The spin correlation coefficients in the neutron-deuteron elastic scattering process at incoming neutron laboratory energies $$\hbox {E}=10$$
E
=
10
, 135, 190, and 250 MeV are determined by solving the momentum space three-nucleon (3N) Faddeev equations. The chiral two-nucleon (2N) interaction with momentum-space semi-local (SMS) regularization up to the fifth order of chiral expansion ($$\hbox {N}^4\hbox {LO}$$
N
4
LO
), supplemented by the F-waves terms from the sixth order ($$\hbox {N}^5\hbox {LO}$$
N
5
LO
), is used. Additionally, the consistent 3N force (3NF) at the third order of chiral expansion, supplemented by the short-range contributions from $$\hbox {N}^4\hbox {LO}$$
N
4
LO
is applied. As a results, we give predictions for the complete set of spin correlation coefficients $$C_{\alpha ,\beta }$$
C
α
,
β
. We find that the effect of the investigated three-nucleon $$\hbox {N}^4\hbox {LO}$$
N
4
LO
components amounts up to several dozen percent, depending on reaction energy, scattering angle and type of spin correlation coefficient itself. Our results can serve as a guide for future measurements of the spin correlation coefficients.