Thermodynamic signature of a phase transition in the pseudogap phase of $YBa_2Cu_3O_{x}$ high-$T_C$ superconductor

We present here high precision magnetisation measurements in polycrystalline $YBa_2Cu_3O_{x}$ samples, with oxygen content ranging from $x=6.19$ to $x=7.00$. By analysing the temperature derivative of the susceptibility, we found in the underdoped superconducting samples a singular point at a temperature corresponding to $T_{mag}$, the temperature below which polarised neutrons experiments have evidenced a symmetry breaking. We believe that this is a thermodynamic indication for the existence of a phase transition in the pseudogap state of underdoped $YBa_2Cu_3O_{x}$.