Rashba spin splitting and perpendicular magnetic anisotropy of Gd-adsorbed zigzag graphene nanoribbon modulated by edge states under external electric fields

Zhenzhen Qin, Guangzhao Qin, Bin Shao, and Xu Zuo

Phys. Rev. B 101, 014451 – Published 31 January 2020

Abstract

The one-dimensional (1D) Rashba effect has become quite important due to its key role in basic science to realize exotic electronic phenomena, such as Majorana bound states. Similar to the two-dimensional or three dimensional systems, the modulation of Rashba effect in 1D matrix is the kernel of spintronics for manipulating electron spin. Herein, by investigating the effects of transverse and vertical external electric field (EEF) on the Rashba spin splitting and magnetic anisotropy energy (MAE) in a type of highly flexible 1D system (Gd-adsorbed zigzag graphene nanoribbons) from first principles, we found that the Rashba spin splitting in such 1D system can be effectively regulated by the transverse EEF. Moreover, perpendicular magnetic anisotropy holds with either transverse or vertical EEF applied, despite obvious modulation of the MAE contributions in $k$ space as well as the Rashba spin splitting. The modulation mechanism is further analyzed from the orbital-decomposed band structures and spin density for Gd-zigzag graphene nanoribbons (ZGNRs) at different electric-field values. It is found the modulation of $Gd 5 d_{x^{2} - y^{2}}, d_{x y}$ by C $p_{z}$ orbitals of edge states is the key to manipulating the magnetic anisotropy, which even plays a decisive role in modifying the Rashba spin splitting in such 1D nanoribbon system. The MAE and 1D Rashba spin splitting are expected to be controlled through modifying the edge states in such systems via EEF or other means. Our study introduces a strategy to manipulate Rashba spin splitting by edge states and provides insight into the magnetic anisotropy in 1D Rashba system, which would revitalize further research in ZGNR-based systems within the spintronics and exotic electronic phenomena.

Received 23 April 2019
Revised 1 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.014451

Physics Subject Headings (PhySH)

Edge states Electronic structure Magnetic anisotropy Spin-orbit coupling

Nanoribbon

Density functional theory First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhenzhen Qin ^1,5,*, Guangzhao Qin ^2,3,†, Bin Shao ^4,‡, and Xu Zuo ^5,§

¹International Laboratory for Quantum Functional Materials of Henan, and School of Physics and Microelectronics, Zhengzhou University, Zhengzhou 450001, China
²State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
³Department of Mechanical Engineering, University of South Carolina, Columbia, South Carolina 29201, USA
⁴Bremen Center for Computational Material Science, Bremen University, Am Fallturm 1, Bremen 28359, Germany
⁵College of Electronic Information and Optical Engineering, Nankai University, Tianjin 300350, China

^*qzz@zzu.edu.cn
^†qin.phys@gmail.com
^‡Present address: Shenzhen JL Computational Science and Applied Research Institute, Longhua District, Shenzhen 518110, China.
^§xzuo@nankai.edu.cn

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Issue

Vol. 101, Iss. 1 — 1 January 2020

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Images

Figure 1
(a) The magnetic moment ( $a_{1}$ ) and MAE ( $a_{2}$ ) of Gd-ZGNR with $E_{y}$ applied. The $E_{y}$ is parallel with the nanoribbon plane but perpendicular with the edges of nanoribbon as shown in the inset figure. (b) Similar with (a), but the EEF is applied along the $z$ direction ( $E_{z}$ ). The $E_{z}$ is perpendicular with the plane of nanoribbon. Positive and negative MAE represent the out-of-plane and in-plane magnetization, respectively.
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Figure 2
Angle (θ)-dependent MAE of Gd-ZGNR with EEF applied. (a)–(d) $E_{y} = - 0.8$ , −0.4, 0.4, 0.8 V/Å. (e)–(h) $E_{z} = - 0.8$ , −0.4, 0.4, 0.8 V/Å. The angle θ (0°≤θ ≤ 180°) is defined as the angle between $z$ axis and spin direction. Blue triangular line represents the calculated data and red solid line represents fitting curve.
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Figure 3
The MAE contributions in FBZ (−M-Γ-M) calculated by $E_{100} - E_{001}$ of Gd-ZGNR with (a) $E_{y}$ and (b) $E_{z}$ ( $E_{y / z} = - 0.8$ , −0.4, 0.4, 0.8 V/Å) applied, respectively. (c) Schematic diagram of Rashba spin splitting under EEF. The moment splitting $Δ k_{R}$ is defined as the horizon shift. (d) The $Δ k_{R}$ as a function of $E_{y / z}$ , where different directions are labeled by red and black solid circles, respectively.
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Figure 4
The first- and second-order part of MAE contributions in FBZ (−M-Γ-M) of Gd-ZGNR applied with $E_{y / z} =$ (a, e) −0.8 V/Å, (b, f) −0.4 V/Å, (c, g) 0.4 V/Å, and (d, h) 0.8 V/Å.
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Figure 5
The second-order MAE contributions along Γ∼M and the orbital-projected band structures ( $Gd - s d$ spin-up states and $C - p_{z}$ spin-up/down states) of Gd-ZGNR (b) without applying an EEF, with applying the $E_{y}$ in value of (a) −0.4 V/Å and (c) 0.4 V/Å, and $E_{z}$ in value of (d) −0.4 V/Å and (e) 0.4 V/Å. The orange, blue, green, rose, and red colors represent the occupation of Gd- $s$ , $d_{x y}$ , $d_{x^{2} - y^{2}}$ , $d_{x z}$ , $d_{y z}$ and $d_{z^{2}}$ orbitals, respectively. The $C - p_{z}$ spin-up/down states in the lower part are indicated by the rose/green circle, respectively. The size of color circles measures the occupied proportion of each orbital. The red and blue circles are labeled in the $C - p_{z}$ orbital part to better show the relative shift of band 1 and band-down 1 around $E_{f}$ .
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Figure 6
(a) The differences between spin densities $Δ ρ = ρ_{E_{y / z}} - ρ_{E_{0}}$ for the ZGNR plane of system without and with EEF. The atom location in the ZGNR plane is provided for an intuitive comparison with other cases. The color bar is given in the units of $e / Å^{3}$ (the red regions indicate gain electrons; the blue regions indicate lost electrons). In the left subfigure of (a), the green “−” represent the location of spin-down states, while red “+” represent the location of spin-up states. (b), (c) Schematic diagrams of spin charge transfer in Gd-ZGNR and pure ZGNR. In pure system with EEF applied (c), the spin-up electrons moved from one side to another side and further neutralized the spin-down electrons at the other side, leading the degradation of two edge states. While in Gd-ZGNR (b), the situation is changed due to existence of Gd.
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