  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.
