Hydrogenated graphene nanoribbons for spintronics

We show how hydrogenation of graphene nanoribbons at small concentrations can open venues toward carbon-based spintronics applications regardless of any specific edge termination or passivation of the nanoribbons. Density-functional theory calculations show that an adsorbed H atom induces a spin density on the surrounding $\pi$ orbitals whose symmetry and degree of localization depends on the distance to the edges of the nanoribbon. As expected for graphene-based systems, these induced magnetic moments interact ferromagnetically or antiferromagnetically depending on the relative adsorption graphene sublattice, but the magnitude of the interactions are found to strongly vary with the position of the H atoms relative to the edges. We also calculate, with the help of the Hubbard model, the transport properties of hydrogenated armchair semiconducting graphene nanoribbons in the diluted regime and show how the exchange coupling between H atoms can be exploited in the design of novel magnetoresistive devices.

Figure 1

(Color online) (a) Armchair graphene nanoribbon of width $N$ (where $N$ is the number of dimer lines) with two H atoms adsorbed in the middle of the ribbon at a distance $d$ from each other. The inset shows a detail of the adsorption geometry. (b) Pictorial representation of the one-orbital tight-binding model where the presence of H atoms is simulated by removing sites in a head-to-head configuration. (c) Same as in (b) but for the opposite ordering (tail to tail). (d) Same as in (b) but for a finite semiconducting AGNR connected to metallic nanoribbons at the edges.

Figure 2

(Color online) (a) Pictorial view of the antiferromagnetic state and (b) the magnetic-field driven ferromagnetic state where the magnetic moments localized around two hydrogen atoms are depicted by red arrows (the orientation of the arrows with respect to the graphene plane is arbitrary since spin-orbit coupling is neglected here).

Figure 3

(Color online) (a) Total energy referred to $E_0$ [lowest energy in case (b)] as a function of the distance between H atoms for the ferromagnetic (dashed) and the antiferromagnetic (solid) state when placed in the middle of the ribbon. Upper inset: picture of a nanoribbon with two H atoms. Lower inset: energy difference between both states and extrapolation to large distances (solid line). The vertical line in the inset denotes the distance above which the energy difference becomes less than 1 meV. (b) Same as in (a) but for both H atoms near the same edge. (c) Same as in (a) but for H atoms placed on opposite edges. Here the width of the ribbon is larger $\left(N=13\right)$ and $E_0$ is the minimum energy among all the AF solutions.

Figure 4

(Color online) Magnetic moments (whose magnitude is represented by the size of the circles) on individual C atoms when the H atoms are placed head to head in the middle of an $N=9$ armchair graphene nanoribbon at a distance $d=32.0\text{Å}$: [(a) ferromagnetic state and (b) antiferromagnetic state] and at a distance $d=15.4\text{Å}$: close to the edge [(d) ferromagnetic state and (e) antiferromagnetic state]. Panels (c) and (f) show the magnetization (see definition of $\Sigma$ in text) as a function of the distance between H atoms.

Figure 5

(Color online) Spin-resolved transmission as a function of energy for the ferromagnetic state of an armchair graphene nanoribbon of width $N=9$ with two H atoms adsorbed in the middle at a mutual distance $d=32\text{Å}$: calculated in the (a) local spin-density approximation and (d) with a one-orbital mean-field Hubbard model. (b) and (e) panels show the same but for the antiferromagnetic state. The resulting magnetoresistance in both approximations is shown in (c) and (f).

Figure 6

Tunneling magnetoresistance for four different atomic H configurations obtained with the Hubbard model. Two H atoms in a head-to-head configuration located in the middle of an armchair graphene nanoribbon of length $L=73.7\text{Å}$: with a width of (a) $N=9$ and (b) $N=15$, and two H atoms located near one edge (c) in a head-to-head and (d) in a tail-to-tail configuration for a ribbon width of $N=9$ and length of $L=57.0\text{Å}$.

Figure 7

Tunneling magnetoresistance (obtained with the Hubbard model) as a function of the longitudinal distance between H atoms for three different armchair graphene nanoribbon widths. The H atoms are located on opposite edges of the ribbon.