Giant dielectric nonlinearities at a magnetic Bose-Einstein condensation

We experimentally investigate the dielectric response of the low-dimensional gapped quantum magnet Cu$_2$Cl$_{4}\cdot$H$_8$C$_4$SO$_2$ near a magnetic field-induced quantum critical point, which separates the quantum-disordered and helimagnetic ground states. The observed magnetocapacitive effect originates from an improper ferroelectric nature of the transition, which itself is perhaps one of the best known realizations of Bose--Einstein condensation of magnons. Despite that, we find that the magnetocapacitive effect associated with the transition exhibits huge and very unusual anharmonicities.