  We study a mechanism by which nuclear hyperpolarization due to the
polarization transfer from a microwave-pulse-controlled electron spin is
suppressed. From analytical and numerical calculations of the unitary dynamics
of multiple nuclear spins, we uncover that, combined with the formation of the
dark state within a cluster of nuclei, coherent higher-order nuclear spin
dynamics impose limits on the efficiency of the polarization transfer even in
the absence of mundane depolarization processes such as nuclear spin diffusion
and relaxation. Furthermore, we show that the influence of the dark state can
be partly mitigated by introducing a disentangling operation. Our analysis is
applied to the nuclear polarizations observed in $^{13}$C nuclei coupled with a
single nitrogen-vacancy center in diamond [Science 374, 1474 (2021) by J.
Randall et al.]. Our work sheds light on collective engineering of nuclear
spins as well as future designs of pulsed dynamic nuclear polarization
protocols.
