  Edge magnetism in zigzag transition metal dichalcogenide nanoribbons is
studied using a three-band tight-binding model with local electron-electron
interactions. Both mean field theory and the unbiased, numerically exact
determinant quantum Monte Carlo method are applied. Depending on the edge
filling, mean field theory predicts different phases: gapped spin dimer and
antiferromagnetic phases appear for two specific fillings, with a tendency
towards metallic edge-ferromagnetism away from those fillings. Determinant
quantum Monte Carlo simulations confirm the stability of the antiferromagnetic
gapped phase at the same edge filling as mean field theory, despite being
sign-problematic for other fillings. The obtained results point to edge filling
as yet another key ingredient to understand the observed magnetism in
nanosheets. Moreover, the filling dependent edge magnetism gives rise to
spin-polarized edge currents in zigzag nanoribbons which could be tuned through
a back gate voltage, with possible applications to spintronics.
