  We combine tensor-network approaches and high-order linked-cluster expansions
to investigate the quantum phase diagram of the antiferromagnetic Kitaev's
honeycomb model in a magnetic field for general spin values. For the pure
Kitaev model, tensor network calculations confirm the absence of fluxes and
spin-spin correlations beyond nearest neighbor in the ground state, but signal
a breaking of the discrete orientational symmetry for $S\in\{1,3/2,2\}$ inline
with the semiclassical limit. An intermediate region between Kitaev phases and
the high-field polarized phase is demonstrated for all considered spin values.
The analysis of the high-field gap and the associated spectral weight of the
polarized phase for general spin S is consistent with an unconventional quantum
critical breakdown of the high-field polarized phase in accordance with the
presence of exotic physics at intermediate Kitaev couplings.
