# Perfect Spin Filter in a Tailored Zigzag Graphene Nanoribbon

- Dawei Kang
^{1}Email author, - Bowen Wang
^{1}, - Caijuan Xia
^{2}and - Haisheng Li
^{1}

**Received: **1 March 2017

**Accepted: **9 May 2017

**Published: **18 May 2017

## Abstract

Zigzag graphene nanoribbons (ZGNRs) are expected to serve as the promising component in the all-carbon spintronic device. It remains challenging to fabricate a device based on ZGNRs with high spin-filter efficiency and low experimental complexity. Using density functional theory combined with nonequilibrium Green’s function technique, we studied the spin-dependent transport properties of the tailored zigzag graphene nanoribbon. A perfect spin-filtering effect is found in the tailored structure of ZGNR. The nearly 100% spin-polarized current and high magneto-resistance ratio can be obtained by applying a homogeneous magnetic field across the device. The distribution of spin up and spin down states at the bridge carbon atom plays a dominant role in the perfect spin filtering. The tailoring of ZGNR provides a new effective approach to graphene-based spintronics.

## Background

Graphene has attracted much attention since it was discovered experimentally in 2004 [1]. Among all its exceptional properties, the long spin diffusion length and spin relaxation time [2] due to the low intrinsic spin-orbit and hyperfine couplings [3] are most suitable for spintronics [4], which aims at generating, controlling, and detecting spin-polarized current. Especially, zigzag graphene nanoribbons (ZGNRs) are expected to host spin-polarized electronic edge states and can serve as the promising graphene-based spintronic device. The ZGNRs are predicted to have a magnetic insulating ground state with ferromagnetic ordering at each edge and antiparallel spin orientation between two edges [5]. The graphene nanoribbons can be fabricated by cutting graphene [6], patterning epitaxially grown graphene [7] or unzipping carbon nanotubes [8, 9]. Quite recently, ZGNRs with narrow width and atomically precise zigzag edges are synthesized by a bottom-up fashion and the spin-polarized edge states are directly observed by using scanning tunneling spectroscopy [10]. A variety of spintronic devices based on GNRs with edge hydrogenations [11], nanopore [12] and different connection methods [13] have been devised. The graphene nanoscale junctions formed by two GNRs leads with different widths [14, 15] or shape [16] are found to create a spin-polarized current. A trigonal graphene [17], biphenyl molecule [18], carbon atomic chains [19], single-molecule magnet Fe_{4} [20] are inserted between two GNRs to act as a spin filter. Zeng et al. studied the spin polarized current drove by source-drain voltage in ZGNRs and found that the device can behave as a bipolar spin diode [21] or spin logic gate [22]. However, devising devices based on ZGNRs with high spin-filter efficiency and a low experimental complexity still remains a challenge.

Recent progresses in graphene engineering have made it feasible to tailor graphene into desired shapes to form a device. This method avoids the difficulties of assembling nanoscale components in the realization of complete integrated circuits. The engineering of graphene with nanometer precision has been successfully realized by scanning tunneling microscope lithography [23] and electron beam etching [24]. Actually single carbon atom can be knocked off by focused electron beam of 1 Å diameter [25]. These progresses in graphene engineering make it feasible to tailor graphene with atomic resolution into desired shape studied in this paper.

In the present work, we explore spin-dependent electron transport in a tailored zigzag graphene nanoribbon. A perfect spin-filtering effect, which only one type of spin is allowed to transport while the other type is fully blocked, is found in this structure. The designed structure can be realized by removing several carbon atoms in the selected region of zigzag graphene nanoribbon. The tailoring of GNRs to obtain a pure-spin polarized current provides a new approach to graphene-based spintronics.

## Methods

The spin-dependent transport and geometry relaxation calculation are performed by the Atomistix ToolKit [26, 27] version 2016.2 which combines density functional theory with nonequilibrium Green’s function technique. The double zeta-polarized basis sets are used for carbon and hydrogen atoms. The exchange correlation potential is described by the generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The density mesh cut-off is set to 150 Ry and the k-point sampling is set as 1 × 1 × 100. Geometry optimization is performed until the force becomes less than 0.01 eV/Å.

^{2}hybridization of carbon atoms. Hereafter we label the relaxed structure in Fig. 1b as S1 and the relaxed structure in Fig. 1d as S2. In order to test the stability of the tailored structure, we performed the ab initio molecular dynamics (MD) simulations (3 ps, with 1 fs/step) in the canonical ensemble using the VASP code [28, 29], which is verified as a powerful method to find ground state in our previous works [30, 31]. The length variation of the two bonds which connect the bridge carbon atom labeled as 2 in Fig. 1b is depicted in Fig. 2. The amplitude of the oscillation of the two bonds is about 0.1 angstrom. After running 3000 steps, the geometry is still kept, suggesting the tailored structure is stable.

