  Magnetization, magnetocaloric, calorimetric, neutron and X-ray diffraction
and inelastic neutron scattering measurements are performed on single crystals
of BaCdVO(PO$_4$)$_2$. The low-temperature crystal structure is found to be of
a lower symmetry than previously assumed. The result is a more complicated
model spin Hamiltonian, which we infer from measurements of the spin wave
dispersion spectrum. The main finding is a novel spin state which emerges in
high magnetic fields after antiferromagnetic order is terminated at
$H_{c1}\simeq 4.0$ T. It is a distinct thermodynamic phase with a well-defined
phase boundary at $H_{c2}\simeq 6.5$ T and is clearly separate from the fully
saturated phase. Yet, it shows no conventional (dipolar) magnetic long range
order. We argue that it is fully consistent with the expectations for a quantum
bond-nematic state.
