  We study the quantum synchronization of a single spin driven by an external
semiclassical signal for spin numbers larger than $S = 1$, the smallest system
to host a quantum self-sustained oscillator. The occurrence of
interference-based quantum synchronization blockade is found to be
qualitatively different for integer vs. half-integer spin number $S$. We
explain this phenomenon as the interplay between the external signal and the
structure of the limit cycle in the generation of coherence in the system.
Moreover, we show that the same dissipative limit-cycle stabilization mechanism
leads to very different levels of quantum synchronization for integer vs.
half-integer $S$. However, by choosing an appropriate limit cycle for each spin
number, comparable levels of quantum synchronization can be achieved for both
integer and half-integer spin systems.
