Magnetic Correlations at Graphene Edges

Magnetic zigzag edges of graphene are considered as a basis for novel spintronics devices despite the fact that no true long-range magnetic order is possible in one dimension. We study the transverse and longitudinal fluctuations of magnetic moments at zigzag edges of graphene from first principles. We find a high value for the spin wave stiffness $D$ = 2100 meV \AA${}^2$ and a spin-collinear domain wall creation energy $E_{d}w$ = 114 meV accompanied by low magnetic anisotropy. Above the crossover temperature $T_x \approx$10Kthespincorrelationlength$\xi \propto T^{-1}$ limits the long-range magnetic order to ~1 nm at 300 K while below $T_x$ it grows exponentially with decreasing temperature. We discuss possible ways of increasing the range of magnetic order and effects of edge roughness on it.