Elastocaloric signature of the excitonic instability in Ta$_2$NiSe$_5$

On cooling through a temperature $T_S$ of around 324 K, Ta$_2$NiSe$_5$ undergoes a transition from a semimetallic state to one with a gapped electronic spectrum which is suspected to be an excitonic insulator. However, at this transition the structure also changes, from orthorhombic to monoclinic, leaving open the question of whether it is driven primarily by excitonic ordering or by a lattice instability. A lattice instability of this symmetry would correspond to softening of a B$_{2g}$ optical or acoustic phonon mode. Here, we report that elastocaloric measurements of Ta$_2$NiSe$_5$ with induced B$_{2g}$ strain reveal a thermodynamic susceptibility described by a Curie-Weiss law with a Curie temperature $T^*$ of 298 K. The fact that $T^*$ is close to $T_S$ rules out the possibility that the B$_{2g}$ acoustic mode is responsible for the transition. Since prior Raman measurements have shown minimal softening of the B$_{2g}$ optical mode as well, our finding strengthens the case that the transition is largely excitonic in nature. Our work underscores the potential of using strain as a tool for separating electronic and lattice contributions in phase transitions.