Magnon energies and thermoelectric properties of AB-stacked bilayer zigzag graphene nanoribbons

We computed the magnon energies of AB-stacked bilayer zigzag graphene nanoribbons using the frozen magnon approach. To achieve this, we established the conical spiral formation from the most stable magnetic state while maintaining the directions of magnetic moments at edge carbon atoms. Self-consistent calculations were then performed, employing the generalized Bloch theorem in the primitive cell to determine the magnon energies. The spin stiffness was subsequently obtained by fitting a set of low magnon energies near the Gamma point. We also estimated the critical temperatures using the mean-field approximation by averaging the magnon energies over the first Brillouin zone. High spin stiffnesses and low critical temperatures were observed under all conditions. From the most stable magnetic state, we further investigated thermoelectric properties below the calculated critical temperature up to room temperature. Based solely on the electronic structure, we found figures of merit approximate to 1 near or at the Fermi level for all ribbon widths of graphene nanoribbons at low temperatures, suggesting they are promising candidates for thermoelectric materials.