Multiferroic and Ferroic Topological Order in Ligand-Functionalized Germanene and Arsenene

Liangzhi Kou, Yandong Ma, Ting Liao, Aijun Du, and Changfeng Chen

Phys. Rev. Applied 10, 024043 – Published 28 August 2018

Abstract

Two-dimensional (2D) materials that exhibit ferroelectric, ferromagnetic, or topological order have been a major focal topic of nanomaterials research in recent years. The latest efforts in this field explore 2D quantum materials that host multiferroic or concurrent ferroic and topological order. We present a computational discovery of multiferroic state with coexisting ferroelectric and ferromagnetic order in recently synthesized ${CH}_{2} O {CH}_{3}$ -functionalized germanene. We show that an electric-field-induced rotation of the ligand ${CH}_{2} O {CH}_{3}$ molecule can serve as the driving mechanism to switch the electric polarization of the ligand molecule, while unpassivated $Ge$ $p_{z}$ orbits generate ferromagnetism. Our study also reveals coexisting ferroelectric and topological order in ligand-functionalized arsenene, which possesses a switchable electric polarization and a Dirac transport channel. These findings offer insights into the fundamental physics underlying these coexisting quantum orders and open avenues for achieving states of matter with multiferroic or ferroic-topological order in 2D-layered materials for innovative memory or logic device implementations.

Received 25 April 2018
Revised 23 July 2018

DOI:https://doi.org/10.1103/PhysRevApplied.10.024043

Physics Subject Headings (PhySH)

Electric polarization Electronic materials Electronic structure Ferroelectricity

2-dimensional systems Multiferroics Topological materials

GGA

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Liangzhi Kou^1,*, Yandong Ma², Ting Liao¹, Aijun Du¹, and Changfeng Chen³

¹School of Chemistry, Physics and Mechanical Engineering Faculty, Queensland University of Technology, Garden Point Campus, Brisbane, QLD 4001, Australia
²School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Shandanan Str. 27, 250100 Jinan, People’s Republic of China
³Department of Physics and Astronomy, University of Nevada, Las Vegas, Nevada 89154, USA

^*kouliangzhi@gmail.com

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Vol. 10, Iss. 2 — August 2018

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Images

Figure 1
(a) Side and (b) top views of the structural model for ${CH}_{2} O {CH}_{3}$ -functionalized germanene layer, where the cyan, gray, red, and white balls represent $Ge$ , $C$ , $O$ , and $H$ atoms, respectively; the red dashed lines highlight the unit cell used in the present work, and the red arrow in (a) indicates the rotation direction of the ligand molecules. (c) The electronic band structure of functionalized germanene.
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Figure 2
(a) Energy variation and kinetic barrier of ligand molecule rotation. Four stable configurations are labelled as I, II, III, and IV. (b) The configurations of the four stable structures indicated in (a); for clarity, only the atoms in the rotating ${CH}_{2} O {CH}_{3}$ molecule on the top surface are shown, while all other atoms and bonds are represented by lines. The red and blue arrows indicate the polarization directions of the ${CH}_{2} O {CH}_{3}$ molecule on the bottom (without rotation) and top (with rotation) surfaces, respectively. (c) Variation of the polarization along the x and y directions [as indicated in (b)] when the ${CH}_{2} O {CH}_{3}$ molecule rotates; the polarization direction along the y axis reverses, achieving in-plane ferroelectricity.
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Figure 3
(a) Partial functionalization of the germanene layer; the dashed circles represent the unpassivated $Ge$ atoms. (b) Orbitally resolved density of states for $Ge$ , which clearly shows that the magnetism stems from the unoccupied p_z orbit of the $Ge$ atoms, the inset shows the spatial spin density distribution with an isosurface of 5 × 10⁻³ e/Å³. Electronic properties and polarization direction of half-passivated germanene by ligand ${CH}_{2} O {CH}_{3}$ . (c) Projected electronic density of states (DOS) for $Ge$ atoms of half-passivated germanene by ligand ${CH}_{2} O {CH}_{3}$ ; the inset shows the corresponding spin distribution. (d) Polarization (directions indicated by the arrows) reversal when ligand ${CH}_{2} O {CH}_{3}$ molecules are rotated by 180°.
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Figure 4
(a) Energy variation and kinetic barrier for ${CH}_{2} O {CH}_{3}$ rotations in functionalized arsenene; the insets show the structural models. (b) Variation of the polarization along the x and y directions. (c),(d) Electronic band structures of the symmetric ligand configuration with the rotation angle of 0° and the asymmetric ligand configuration with the rotation angle of 120^o. The topological order is preserved under the ligand rotation, although there is a band splitting due to an out-of-plane symmetry breaking.
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Figure 5
(a) A schematic diagram of the electric-field-induced ligand rotation. (b) Charge distributions on the ligand molecule ${CH}_{2} O {CH}_{3}$ and (c) the associated force analysis.
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