Strain-engineered magnon states in two-dimensional ferromagnetic monolayers

Open Access

Strain-engineered magnon states in two-dimensional ferromagnetic monolayers

Bin Wei, Jia-Ji Zhu, Yun Song, and Kai Chang

Phys. Rev. Research 6, 013210 – Published 27 February 2024

Abstract

We systematically investigate the strain-engineered magnon states in two-dimensional (2D) ferromagnetic monolayers. By suitable engineering of an inhomogeneous strain, we demonstrate the emergence of magnon Landau levels and magnon snake states in 2D ferromagnetic monolayers. We show a magnon valley Hall effect and valley filter without relying on any external fields. Our proposal offers us another way to manipulate magnon valley transport and construct different types of flexible spintronic devices, and is experimentally feasible for 2D ferromagnetic materials by using state-of-art techniques.

Received 22 September 2023
Accepted 25 January 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.013210

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Hall effect Landau levels Magnons Strain Valley degrees of freedom

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Bin Wei ¹, Jia-Ji Zhu ^2,3,*, Yun Song ^4,†, and Kai Chang^1,5,‡

¹SKLSM, Institute of Semiconductors,Chinese Academy of Sciences, Beijing 100083, China
²School of Science and Institute for Advanced Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400061, China
³Southwest Center for Theoretical Physics, Chongqing University, Chongqing 401331, China
⁴Department of Physics, Beijing Normal University, Beijing 100875, China
⁵School of Physics, Zhejiang University, Hangzhou 310027, China

^*zhujj@cqupt.edu.cn
^†yunsong@bnu.edu.cn
^‡kchang@semi.ac.cn

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand

Issue

Vol. 6, Iss. 1 — February - April 2024

Subject Areas

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic diagram of strain-engineered magnon states. The 2D magnetic monolayer, e.g., ${CrI}_{3}$ , is placed on a soft substrate. By employing symmetric and antisymmetric strain, magnon Landau levels and snake states arise in the armchair and zigzag ribbons. The strain-induced pseudomagnetic fields point in the $\pm z$ direction for different valleys in the zigzag ribbon. The magnon valley Hall effect emerges, denoted by the blue and red arrows indicating the drift of magnon wave packets to the upper and lower edges of the system, respectively.
Reuse & Permissions
Figure 2
The magnon spectrum of the zigzag ribbon with different strain strengths (a) $C_{s} = 0$ and (b) $C_{s} = 0.2 \times 10^{- 3} / a_{0}$ . Gray lines depict numerical results for all the magnon bands, and the thick yellow (green) line segments depict the representative bulk (edge) state. The insets show the wave-function spatial distributions for corresponding states. The blue and red lines represent the $A$ sublattice and $B$ sublattice, respectively. (c) The magnon spectrum near the Dirac frequency, where the magnon LLs emerge. The blue circles indicate the magnon LLs $n = \pm 1, \pm 2, \pm 3$ , and $\pm 4$ . The symbols $\otimes$ and $⊙$ denote the signs of the PMFs. (d) The energies of magnon LLs depend on the index ( $n$ ) of the LLs. The blue circles correspond to the blue circles in (c), and the red dotted line is the theoretical fitting by Eq. (9). (e) The wave-function spatial distributions for $K$ and $K^{'}$ valleys of the first magnon LLs.
Reuse & Permissions
Figure 3
(a) The magnon spectrum of the strain-free armchair ribbon with different widths $N = 100$ and 101. (b) The magnon spectrum and density of states of an 822-nm-wide armchair ribbon at strain strength $C_{s} = 0.3 \times 10^{- 3} / a_{0}$ , where $t_{0} = 6.43$ . The red dots and dashed lines in (b) indicate the magnon LLs $n = 0, \pm 1, \pm 2, \pm 3, \pm 4$ according to Eq. (9) with $B_{eff} = 2.53$ T. (c) Distribution of zeroth magnon LLs at $k = 0, | k | = 0.1 π / a_{0}$ , and $| k | = 0.2 π / a_{0}$ . At finite $k$ , the magnons are pushed toward the edges due to the PMF induced by the inhomogeneous strain.
Reuse & Permissions
Figure 4
The magnon spectrum of (a) the armchair ribbon and (b) the zigzag ribbon, with $C_{s} = 0.3 \times 10^{- 3} / a_{0}$ , respectively. The probability densities of the magnon states are illustrated in the insets, where the dots marked with $S, E 1$ , $E 2$ , and $M$ correspond to magnon snake states, edge states, and mixed states. $Ψ_{A}$ (red line) and $Ψ_{B}$ (blue line) represent the two sublattices.
Reuse & Permissions
Figure 5
(a) Schematic drawing of a magnon valley filter in the ferromagnetic monolayer with a Gaussian bump, where $h_{0}$ is the maximal deformation in the $z$ direction and $σ$ is the width of the Gaussian bump. The blue (red) arrows represent the $K$ -valley ( $K^{'}$ -valley) polarized magnons. The inset shows a ${CrI}_{3}$ -sealed microcavity in the pressure chamber. (b) Profile of the pseudomagnetic field induced by a Gaussian bump in the $K$ valley, where height $h_{0} = 0.5 µ m$ , and width $σ = 3 µ m$ . Blue (red) lines are the $K$ - ( $K^{'}$ -) valley magnon trajectories incident from the left.
Reuse & Permissions

Physical Review Research