Giant Low Temperature Heat Capacity of GaAs Quantum Wells near Landau Level Filling $ u$=1

We report low temperature ($T$) heat capacity ($C$) data on a multiple-quantum-well GaAs/AlGaAs sample in the quantum Hall regime. Relative to its low field magnitude, $C$ exhibits up to 10^5-fold enhancement near $ u$=1 where Skyrmions arethe ground state of the confined two-dimensional electrons. We attribute the large $C$ to a Skyrmion-induced, strong coupling of the nuclear spin system to the lattice. The data are consistent with the Schottky nuclear heat capacity of Ga and As atoms in the quantum wells, except at very low $T$ where $C$ vs $T$ exhibits a remarkably sharp peak suggestive of a phase transition in the electronic system.