Topological phase and edge states dependence of the RKKY interaction in zigzag silicene nanoribbon

Moslem Zare, Fariborz Parhizgar, and Reza Asgari

Phys. Rev. B 94, 045443 – Published 29 July 2016

Abstract

We propose versatile materials based on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in a zigzag silicene nanoribbon (ZSNR) on half filling in the presence of an out-of-plane electric field. We show that the topological phase transition in the band dispersion of ZSNR can be probed by using the RKKY interaction. We find that, due to the zero-energy edge states of the ZSNR, the exchange coupling is significantly enhanced when the impurities are located on the zigzag edges, and also explore that the strength of the interaction in the topological insulator phase is much greater than that when the system is in the band insulator region. We present a model to investigate the phase of a system of two magnetic impurities located on the edge of the ZSNR and find that three different magnetic phases, spiral, ferromagnetic, and antiferromagnetic, are possible for different values of the electric field. This electrical tunability of the magnetic phases in silicene can be explored by using current experimental techniques and can be of interest in the field of spintronics.

Received 3 July 2015
Revised 18 July 2016

DOI:https://doi.org/10.1103/PhysRevB.94.045443

Physics Subject Headings (PhySH)

Edge states RKKY interaction

Nanoribbon Silicene

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Moslem Zare, Fariborz Parhizgar^*, and Reza Asgari^†

School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran

^*fariborz.parhizgar@ipm.ir
^†asgari@ipm.ir

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Issue

Vol. 94, Iss. 4 — 15 July 2016

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Images

Figure 1
Lattice structure of the zigzag silicene nanoribbon. The edge and inside configurations are marked with black and green spins, respectively. The dashed box is a unit cell and $m, n$ represent the $x$ and $y$ coordinates of the lattice points. The length ( $L$ ) and the width ( $N$ ) of the nanoribbon are defined as the number of unit cells and the number of atoms in a unit cell, respectively. Here, we have taken $N = 12$ .
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Figure 2
Various terms of the RKKY interaction scaled by $J_{c}^{2}$ as a function of the impurity distances for the ZSNR with $N = 12, L = 300$ . (a), (b) Impurities located on the edge (black arrows) such that the first impurity is fixed at the sublattice $(11, 1)$ and the second one is located at $(m, 1)$ , where $m = 12, 13, ...$ . (c), (d) Impurities located inside the ZSNR (green arrows) such that the first impurity is located on the sublattice $(11, 6)$ and the second one is placed at $(m, 6)$ with $m = 12, 13, ...$ . In these figures, the electric field is fixed at $l E_{z} = 1$ meV in (a) and (c) and $l E_{z} = 6.8$ meV in (b) and (d). Note that $J_{RKKY}$ shows an oscillatory behavior in $R$ and decays fast with a short-ranged behavior. The RKKY coupling is significantly larger than the situation where both impurities are in the bulk due to the existence of nearly-zero-energy states at the edge of the ZSNR.
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Figure 3
Root mean square of various terms of the RKKY interaction scaled by $J_{c}^{2}$ as a function of the perpendicular electric potential for the ZSNR with $N = 22, L = 300$ . Here, the first impurity is fixed at the sublattice $(147, 1)$ and the position of the second one is varied from sublattices $(148, 1)$ to $(157, 1)$ . $E_{c}$ in this figure has been labeled by a black vertical arrow.
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Figure 4
Various terms of the RKKY interaction scaled by $J_{c}^{2}$ as a function of the perpendicular electric potential for $L = 300$ , when two impurities are fixed at the zigzag edge at $(148, 1)$ and $(153, 1)$ lattice points: (a) the Heisenberg and Ising terms and (b) the Dzyaloshinskii-Moriya term. In both cases, $R / a = 5$ . Noticeably, the RKKY coupling increases with ZSNR width due to the increase of the density of states of the edge mode. Black vertical arrows show the position of $E_{c}$ .
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Figure 5
Sign ( $D_{1, 2}$ ) and phase diagram of a system of two magnetic impurities placed on the edge of ZSNR with $N = 12, L = 300$ as a function of the external potential. Here, impurities are located with five lattice vectors ( $R / a = 5$ ) from each other, at $(148, 1)$ and $(153, 1)$ lattice points.
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