There are a whole lot of reasons for which high temperature superconductivity in the cuprates is a hard problem but it is now clear that the occurrence of superconductivity is itself part of the problem.

Various experiments over the last two decades have indeed revealed that ordering (i.e. symmetry-breaking) phenomena have remained “hidden” in a number of circumstances as their development is hampered by superconductivity with which they turn out to be in competition. This situation hinders understanding of the electronic properties of these materials.

These competing orders can however be revealed, and studied in great detail, if superconductivity is quenched by very high magnetic fields. Based on results from our NMR group, I will illustrate such field-tuned competition through two examples: glassy spin-freezing in La2-xSrxCuO4 and charge-density waves in YBa2Cu3Oy and I will discuss why competing orders are an important piece of the high-Tc puzzle.