  We investigated the low-temperature and high-field thermodynamic and
ultrasonic properties of SrCu2(BO3)2, which exhibits various plateaux in its
magnetization curve above 27~T, called a magnetic Devil's staircase. The
results of the present study confirm that magnetic crystallization, the first
step of the staircase, occurs above 27~T as a 1st-order transition accompanied
by a sharp singularity in heat capacity $C_p$ and a kink in the elastic
constant. In addition, we observe a thermodynamic anomaly at lower fields
around 26~T, which has not been previously detected by any magnetic probes. At
low temperatures, this magnetically hidden state has a large entropy and does
not exhibit Schottky-type gapped behavior, which suggests the existence of
low-energy collective excitations. Based on our observations and theoretical
predictions, we propose that magnetic quadrupoles form a spin-nematic state
around 26~T as a hidden state on the ground floor of the magnetic Devil's
staircase.
