The ferromagnetism of the two dimensional (2D) Cr ₂ Ge ₂ Te ₆ atomic layers with the perpendicular magnetic anisotropy and the Curie temperature 30–50 K has recently been experimentally confirmed. By performing the density-functional theory calculations, we demonstrate that the magnetic properties of bilayer Cr ₂ Ge ₂ Te ₆ can be flexibly tailored, due to the effective band structure tuning by the external electric field. The electric field induces the semiconductor-metal transition and redistributes charge and spin between the two layers. Furthermore, the magnetic anisotropy energy of the bilayer Cr ₂ Ge ₂ Te ₆ can be obviously enhanced by the electric field, which is helpful to stabilize the long-range ferromagnetic order. Our study about the electric manipulation of magnetism based on the band structure engineering generally exists in 2D magnetic systems and will be of great significance in low-dimensional all-electric spintronics.

The magnetic property and band structures of Co-monolayer doped graphene were examined on the basis of density-functional theory. The magnetic moment of the system is closely related to the interfacial spacing. Magnetic-nonmagnetic transition would be produced by decreasing the layer distance. Although the magnetic moment can also be reduced by increasing the lattice constant, the ground states are magnetic states under tension. Besides, the increase of lattice constant greatly enlarges the direct and indirect gaps of spin-down bands near the Fermi level. With a little increase of the Fermi level or the electron density, half-metal behavior would be expectable in the Co-doped graphene under tension.