Confined dipole and exchange spin waves in a bulk chiral magnet with Dzyaloshinskii-Moriya interaction

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Confined dipole and exchange spin waves in a bulk chiral magnet with Dzyaloshinskii-Moriya interaction

Ping Che, Ioannis Stasinopoulos, Andrea Mucchietto, Jianing Li, Helmuth Berger, Andreas Bauer, Christian Pfleiderer, and Dirk Grundler

Phys. Rev. Research 3, 033104 – Published 30 July 2021

Abstract

The Dzyaloshinskii-Moriya interaction (DMI) has an impact on excited spin waves in the chiral magnet ${Cu}_{2} {OSeO}_{3}$ by means of introducing asymmetry in their dispersion relations. The confined eigenmodes of a chiral magnet are hence no longer the conventional standing spin waves. Here we report a combined experimental and micromagnetic modeling study by broadband microwave spectroscopy, and we observe confined spin waves up to eleventh order in bulk ${Cu}_{2} {OSeO}_{3}$ in the field-polarized state. In micromagnetic simulations we find similarly rich spectra. They indicate the simultaneous excitation of both dipole- and exchange-dominated spin waves with wavelengths down to ( $47.2 \pm 0.05$ ) nm attributed to the exchange interaction modulation. Our results suggest the DMI to be effective in creating exchange spin waves in a bulk sample without the challenging nanofabrication and thereby in exploring their scattering with noncollinear spin textures.

Received 14 April 2021
Revised 3 June 2021
Accepted 3 June 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.033104

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)

Dzyaloshinskii-Moriya interaction Spin waves

Chiral magnets

Micromagnetic modeling Microwave techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ping Che ¹, Ioannis Stasinopoulos ², Andrea Mucchietto ¹, Jianing Li¹, Helmuth Berger³, Andreas Bauer ^4,5, Christian Pfleiderer^4,5,6, and Dirk Grundler^1,7,*

¹Laboratory of Nanoscale Magnetic Materials and Magnonics, Institute of Materials (IMX), École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
²Physik Department E10, Technische Universität München, 85748 Garching, Germany
³Institut de Physique de la Matière Complexe, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
⁴Physik Department E51, Technische Universität München, 85748 Garching, Germany
⁵Zentrum für QuantumEngineering (ZQE), Technische Universität München, D-85748 Garching, Germany
⁶Munich Center for Quantum Science and Technology (MCQST), Technische Universität München, D-85748 Garching, Germany
⁷Institute of Electrical and Micro Engineering, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland

^*dirk.grundler@epfl.ch

Article Text

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Issue

Vol. 3, Iss. 3 — July - September 2021

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Images

Figure 1
(a) Sketch of the dispersion relation of $k ∥ H$ mode with and without the DMI. (b) Schematic diagram of bulk ${Cu}_{2} {OSeO}_{3}$ sample placed on a CPW (yellow colored). (c) Color-coded maps of broadband spin wave spectra taken as a function of the applied field $μ_{0} H$ along $y$ at 5 K. The color scale bar represents $Δ S_{12} / μ_{0} Δ H (\times 10^{- 3} T^{- 1})$ . Black and gray arrows indicate where the line plots in panel (d) were taken. (d) Line plots of spectra $Δ S_{12} / μ_{0} Δ H$ at 5 K and $μ_{0} H = 100$ mT (black line) and 96 mT (gray line) indicated by arrows in panel (c). Solid blue (and light blue) arrows mark the frequencies which we attribute to discrete $k ∥ H$ modes and dashed blue (and light blue) arrows mark the frequencies that we categorize in terms of discrete $k ⊥ H$ modes.
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Figure 2
(a) Peak-to-peak intensity of resonances in a double-logarithmic plot corresponding to confined $k ∥ H$ mode sequences. Error bars represent the noise level in the spectra and the deviation in reading out the peaks. (b) Dispersion relation of spin waves extracted experimentally. Error bars reflect the frequency resolution of the VNA and the deviation in reading out the peaks. (c) Group velocities calculated as $2 π Δ f / Δ k_{y}$ from panel (b). Error bars originate from the frequency uncertainty in panel (b). In panels (a), (b), and (c), blue squares were extracted from the solid blue arrows in Fig. 1 of $H ∥ y$ ; red squares were extracted from data taken at $μ_{0} H = 112$ mT at $T = 20$ K (Supplemental Material, Fig. S2 [22]); yellow circles were extracted from data taken at $μ_{0} H = 150$ mT at $T = 5$ K when $H ∥ z$ (Supplemental Material, Fig. S3 [22]). Spin-wave dispersion relations evaluated from three different experiments are consistent; see panel (b).
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Figure 3
Spin wave spectra for different DMI constants. The color bar represents the integrated Fourier transform (FFT) amplitude of the magnetization component $m_{z}$ .
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Figure 4
(a) Color-coded maps of spin wave spectra from micromagnetic simulations in layer 6 in the $z$ direction. The color scale bar represents the amplitude of Fourier transform of $m_{z}$ . (b) Color-coded maps of amplitude $A$ and phase $Φ$ in the $x − y$ plane of the $z$ layer $i z = 6$ , with $D = 7.4 \times 10^{- 5} J / m^{2}$ at the field value indicated in panel (a) by the red star. The color scales of amplitude maps are normalized so that blue represents 0 and yellow represents 1. In the phase maps, blue and yellow represent $- π$ and $π$ , respectively. The wavelengths of the SWSW and LWSW are marked. (c) Dispersion relation of resonance frequencies extracted from the micromagnetic simulations. Red squares are taken from $μ_{0} H = 160$ mT with $D = 7.4 \times 10^{- 5} J / m^{2}$ . Black triangles are taken from $μ_{0} H = 160$ mT with $D = 10 \times 10^{- 5} J / m^{2}$ . Open symbols are LWSWs and correspond to the dashed red arrow in panel (b). Solid symbols are SWSWs and correspond to the solid red arrows in panel (b).
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