  BaCuSi$_2$O$_6$ is a quasi-two-dimensional (2D) quantum antiferromagnet
containing three different types of stacked, square-lattice bilayer hosting
spin-1/2 dimers. Although this compound has been studied extensively over the
last two decades, the critical applied magnetic field required to close the
dimer spin gap and induce magnetic order, which exceeds 23 T, has to date
precluded any kind of neutron scattering investigation. However, the HFM/EXED
instrument at the Helmholtz-Zentrum Berlin made this possible at magnetic
fields up to 25.9 T. Thus we have used HFM/EXED to investigate the
field-induced ordered phase, in particular to look for quasi-2D physics arising
from the layered structure and from the different bilayer types. From neutron
diffraction data, we determined the global dependence of the magnetic order
parameter on both magnetic field and temperature, finding a form consistent
with 3D quantum critical scaling; from this we deduce that the quasi-2D
interactions and nonuniform layering of BaCuSi$_2$O$_6$ are not anisotropic
enough to induce hallmarks of 2D physics. From neutron spectroscopy data, we
measured the dispersion of the strongly Zeeman-split magnetic excitations,
finding good agreement with the zero-field interaction parameters of
BaCuSi$_2$O$_6$. We conclude that HFM/EXED allowed a significant extension in
the application of neutron scattering techniques to the field range above 20 T
and in particular opened new horizons in the study of field-induced magnetic
quantum phase transitions.
