  Recent experiments on the antiferromagnetic intercalated transition metal
dichalcogenide $\mathrm{Fe_{1/3}NbS_2}$ have demonstrated reversible
resistivity switching by application of orthogonal current pulses below its
magnetic ordering temperature, making $\mathrm{Fe_{1/3}NbS_2}$ promising for
spintronics applications. Here, we perform density functional theory
calculations with Hubbard U corrections of the magnetic order, electronic
structure, and transport properties of crystalline $\mathrm{Fe_{1/3}NbS_2}$,
clarifying the origin of the different resistance states. The two
experimentally proposed antiferromagnetic ground states, corresponding to
in-plane stripe and zigzag ordering, are computed to be nearly degenerate.
In-plane cross sections of the calculated Fermi surfaces are anisotropic for
both magnetic orderings, with the degree of anisotropy sensitive to the Hubbard
U value. The in-plane resistance, computed within the Kubo linear response
formalism using a constant relaxation time approximation, is also anisotropic,
supporting a hypothesis that the current-induced resistance changes are due to
a repopulating of AFM domains. Our calculations indicate that the transport
anisotropy of $\mathrm{Fe_{1/3}NbS_2}$ in the zigzag phase is reduced relative
to stripe, consistent with the relative magnitudes of resistivity changes in
experiment. Finally, our calculations reveal the likely directionality of the
current-domain response, specifically, which domains are energetically
stabilized for a given current direction.
