  Boosted dark matter provides a promising approach to probe the light dark
matter, whose computational framework in the spin-independent scattering
process is well developed. However, the spin-dependent one lacks a unified
treatment. The novelty of this paper is to give the first comprehensive
derivation of the cross-section for boosted dark matter in spin-dependent
scattering. When the transfer momentum is sufficiently large, there is a
sizable enhancement to the proton structure factor from the time component.
Besides, we find a residue momentum dependence in the quark-nucleon matching
procedure, even without a light mediator. Such behavior can enhance the
sensitivity compared with conventional contact interaction. We promote this
endeavor by deriving direct limits on sub-GeV spin-dependent boosted dark
matter through terrestrial data. The numerical results of the boosted structure
factor and the non-relativistic structure factor are given explicitly in the
paper and it shows that the excluded region of the boosted structure factor is
about six orders larger than the non-relativistic structure factor.