*σ*is the spin index.

*G*(

*E*)and

*G*

^{+}(

*E*)are retarded and advanced Green’s function of the scattering region.

*Γ*

_{ L/R }denotes the coupling matrix between the scattering region and the left/right electrode. The spin-dependent current through the system can be calculated with the Landauer–Buttiker formula

where *f*(*E* − *μ*
_{
L/R
}) = {1 + exp [(*E* − *μ*
_{
L/R
})/*k*
_{
B
}
*T*]}^{−1} is the Fermi distribution function. *μ*
_{
L/R
} is the chemical potential of the left (right) electrode, whose value depends on the applied bias.

## Results and discussion

The magnetic edges of ZGNR electrodes have an anti-ferromagnetic coupling if no magnetic field is applied, which leads to an anti-ferromagnetic ground state. The magnetization at the two edges can be turned into the same direction by applying a magnetic field. Here, we consider two magnetic configurations of the leads which can be realized easily in experiments. The [0,0] magnetic configuration means that the two ZGNR electrodes both are anti-ferromagnetic and in ground state if there is no applied magnetic field. The [1,1] magnetic configuration means that the magnetization of the two ZGNR electrodes are parallel by applying a homogeneous magnetic field across the device [32, 33].

*I*

_{[1,1]}−

*I*

_{[0.0]})/

*I*

_{[1,1]}, where

*I*

_{[1,1]}and

*I*

_{[0,0]}is the sum of both spin up and down currents. The magneto-resistance ratio can be calculated as 100% through the equation because of the zero current at [0.0] configuration. Apart from the Fermi level, the transmission of spin down state is also blocked, but the transmission of spin up state remains finite for a wide energy range. This huge difference of the transmission for spin up and down states around Fermi level indicates that the structure S1 possesses the potential to be a perfect spin filter. As for structure S2 at magnetic configuration [1,1], which is shown in Fig. 3d, the transmission of spin up and down states also have different behaviors, but both have finite values around Fermi level. The structure S2 has the potential of spin filter to some extent, but it is not a perfect filter as the structure S1. Although the structure S2 is obtained by the removing of atoms under the same mask area, the conductance shows strong difference with structure S1 and no longer possesses the perfect spin-filtering effect.

*SP*= (

*I*

_{↑}−

*I*

_{↓})/(

*I*

_{↑}+

*I*

_{↓}) reaches nearly 100% as shown in the inset of Fig. 4. The spin resolved currents of the structure S2 both increase with the applied bias and show lower spin polarization compared with structure S1. The unique structure of S1 is favorable for a nearly 100% spin polarization current. One possible application of the structure S1 may be controlling the spin current by an applied magnetic field and we can also obtain a high magneto-resistance ratio. Without magnetic field, neither spin up nor spin down current are transmitted. Applying a magnetic field will generate a nearly 100% spin polarized current.

*π*-orbitals can form between the bridge carbon atom and the carbon pentagons for spin up state, but there is no extended

*π*-orbitals for spin down state. As a result, the spin down channel will be blocked and the spin up channel is permitted at the Fermi level. But for structure S2 at [1,1] configuration as shown in Fig. 5e, f the spin up and spin down state has the similar discontinuous distribution on the three bridging carbon atoms. As a result, the spin up and down channels are all suppressed with low transmission values as shown in Fig. 3d.

## Conclusions

In summary, we studied the spin dependent transport in the tailored ZGNR devices. The perfect spin filtering is found in structure S1, which has a bridging carbon atom between two carbon pentagons. The spin-polarized current can be controlled by an applied magnetic field. The underlying physical origin is also explained by the LDOS distribution on the bridging carbon atom. The perfect spin filter effect is steady for tailoring with different lengths and widths. The tailoring of ZGNR to obtain the desired spin polarized current provides a new way to graphene-based spintronics.

## Declarations

### Acknowledgements

None.

### Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 11204066, 11147166 and 11404098), the Science and Technology Star Project of Shaanxi Province (Grant No. 2016KJXX-45).

### Authors’ contributions

DWK generated the main idea, analyzed the data, and wrote the paper. BWW calculated the data. CJX took part in the discussion and revised the original manuscript. All authors read and approved the final manuscript.

### Competing interests

The authors declare that they have no competing interests.

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## Authors’ Affiliations

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