Magnetoresistance and negative differential resistance in Ni/graphene/Ni vertical heterostructures driven by finite bias voltage: A first-principles study

Using the nonequilibrium Green's function formalism combined with density functional theory, we study finite bias quantum transport in Ni/Gr${}_n/$Ni vertical heterostructures where $n$ graphene layers are sandwiched between two semi-infinite Ni(111) electrodes. We find that the recently predicted “pessimistic” magnetoresistance of 100$\%$ for $n\ge 5$ junctions at zero bias voltage $V_b\to 0$ persists up to $V_b\simeq 0.4$ V, which makes such devices promising for spin-torque-based device applications. In addition, for parallel orientations of the Ni magnetizations, the $n=5$ junction exhibits a pronounced negative differential resistance as the bias voltage is increased from $V_b=0$ V to $V_b\simeq 0.5$ V. We confirm that both of these nonequilibrium transport effects hold for different types of bonding of Gr on the Ni(111) surface while maintaining Bernal stacking between individual Gr layers.

Figure 1

(a) Schematic view of Ni$/$Gr${}_5/$Ni junction where Gr${}_5$ represents five layers of graphene and Ni is (111) fcc nickel. The device extends to infinity along the transverse directions, while the Ni electrode (orange) is semi-infinite in the longitudinal (transport) direction. The two investigated types of bonding (Refs. 11, 12, and 20) for Gr on the Ni(111) surface are illustrated in panel (b), as the AB configuration where the two carbon atoms in the graphene unit cell cover Ni atoms in layers A (surface) and B (second layer), and in panel (c) as the AC configuration in which carbon atoms are placed directly above the Ni atoms in layers A (surface) and C (third layer). Here, ABC refers to three close-packed layers within a fcc crystal.

Figure 2

(a) The “pessimistic” TMR for Ni$/$Gr${}_n/$Ni junctions as a function of the number of graphene layers $n$ and for two different (AB and AC) bonding configurations for Gr on the Ni(111) surface illustrated in Figs. 1b and 1c, respectively. (b) The “pessimistic” TMR for $n=5$ junction versus finite bias voltage for AC and AB bonding configurations.

Figure 3

The finite bias transmission function $T^{\min }(E,V_b)$ for Ni$/$Gr${}_n/$Ni junction in AC bonding configuration at the Ni(111)$/$Gr interface [Fig. 1c] for (a) P and (b) AP orientations of the Ni magnetizations. Since in P orientation minority spin contribution dominates, while in AP setup both minority and majority spins contribute the same, only $T^{\min }(E,V_b)$ is presented here for both P and AP orientations with curves at different $V_b$ shifted along the $y$ axis for clarity. Panels (c) and (d) show I-V characteristics for P and AP orientations, respectively. The NDR is conspicuous in P orientation in panel (c) for both AC and AB bonding configurations.

Figure 4

The comparison of first-principles computed band structure of a periodic $...$Ni$/$Gr${}_5/$Ni$/$Gr${}_5...$ superlattice [with AC bonding configuration for Gr on the Ni(111) surface] obtained using either real-space grid PAW method implemented via the gpaw code (Ref. 25) or localized orbitals with pseudopotentials (SZP basis for C atoms and DZP basis for Ni atoms), implemented via the atk code (Ref. 26).

Figure 5

The position-dependent LDOS from left to right electrodes in Ni$/$Gr${}_5/$Ni junction, in AC bonding configuration at the Ni(111)$/$Gr interface and P orientation of the Ni magnetizations, at different bias voltages $V_b$. The electrochemical potentials ${\mu }_L$ and ${\mu }_R$ of the two Ni electrodes are marked by dashed horizontal lines, while the zero of energy is set at (${\mu }_L$ $+$ ${\mu }_R$)/2. The LDOS exhibits high values in the Ni electrodes (white regions), while the central colored region corresponds to the Gr${}_5$ barrier. The dashed ovals indicate the position of the resonant states which contribute to transport. Note that a strong coupling of the resonant states of the electrodes and the Gr barrier at a given energy level is required for large transmission $T(E,V_b)$ through the junction.