Journal of Nanomaterials

Volume 2015 (2015), Article ID 810659, 10 pages

http://dx.doi.org/10.1155/2015/810659

## Symmetry-Dependent Spin Transport Properties and Spin-Filter Effects in Zigzag-Edged Germanene Nanoribbons

^{1}School of Physics and Electronics, Central South University, Changsha 410083, China^{2}School of Geosciences and Info-Physics, Central South University, Changsha 410083, China

Received 26 March 2015; Revised 2 July 2015; Accepted 5 July 2015

Academic Editor: Christian Brosseau

Copyright © 2015 Can Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We performed the first-principles calculations to investigate the spin-dependent electronic transport properties of zigzag-edged germanium nanoribbons (ZGeNRs). We choose of ZGeNRs with odd and even widths of 5 and 6, and the symmetry-dependent transport properties have been found, although the mirror plane is absent in ZGeNRs. Furthermore, even- and odd- ZGeNRs have very different current-voltage relationships. We find that the even 6-ZGeNR shows a dual spin-filter effect in antiparallel (AP) magnetism configuration, but the odd 5-ZGeNR behaves as conventional conductors with linear current-voltage dependence. It is found that when the two electrodes are in parallel configuration, the 6-ZGeNR system is in a low resistance state, while it can switch to a much higher resistance state when the electrodes are in AP configuration, and the magnetoresistance of 270% can be observed.

#### 1. Introduction

Graphene and graphene nanoribbons (GNRs) have attracted broad academic and industrial interests owing to their amazing properties [1, 2] and potential applications in nanodevices [3–5]. In particular, their applications in spintronics field [6–8] offer the most promising solutions for future high operating speed and energy-saving electronic devices. For instance, the zigzag graphene nanoribbon (ZGNR) is an anti-ferromagnetic insulator with considerable magnetic moment located at edge sites, which give rise to many unusual properties, such as half metallic [9], magnetoelectric effect [10, 11], and spin-filter effect [11, 12].

These interesting behaviors of graphene motivate the further exploration of honeycomb lattice with higher group IV elements. Walking down the periodic table from carbon to silicon (Si) to germanium (Ge) enhances the -orbital participation in their electronic behavior and thus develops strong electronic correlation. And there are many interesting magnetic and charge excitations behaviors that would be introduced. Theory predicts free standing silicene or germanene sheets and ribbons to be stable in a low puckered configuration [13–16]. Different from graphene, in silicene or germanene, two adjacent atoms belonging to the same sublattice are not in the same plane owing to the buckled structure of silicene or germanene. Thus, the buckled structural feature would give rise to tunable spin-valley coupled band structures, which accounts for many exotic transport [17, 18] and superconducting phenomena [19] and makes silicene and germanene good candidates for the spintronics [20–23]. The first-principle calculations show that the intrinsic carrier mobility of germanene sheet can even reach ~6 × 10^{5} cm^{2} V^{−1} s^{−1}, which is larger than that of graphene [24]. In particular, compared with Si, Ge has longer spin-diffusion length and the relative strong spin-orbit coupling would be helpful to the spin injection and the manipulation of spin [25, 26]. Thus, the developments of multifunctional germanene-based spintronics components and the corresponding nanodevices design are more worth studying thoroughly. A feasible approach to realize germanene-based spintronics is to construct the device junctions of germanium nanoribbons (ZGeNRs) and then systematically study the transport properties as fundamental and crucial components of germanene-based circuits. Recently, intriguing transport phenomena have been found in zigzag graphene nanoribbons (ZGNRs) [27], zigzag -graphyne nanoribbons [28], and silicene nanoribbons (ZSiNRs) with buckled structure [21], where symmetric and asymmetric zigzag ribbons are found to have completely different - characteristics despite the similarity of their band structure. More interestingly, bipolar spin diode behavior was observed in symmetry devices. Spin polarization and direction of the current through the device can be controlled through either the voltage or magnetic configuration of the electrodes. Such freedom in controlling the spin-polarized current is useful in design of spin devices such as rectification and amplification for spintronics. However, until now, no one is working on the spin transport property of symmetric and asymmetric ZGeNRs. Developments of multifunctional germanium-based spintronics devices that offer effective manipulation of spin-polarized current are an important supplement of exploration of spintronics.

So, in this work, we investigate the spin-dependent transport properties of ZGeNRs by first-principles calculations. Our results show that although the plane is absent in ZGeNRs due to the low puckered configuration, the ZGeNRs still exhibit symmetry-dependent transport properties. And the magnetoresistance effect is also observed in ZGeNRs. Our works suggest a route to manipulate spin-polarized current and to design the germanene-based spintronic devices.

#### 2. Models and Theoretical Method

ZGeNRs can be classified by the number of Ge atoms along the width of the ribbon. We choose ZGeNRs with odd and even widths of 5 and 6, which are denoted here as 5-ZGeNR and 6-ZGeNR, respectively. The geometric structures from top view and cross section view of 6-ZGeNR are shown in Figures 1(a) and 1(b), respectively. The system is divided into three regions: left electrode, right electrode, and the central scattering region. Each electrode is described by a supercell with two repeated ZGeNR unit cells along transport direction, and the scattering region is ZGeNR with length of 6 unit cells. An external magnetic field controlling the magnetization of the left (right) ZGeNR electrode can be set to be 1 or −1, corresponding to magnetization along the or direction. In this paper, we use and to represent the magnetization of the left and right electrodes; that is, shows that the left and right electrodes are parallel (P) in spin orientation, while shows that the left and right electrodes are antiparallel (AP) in spin orientation. The geometric optimization and spin-resolved electronic transport properties are calculated by a developed* ab initio* software package Atomistix ToolKit [29, 30], which is based on the spin-polarized density-functional theory combined with the nonequilibrium Green functions. In the calculation, the Troullier-Martins norm-conserving pseudopotential, the local spin density approximation (LSDA) for exchange-correlation potential, and -point grid 1 × 1 × 100 are used. The real space grid techniques are used with the energy cutoff of 150 Ry as a required cutoff energy in numerical integrations and the solution of Poisson equation using fast Fourier transform (FFT). The geometry optimization is performed using quasi-Newton method until the absolute value of force acting on each atom is <0.05 eV/Å. The wave functions of Ge and H atoms are expanded by single-zeta polarized (SZP) basis set. The spin-resolved current is calculated using the Landauer formula:where (spin up) and (spin down), is the electrochemical potential of the left/right electrode, and the difference of them is , and is the spin-resolved transmission defined aswhere is the retarded (advanced) Green functions of the central region and is the contact broadening functions.