Observation and control of collective spin-wave mode hybridization in chevron arrays and in square, staircase, and brickwork artificial spin ices

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Observation and control of collective spin-wave mode hybridization in chevron arrays and in square, staircase, and brickwork artificial spin ices

T. Dion, J. C. Gartside, A. Vanstone, K. D. Stenning, D. M. Arroo, H. Kurebayashi, and W. R. Branford

Phys. Rev. Research 4, 013107 – Published 11 February 2022

Abstract

Dipolar magnon-magnon coupling has long been predicted in nanopatterned artificial spin systems. However, observation of such phenomena and related collective spin-wave signatures have until recently proved elusive or been limited to low-power edge modes which are difficult to measure experimentally. Here we describe the requisite conditions for dipolar mode-hybridization, how it may be controlled, why it was not observed earlier, and how strong coupling may occur between nanomagnet bulk modes. We experimentally investigate four nanopatterned artificial spin system geometries: chevron arrays, square, staircase, and brickwork artificial spin ices. We observe significant dynamic dipolar-coupling in all systems with relative coupling strengths and avoided-crossing gaps supported by micromagnetic-simulation results. We demonstrate reconfigurable mode-hybridization regimes in each system via microstate control, and in doing so elucidate the underlying dynamics governing dynamic dipolar-coupling with implications across reconfigurable magnonics. We demonstrate that confinement of the bulk modes via edge effects plays a critical role in dipolar hybridized modes, and treating each nanoisland as a coherently precessing macro-spin or a standing spin-wave is insufficient to capture experimentally observed coupling phenomena. Finally, we present a parameter-space search detailing how coupling strength may be tuned via nanofabrication dimensions and material properties.

Received 10 December 2021
Accepted 4 January 2022

DOI:https://doi.org/10.1103/PhysRevResearch.4.013107

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)

Dipolar interaction Magnetization dynamics Magnonic crystals Spin waves

2-dimensional systems

Ferromagnetic resonance Landau-Lifschitz-Gilbert equation Micromagnetic modeling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

T. Dion ^1,2,*, J. C. Gartside ³, A. Vanstone ³, K. D. Stenning ³, D. M. Arroo ^4,5, H. Kurebayashi ², and W. R. Branford ^3,4

¹Solid State Physics Lab., Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
²London Centre for Nanotechnology, University College London, London WC1H 0AH, United Kingdom
³Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
⁴London Centre for Nanotechnology, Imperial College London, London SW7 2AZ, United Kingdom
⁵Department of Materials, Imperial College London, London SW7 2AZ, United Kingdom

^*troy.dion@phys.kyushu-u.ac.jp

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Issue

Vol. 4, Iss. 1 — February - April 2022

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Images

Figure 1
(a) Power distributions of single nanoisland modes; standing spin-wave (SSW) modes, edge modes (EMs), and bulk modes (BMs). BMs observed experimentally and simulations are a combination of EMs and SSWs. Stray fields can emanate from long edges and short edges. *Not excited in uniform field. (b) Two parallel-magnetized nanoislands precess coherently, analogous to two uncoupled masses (shown underneath). (c) Acoustic mode where oppositely magnetized nanoislands' $x$ components of dynamic magnetization precess in phase, analogous to two spring-coupled masses moving coherently. (d) Optical mode where oppositely magnetized nanoislands' $x$ components move out of phase, analogous to two spring-coupled masses moving in opposite directions. (e) Type-2 ASI microstate with field applied parallel to sublattice. (f) Type-2 ASI magnetized perpendicular to the applied field direction. Hybridization occurs only near avoided crossing. (g) Type-2 ASI microstate with parallel preparation and measurement field.
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Figure 2
(a)–(f) Simulated spectra for diagonal [(a), (b)] and chevron [(c)–(f)] two-nanoisland configurations. Microstates are shown inset for each plot, corresponding power and phase maps shown below. Applied field direction is along $x$ axis and swept from positive to negative as indicated by red arrow in (a). (g)–(j) Experimental (blue/white/red) and corresponding simulation (black/red/white) for each microstate/field configuration. Two peaks are not immediately resolvable in (g), (i) but broader tails on high-frequency (g) and low-frequency sides (i) are evidence of a second lower-power peak, consistent with simulations (c) and (e). Lorentzian fits represented by green and pink dots (g)–(j).
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Figure 3
(a) Spectra for the type-2 microstate shown inset, saturated along the swept field direction (indicated by red arrow). Modes i–iv are indicated on the right side of the spectra. Modes i and ii are similar to those in Fig. 1 with power concentrated in nanoisland center. Modes ${BM}_{3}^{opt}$ and ${BM}_{3}^{aco}$ have shorter wavelengths and backward-volume magnetostatic spin wave character (BVMSW). (b) Spectra for type-2 microstate saturated perpendicular to the swept-field direction. (c)–(f) Experimental and simulation results for (c) square ASI (d), (e) staircase ASI, and (f) brickwork ASI. Black arrows illustrate microstates.
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Figure 4
(a) Peak extraction of $\pm 20 mT$ high frequency-resolution sweep for same chevron state in Fig. 2. Avoided crossings are observed at higher fields between modes ${BM}_{1}$ (ix) and ${BM}_{3}$ (x). (b) Power and out-of-plane phase maps for each of the labeled modes at 5 Oe and 120 Oe also indicated by white dotted lines in (a). Analysis is applied to demagnetizing field to visualize dynamic stray field. Stray-field value is displayed under phase maps. Time-domain simulations for (c) ${BM}_{1}^{opt}$ and (d) ${SSW}_{1}$ mode where one precession cycle is shown. Precession for ${SSW}_{1}$ is purely out of plane. ${BM}_{1}^{opt}$ shows more coherent in-plane mode structure and is a combination of EM and SSW. (e) Stray-field outside nanoisland is integrated over time and plotted for each mode.
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Figure 5
Upper panels show the spectra and lower panels show the extracted $δ$ for the $δ^{0} (f_{i} - f_{i i})$ and $δ^{1} (f_{i i i} - f_{i v})$ modes as a function of (a) nanoisland length, (b) width, (c) thickness, (d), lateral scaling, (e) saturation magnetization, and (f) lattice parameter. Insets show geometry being changed and are all to scale with (e) showing geometry common to all panels. The dotted line in (c) indicates the point where the ${BM}_{1}^{opt}$ and ${BM}_{1}^{aco}$ modes switch positions in frequency with the higher order ${BM}_{3}^{aco}$ and ${BM}_{3}^{opt}$ modes. This may be treated as another avoided crossing.
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