  We study information scrambling, as diagnosed by the out-of-time order
correlations (OTOCs), in a system of large spins collectively interacting via
spatially inhomogeneous and incommensurate exchange couplings. The model is
realisable in a cavity QED system in the dispersive regime. Fast scrambling,
signalled by an exponential growth of the OTOCs, is observed when the couplings
do not factorise into the product of a pair of local interaction terms, and at
the same time the state of the spins points initially coplanar to the equator
of the Bloch sphere. When one of these conditions is not realised, OTOCs grow
algebraically with an exponent sensitive to the orientation of the spins in the
initial state. The impact of initial conditions on the scrambling dynamics is
attributed to the presence of a global conserved quantity, which critically
slows down the evolution for initial states close to the poles of the Bloch
sphere.
