitions in condensed
matter physics. Utilizing an advanced AC-temperature dilatometer with picometer
resolution, this study clearly resolves the antiferromagnetic and structural
transition in BaFe$_2$As$_2$. The implementation of temperature oscillation
reveals a hysteresis near the transition temperature $T_\mathrm{N}$ with
unprecedented resolution. Unexpectedly, we find that the hysteretic width
exhibits a universal dependence on the parameters of temperature oscillation
and the sample's longidutinal dimension, which in turn reveals a finite
transition speed. Our quantitative analysis shows that this phase boundary
propagates at a mere 188 $\mu$m/s - a speed seven orders of magnitude slower
than acoustic waves. It suggests a hidden thermodynamic constraint imposed by
the electronic degrees of freedom. Our research not only sheds light on the
dynamics of phase transitions between different correlated phases, but also
establishes high precision dilatometry as a powerful tool for material studies.
This measurement technique, when properly modified, can be extended to studies
of other material properties such as piezoelectric, magneto-restriction,
elastic modulus, etc.
