Search for a thermodynamic evidence of a phase transition in the pseudogap state of YBa$_{2}$Cu$_{3}$O$_{6+x}$

Recent polarized neutrons diffraction experiments have evidenced a symmetry breaking in the underdoped phase of superconducting cuprates [1,2,3]. This symmetry breaking takes place below a temperature T$_{MAG}$ which increases when the number of charge carriers in the superconducting planes is decreased. We present here magnetic susceptibility measurements in YBa$_{2}$Cu$_{3}$O$_{6+x}$ ceramics. We have measured the magnetization of about twenty samples with different oxygen contents under 1T magnetic field. In some of them, we have observed an anomaly in the temperature derivative of the susceptibility at a temperature T$_{1}$ which seems to be in good agreement to the temperature T$_{MAG}$. We show here the resulting phase diagram for underdoped YBa$_{2}$Cu$_{3}$O$_{6+x}$. These findings raise the question of a thermodynamic evidence for a phase transition in relation to the symmetry breaking observed by neutrons.\\[4pt] [1] B. Fauque et al, Phys. Rev. Letters 96, 197001 (2006). \\[0pt] [2] H. A. Mook et al, Phys. Rev. B 78 ,020506(2008) \\[0pt] [3] Y. Li, Nature 455, 372 (2008)