Due to the small coherence lengths, large anisotropies and high critical temperatures cuprate superconductors exhibit extremely strong superconducting fluctuations. High-resolution capacitance dilatometry on YBa₂Cu₃O_x has proven to be particularly useful in studying these fluctuation [1-3]. At optimal doping the sc transition is described well by a 3D-XY phase-ordering transition (analogous to the lambda transition in superfluid 4He) [1,2]. For underdoped crystals fluctuations increase and were attributed to anisotropic 3D-XY behavior [3]. Here, using magnetostriction measurements up to 30 T, we investigate how large a magnetic field is necessary to suppress the superconducting transition in an underdoped crystal with an oxygen content of 6.7. We find that 30 T is far from sufficient to fully suppress the transition, in stark contrast to previous work claiming an H_c2 of roughly 20-25 T for this doping [4,5]. Further, we see little thermodynamic evidence in the magnetostriction data at 10 K for a field-induced charge-ordering transition [6].

[1] V. Pasler et al., Phys. Rev. Lett. 81, 1094 (1998).

[2] R. Lortz et al., Phys. Rev. Lett. 91, 207001 (2003).

[3] C. Meingast et al., Phys. Rev. Lett. 86, 1606 (2001).

[4] G. Grissonnanche et al., Nat. Comm. 5, 3280 (2014).

[5] C. Marcenat et al., Nature Comm. 6, 7927 (2015).

[6] J. Chang et al., Nat. Comm 7, 11494 (2016).