  Molybdenum disulfide nanoribbons with zigzag edges show ferromagnetic and
metallic properties based on previous \emph{ab-initio} calculations. The
investigation of the role of disorder on the magnetic properties is, however,
still lacking due to the computational costs of these methods. In this work we
fill this gap by studying the magnetic and electronic properties of several
nanometer long MoS$_2$ zigzag nanoribbons using tight-binding and Hubbard
Hamiltonians. Our results reveal that proper tight-binding parameters for the
edge atoms are crucial to obtain quantitatively the metallic states and the
magnetic properties of MoS$_2$ nanoribbons. With the help of the fine-tuned
parameters, we perform large-scale calculations and predict the spin
domain-wall energy along the edges, which is found to be significantly lower
compared to that of the zigzag graphene nanoribbons. The tight-binding approach
allows us to address the effect of edge disorder on the magnetic properties.
Our results open the way for investigating electron-electron effects in
realistic-size nanoribbon devices in MoS$_2$ and also provide valuable
information for spintronic applications.
