Efficient Spin Injection into Graphene through a Tunnel Barrier: Overcoming the Spin-Conductance Mismatch

Employing first-principles calculations, we investigate the efficiency of spin injection from a ferromagnetic electrode (Ni) into graphene and a possible enhancement by using a barrier between the electrode and graphene. Three types of barriers, $h$-BN, Cu(111), and graphite, of various thickness (0–3 layers) are considered, and the electrically biased conductance of the $\mathrm{Ni}/\text{barrier}/\text{graphene}$ junction is calculated. It is found that the minority-spin-transport channel of graphene can be strongly suppressed by the insulating $h$-BN barrier, resulting in a high spin-injection efficiency. On the other hand, the calculated spin-injection efficiencies of $\mathrm{Ni}/\mathrm{Cu}/\text{graphene}$ and $\mathrm{Ni}/\text{graphite}/\text{graphene}$ junctions are low, due to the spin-conductance mismatch. Further examination of the electronic structure of the system reveals that the high spin-injection efficiency in the presence of a tunnel barrier is due to its asymmetric effects on the two spin states of graphene.

Figure 1

Side and top views of the $\mathrm{Ni}(111)/h$-BN/graphene model. The thickness of the $h$-BN tunnel layer (or Cu, graphite) is varied from 0 (without a tunnel barrier) to 3 atomic layers. The model shown here has three atomic layers of $h$-BN. The supercell used for structural optimization and band structure calculation is indicated by the brown dashed box. The device is built with two semi-infinite leads and a scattering region.

Figure 2

(a) Model for $\mathrm{Ni}(111)/\text{graphene}$. (b) The calculated $I$-$V$ curve of $\mathrm{Ni}(111)/\text{graphene}$. (c) The transmission spectrum of $\mathrm{Ni}(111)/\text{graphene}$ under a bias voltage of 0.3 V.

Figure 3

(a) Model for $\mathrm{Ni}(111)/(h\text{−}\mathrm{BN}{)}_3/\text{graphene}$. The subscript 3 indicates three atomic layers of $h$-BN. (b) The calculated $I$-$V$ curve of $\mathrm{Ni}(111)/(h\text{−}\mathrm{BN}{)}_3/\text{graphene}$. (c) The transmission spectrum of $\mathrm{Ni}(111)/(h\text{−}\mathrm{BN}{)}_3/\text{graphene}$ under a bias voltage of 0.3 V.

Figure 4

The calculated spin-resolved transmission eigenstates of (a) the spin-up channel and (b) the spin-down channel of $\mathrm{Ni}(111)/(h\text{−}\mathrm{BN}{)}_3/\text{graphene}$ under a bias voltage of 0.3 V. (c) Schematic diagram showing the effect of a tunnel barrier on the spin polarization of a current injected from the Ni(111) electrode to graphene.

Figure 5

Models for (a) $\mathrm{Ni}(111)/(\text{graphite}{)}_3/\text{graphene}$ and (b) $\mathrm{Ni}(111)/(\mathrm{Cu}{)}_3/\text{graphene}$. The subscript indicates the thickness of the barrier in the number of atomic layers. (c),(d) The calculated $I$-$V$ curves of the above two devices, respectively.

Figure 6

Spin-resolved band structures of $\mathrm{Ni}(111)/\text{graphene}$ without a tunnel barrier (upper panels) and with one atomic layer of $h$-BN (lower panels), respectively. The spin-up (-down) band structure is shown in the left (right) panel, in each case. The solid circles represent the weight of the graphene-derived $p_z$ orbital.

Figure 7

LDOS of $\mathrm{Ni}(111)/\text{graphene}$ (a) without a tunnel barrier and (b) with one atomic layer of $h$-BN, respectively. The LDOS on B and N orbitals are not shown. To show the details, the LDOS of C $p$ are enlarged by 5 times. As can be seen, the overlap of spin-down states of C $p$ and Ni $d$ disappears after inserting $h$-BN.