  We study spin liquid in the frustrated diamond lattice antiferromagnet
CoAl2O4 by means of single crystal neutron scattering in zero and applied
magnetic field. The magnetically ordered phase appearing below TN=8 K remains
nonconventional down to 1.5 K. The magnetic Bragg peaks at the q=0 positions
remain broad and their profiles have strong Lorentzian contribution.
Additionally, they are connected by weak diffuse streaks along the <111>
directions. These observations are explained within the spiral spin liquid
model as short-range magnetic correlations of spirals populated at these finite
temperatures, as the energy minimum around q=0 is flat and the energy of
excited states with q=(111) is low. The agreement is only qualitative, leading
us to suspect that microstructure effects are also important. Magnetic field
significantly perturbs spin correlations. The 1.5 K static magnetic moment
increases from 1.58 mB/Co at zero field to 2.08 mB/Co at 10 T, while the
magnetic peaks, being still broad, acquire almost Gaussian profile. Spin
excitations are rather conventional spin waves at zero field, resulting in the
exchange parameters J1=0.92(1) meV, J2=0.101(2) meV and the anisotropy term
D=-0.0089(2) meV for CoAl2O4. The application of a magnetic field leads to a
pronounced broadening of the excitations at the zone center, which at 10 T
appear gapless and nearly featureless.
