Figure 1

(Color online) Schematic representation of the influence of a lateral electric field on zigzag-ribbon magnetism. The figure on the left represents the Noncollinear ground state of a doped zigzag ribbon with a canted angle $\theta$ between the spin moment orientations on opposite edges. On the right we represent how a lateral electric field represented with large green arrows drives the angle $\theta$ to $\pi$, an antiferromagnetic configuration similar to that of an undoped ribbon.Reuse & Permissions

Figure 2

(Color online) Edge state bands of a zigzag ribbon with $N=20$, nearest-neighbor hopping ${\gamma }_0=2.6\text{eV}$ and on site repulsion $U=3\text{eV}$ under a transverse electric field of $\mathcal{E}=0.2\text{eV}/\text{nm}$. Left panel: In the AF case high-spin (see text) bands shift toward the Fermi energy and the low-spin bands move away. The wave functions of the occupied bands shift density to the low-energy edge. Right panel: In the F case ${\Delta }_{\mathcal{E}}$ shifts the wave vector at which majority and minority spin bands cross to slightly larger values of $\left|k\right|$. The dotted lines show the bands at ${\Delta }_{\mathcal{E}}=0$.Reuse & Permissions

Figure 3

(Color online) Interedge relative spin orientation angle $\theta$ evaluated on the outermost edge atoms as a function of transverse electric field ${\Delta }_{\mathcal{E}}$ for a series of doping $\delta n$ values. For ${\Delta }_{\mathcal{E}}=0$ doping leads immediately to a canting angle $\theta <\pi$ and eventually for ${\delta }_n$ larger than $\sim 0.05$ to a ferromagnetic state with $\theta =0$. A finite ${\Delta }_{\mathcal{E}}$ favors the AF state as explained in the text and drives $\theta$ toward its undoped value.Reuse & Permissions

Figure 4

(Color online) Energy differences (per ribbon unit cell) between the spin collinear AF, F solutions and, for finite-doping, the minimum energy noncollinear (NC) solution. The energy difference between AF and F solutions for $\delta n=0$ has a weak transverse electric field dependence.Reuse & Permissions

Figure 5

(Color online) Top panel: Band structure of $n$ and $p$ gate-doped $N=8$ zigzag graphene nanoribbons in the presence of a transverse electric field, $\mathcal{E}=0.2\text{V}/\text{nm}$, strong enough to produce a collinear $\theta =\pi$ ground state. Note that the edge-state bands are half-metallic in both cases. Bottom panel: Spin resolved occupation $n_{\uparrow /\downarrow }\left(y\right)$ across the ribbon: majority spin electrons ($\sigma =\uparrow$ for $n$-doped and $\sigma =\downarrow$ for $p$-doped) in this figure accumulate on the high potential edge of the ribbon for $\delta n=0.06$ and on the low-potential side for $\delta n=-0.06$.Reuse & Permissions