Electronic Phase Propagation Speed in BaFe$_2$As$_2$ Revealed by Dilatometry

Abstract

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.