▎ 摘　　要

We studied the low-energy spin excitations of zigzag graphene nanoribbons of varying width. We found their energy dispersion at small wave vectors to be dominated by antiferromagnetic correlations between the ribbon's edges, in accordance with previous calculations. We point out that spin wave lifetimes are very long owing to the semi-conducting nature of electrically neutral nanoribbons. However, the application of very modest gate voltages causes a discontinuous transition to a regime of finite spin wave lifetimes. On further increasing doping, the ferromagnetic alignments along the edge become unstable against transverse spin fluctuations. This makes the experimental detection of ferromagnetism in this class of systems very delicate and poses a difficult challenge to the possible use of these nanoribbons as the basis for spintronic devices.