▎ 摘　　要

Materials with competitive spin interactions can show multiple quantum magnetic states under external manipulation, which is important for spin-related research and applications. Although the magnetism in graphene nanoribbons has been intensively studied, robust spin interactions have not been reported. Here, we explored graphene nanoribbons modified with Ti and V atomic chains that show competitive spin interactions and robust spiral magnetism. On the basis of first-principles calculations, we systematically investigate the possibility of inducing robust and competitive magnetic ordering in graphene nanoribbons through transition-metal (TM) atomic chain decoration (denoted as TM-ZGNR, TM = TiCo). On the basis of the Heisenberg XY model including nearest-neighbor (NN) and next-nearest-neighbor (NNN) magnetic interactions, Ti-ZGNR and V-ZGNR are predicted to have spiral magnetic order due to spin frustration. By Monte Carlo simulations, the Neel temperatures for Ti-ZGNR and V-ZGNR are estimated to be 45 and 100 K, respectively. Our studies will benefit further spin-control research on graphene nanoribbons.