Pure magnon valley currents in a patterned ferromagnetic thin film

Shasha Ke, Yun-Mei Li, Wen-Kai Lou, and Kai Chang

Phys. Rev. B 107, 104426 – Published 28 March 2023

Abstract

We propose a new method to generate pure magnon valley currents in ferromagnetic thin films with triangular antidot lattices. We find that inhomogeneous distortions can generate pseudomagnetic fields which can be up to 60 $T$ for magnons, and give rise to well-defined Landau levels. The pseudomagnetic fields push magnons at different valleys $K$ and $K^{'}$ transversely to opposite directions and accumulate at opposite edges, leading to magnon valley Hall effect and forming pure magnon valley edge currents. We also find that the oppositely directed pseudomagnetic fields result in magnon snake states at the center of the ribbon, forming pure magnon valley currents. Our work might pave a new way to manipulate magnon transport by using artificial designed structures.

Received 10 April 2022
Revised 12 March 2023
Accepted 16 March 2023

DOI:https://doi.org/10.1103/PhysRevB.107.104426

Physics Subject Headings (PhySH)

Landau levels Magnetism Magnons Spin waves Spintronics

Honeycomb lattice Magnetic insulators

Strain engineering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shasha Ke ^1,2, Yun-Mei Li ^3,*, Wen-Kai Lou ^1,2,†, and Kai Chang^1,2,‡

¹SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
²College of Materials Science and Opto-electronic Technology, Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
³Department of Physics, School of Physical Science and Technology, Xiamen University, Xiamen 361005, China

^*yunmeili@xmu.edu.cn
^†wklou@semi.ac.cn
^‡kchang@semi.ac.cn

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Issue

Vol. 107, Iss. 10 — 1 March 2023

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Images

Figure 1
(a) Schematic of a triangular antidot lattice consisting of circular-shaped holes in a YIG thin film and the pure magnon valley edge currents $J_{K}$ and $J_{K^{'}}$ arising from $K$ and $K^{'}$ valleys, respectively. The black dashed hexagon denotes the unit cell of the antidot lattices. The two inequivalent sites in a unit cell are denoted as $A$ and $B$ and the two primitive vectors are denoted as $a_{1}$ and $a_{2}$ . The nearest-neighbor distance is $a$ , the distance between two nearest antidots is $d$ and the radius of antidots is $r$ . (b) The lowest two bands of the magnon spectrum of YIG thin film in a triangular antidot lattice. The green, red, and orange solid lines show the magnon band structures obtained from the LLG equation with the DDI, without considering the dynamical components of the DDI and without the DDI, respectively. The gray and blue dashed lines denote the fitting results using the TB model with the nearest- and next-nearest-neighbor interactions, respectively. The inset above shows the first Brillouin zone of the magnonic crystal. Here, $a = 50 nm, r = 25 nm$ , and the thickness of the YIG film is assumed as 4 $nm$ . The spatial distributions of the (c) $| h_{x} |$ , (d) $| h_{y} |$ , (e) $| m_{x} |$ , (f) $| m_{y} |$ , and (g) $| H_{dd}^{z} |$ at the $K$ ( $K^{'}$ ) point with the DDI.
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Figure 2
(a) The illustration of undistorted ribbons of triangular antidot lattices with both the armchair and the zigzag directions. The white dots represent embedded antidots. (b) The illustration of a shear lattice distortion for an armchair-edged ribbon. The magnon band structures of armchair-edged ribbons with a width $L = 8.66$ µm (c) without a shear lattice distortion ( $c = 0$ ) and (d) with a shear lattice distortion ( $c = 0.001 a^{- 1}$ ) obtained from the LLG equation. The inset of (d) shows the relationship (red solid squares) and the linear fitting (blue solid line) between the magnon Landau levels and Landau indexes at $k = 0$ obtained from the LLG equation. (e) The distributions of the in-plane magnetization $| m |$ for the three eigenstates labeled in (d), i.e., two bulk ( $U_{1}$ and $U_{2})$ and two edge ( $U_{3}$ and $U_{4}$ ) states. This distortion corresponds to about 65.4 $T$ for graphene systems.
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Figure 3
(a) The illustration of a gradient antidot distortion for a zigzag-edged ribbon. The magnon band structures of zigzag-edged ribbons with a width $L = 7.575$ µm (b) without a gradient antidot distortion ( $B_{z} = 0$ ) and (c) with a gradient antidot distortion ( $B_{z} = - 0.002 a^{- 2}$ ) obtained from the LLG equation. The inset of (c) shows that Dirac points shift (red hollow circles) in the momentum space ( $δ q_{x}$ ), well fitted by a linear dependence (blue solid line) on the shape factor $ξ$ from the LLG eaquation. The blue solid bars represent the analytically predicted magnon Landau levels. (d) The distributions of the in-plane magnetization $| m |$ for the three eigenstates labeled in (c), i.e., one bulk ( $W_{1}$ ) and two edge ( $W_{2}$ and $W_{3}$ ) states. This distortion corresponds to about $65.4 T$ for graphene systems.
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Figure 4
The illustration of (a) a shear lattice distortion for an armchair-edged ribbon and (d) a gradient antidot distortion for a zigzag-edged ribbon with $\pm B$ configuration. The pure magnon valley snake orbit currents $S_{K}$ and $S_{K^{'}}$ are serpentine and counterpropagating. The magnon band structures of (b) armchair-edged ribbons with a width $L = 8.66$ µm with an antisymmetric shear lattice distortion ( $c = 0.001 a^{- 1}$ ) and (e) zigzag-edged ribbons with a width $L = 7.575$ µm with a symmetric gradient antidot distortion ( $B_{z} = - 0.01 a^{- 2}$ ) obtained from the LLG equation. The distributions of the in-plane magnetization $| m |$ for the (c) two eigenstates ( $M_{1}$ and $M_{2}$ ) labeled in (b), and (f) one eigenstate ( $N$ ) labeled in (e), indicating magnon snake states around the pseudomagnetic field interface.
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