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The Co-intercalated NbS$_2$ (Co$_{1/3}$NbS$_2$) compound exhibits largeanomalous Hall conductance, likely due to the non-coplanar magnetic ordering ofCo spins. In this work, we study the relation between this novel magnetism andthe correlated electronic structure of Co$_{1/3}$NbS$_2$ by adopting dynamicalmean field theory (DMFT) to treat the correlation effect of Co $d$ orbitals. Wefind that the hole doping of Co$_{1/3}$NbS$_2$ can tune the size of the Nb holepocket at the DMFT Fermi surface, producing features consistent with thoseobserved in angle resolved photoemission spectra [Phys. Rev. B 105, L121102(2022)]. We also compute the momentum-resolved spin susceptibility, andcorrelate it with the Fermi surface shape. We find that the magnetic orderingwavevector of Co$_{1/3}$NbS$_2$ obtained from the peak in spin susceptibilityagrees with the one observed experimentally by neutron scattering; it iscompatible with commensurate non-coplanar $3q$ spin structure. We also discusshow results change if some other than Co transition metal intercalations areused.

DFT+DMFT study of the magnetic susceptibility and the correlated electronic structure in transition-metal intercalated NbS$_2$