  Motivated by the potential to suppress the antiferromagnetic long-range order
in favor of the long-sought-after Kitaev quantum spin liquid state, we study
the effect of spin vacancies in the extended Kitaev-Heisenberg model. In
particular, we focus on a realistic model obtained from fitting inelastic
neutron scattering on $\alpha$-RuCl$_3$. We observe that the long-range zigzag
magnetic ordered state only survives when the doping concentration is smaller
than 5\%. Upon further increasing the spin vacancy concentration, the ground
state becomes a short-range ordered state at low temperatures. Compared with
experiments, our classical solution over-stabilizes the zigzag correlation in
the presence of spin vacancies. Our theoretical results provide guidance toward
interpreting inelastic neutron scattering experiments on magnetically diluted
Kitaev candidate materials.
