  Edge states in narrow quasi two-dimensional nanostructures determine, to a
large extent, their electric, thermoelectric and magnetic properties.
Non-magnetic edge states may quite often lead to topological insulator type
behavior. However another scenario develops when the zigzag edges are magnetic
and the time reversal symmetry is broken. In this work we report on the
electronic band structure modifications, electrical conductance and
thermoelectric properties of narrow zigzag nanoribbons with spontaneously
magnetized edges. Theoretical studies based on the Kane-Mele- Hubbard
tight-binding model show that for silicene, germanene and stanene both the
Seebeck coefficient and the thermoelectric power factor are strongly enhanced
for energies close to the charge neutrality point. Perpendicular gate voltage
lifts the spin degeneracy of energy bands in the ground state with antiparallel
magnetized zigzag edges and makes the electrical conductance significantly
spin-polarized. Simultaneously the gate voltage worsens the thermoelectric
performance. Estimated room-temperature figures of merit for the aforementioned
nanoribbons can exceed a value of 3 if phonon thermal conductances are
adequately reduced.
