  Spin-momentum locking is a unique intrinsic feature of strongly spin-orbit
coupled materials and a key to their promise of applications in spintronics and
quantum computation. Much of the existing work, in topological and
non-topological pure materials, has been focused on the orthogonal locking in
the vicinity of the $\Gamma$ point where the directions of spin and momentum
vectors are locked perpendicularly. With the orthogonal case, enforced by the
symmetry in pure systems, mechanisms responsible for non-orthogonal
spin-momentum locking (NOSML) have drawn little attention, although it has been
reported on the topological surface of $\alpha$-$Sn$. Here, we demonstrate
that, the presence of the spin-orbit scattering from dilute spinless impurities
can produce the NOSML state in the presence of a strong intrinsic spin-orbit
coupling in the pristine material. We also observe an interesting coupling
threshold for the NOSML state to occur.
  The relevant parameter in our analysis is the deflection angle from
orthogonality which can be extracted experimentally from the
spin-and-angle-resolved photoemission (S-ARPES) spectra. Our formalism is
applicable to all strongly spin-orbit coupled systems with impurities and not
limited to topological ones. The understanding of NOSML bears on spin-orbit
dependent phenomena, including issues of spin-to-charge conversion and the
interpretation of quasiparticle interference (QPI) patterns as well as
scanning-tunneling spectra (STS) in general spin-orbit coupled materials.
