  There has been tremendous interest in manipulating electron and hole-spin states in low-dimensional structures for electronic and spintronic applications. We study the edge magnetic coupling and anisotropy in zigzag stanene nanoribbons, by first-principles calculations. Taking into account considerable spin-orbit coupling and ferromagnetism at each edge, zigzag stanene nanoribbon is insulating and its band gap depends on the inter-edge magnetic coupling and the magnetization direction. Especially for nanoribbon edges with out-of-plane antiferromagnetic coupling, two non-degenerate valleys of edge states emerge and the spin degeneracy is tunable by a transverse electric field, which give full play to spin and valley degrees of freedom. More importantly, both the magnetic order and anisotropy can be selectively controlled by electron and hole doping, demonstrating a readily accessible gate-induced modulation of magnetism. These intriguing features offer a practical avenue for designing energy-efficient devices based on multiple degrees of freedom of electron and magneto-electric couplings. 
Electric control of the edge magnetization in zigzag stanene nanoribbon