Observation of Collective Resonance Modes in a Chiral Spin Soliton Lattice with Tunable Magnon Dispersion

Y. Shimamoto, Y. Matsushima, T. Hasegawa, Y. Kousaka, I. Proskurin, J. Kishine, A. S. Ovchinnikov, F. J. T. Goncalves, and Y. Togawa

Phys. Rev. Lett. 128, 247203 – Published 17 June 2022

Abstract

A chiral spin soliton lattice (CSL), one of the representative systems of a magnetic superstructure, exhibits reconfigurability in periodicity over a macroscopic length scale. Such coherent and tunable characteristics of the CSL lead to an emergence of elementary excitation of the CSL as phononlike modes due to translational symmetry breaking and bring a controllability of the dispersion relation of the CSL phonon. Using a broadband microwave spectroscopy technique, we directly found that higher-order magnetic resonance modes appear in the CSL phase of a chiral helimagnet ${CrNb}_{3} S_{6}$ , which is ascribed to the CSL phonon response. The resonance frequency of the CSL phonon can be tuned between 16 and 40 GHz in the vicinity of the critical field, where the CSL period alters rapidly. The frequency range of the CSL phonon is expected to extend over 100 GHz as extrapolated on the basis of the theoretical model. The present results indicate that chiral helimagnets could work as materials useful for broadband signal processing in the millimeter-wave band.

Received 2 January 2022
Accepted 15 April 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.247203

Physics Subject Headings (PhySH)

Helicoidal magnetic texture Magnetization dynamics

Chiral magnets Helimagnets

Electron spin resonance Ferromagnetic resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. Shimamoto ^1,2,*, Y. Matsushima¹, T. Hasegawa¹, Y. Kousaka ^1,2, I. Proskurin ^3,4, J. Kishine^5,6, A. S. Ovchinnikov ^4,7, F. J. T. Goncalves⁸, and Y. Togawa ^1,2

¹Department of Physics and Electronics, Osaka Prefecture University, 1-1 Gakuencho, Sakai, Osaka 599-8531, Japan
²Department of Physics and Electronics, Osaka Metropolitan University, 1-1 Gakuencho, Sakai, Osaka 599-8531, Japan
³Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
⁴Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg 620002, Russia
⁵Division of Natural and Environmental Sciences, The Open University of Japan, Chiba 261-8586, Japan
⁶Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan
⁷Institute of Metal Physics, Ural Division, Russian Academy of Sciences, Ekaterinburg 620219, Russia
⁸Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, Bautzner Landstraße 400, 01328 Dresden, Germany

^*y-shimamoto-omu@omu.ac.jp

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Vol. 128, Iss. 24 — 17 June 2022

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Images

Figure 1
(a) and (b) Schematic illustrations of a chiral spin soliton lattice (CSL) in the presence of the magnetic field $H$ applied in the direction perpendicular to the $c$ axis of the crystal. The distance between kinks $L (H)$ increases with increasing $H$ . (c),(d) Sketches of the magnon dispersion (frequency $f$ as a function of wave vector $k$ ) of the CSL phonon in a reduced Brillouin zone (BZ) scheme. The boundaries (vertical dashed lines) of the BZ are given by $π / L (H)$ . Blue circles indicate the expected resonance frequencies in the magnetic resonance measurements, where a driving microwave field acts on the sample uniformly ( $k \sim 0$ ). The frequency of the acoustic mode $Δ_{0} (H)$ and the frequency gaps between the modes $Δ_{1} (H)$ at $k = 0$ are indicated. (e) The normalized CSL period. The solid line shows $L (H) / L (0)$ derived from the 1D chiral sine-Gordon model. The experimental data in Ref. [10] (circles) are fitted by the modified analytical equation $α {[L (H) / L (0)] - 1} + 1$ with an empirical parameter $α = 2.3$ (dashed line). (f) The soliton density $L (0) / L (H)$ given in the same manner as the CSL period. (g) The frequency of the CSL phonon as function of $H$ . Solid lines correspond to Eq. (2) with the parameters of $β_{0} = 1$ and $β_{1} = 1.5$ . Dashed lines are obtained by Eq. (3) with $α = 2.3$ , $β_{0} = 1$ , $β_{1} = 1.5$ , and $γ = 0$ .
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Figure 2
The magnetic resonance data of the bulk single crystal of ${CrNb}_{3} S_{6}$ at a temperature of 100 K. (a) The resonance frequency as a function of $H$ in an intensity plot of the field derivative of the resonance amplitude [27]. The color contrast (arbitrary unit) represents the detection of the resonance. (b) An enlarged view of the CSL phonon modes. The lowest frequency mode ( $n = 1$ ) and three higher-order modes ( $n = 2$ , 3, and 4) are identified. (c) Line traces of $S_{para}$ as a function of $H$ at various frequencies. The resonance peaks of $n = 2$ , 3, and 4 modes are detected. The vertical line is a scale bar for the magnitude of $S_{para}$ (linear scale).
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Figure 3
The analysis of the CSL phonon modes. (a) The amplitude of the $n = 1$ , 2, 3, and 4 modes as a function of $H$ . The experimentally obtained magnetic permeability $l n [S_{para}^{res} / S_{para}^{ref}] / l n [S_{para}^{ref}]$ (markers) and the theoretically obtained magnetic susceptibility of the CSL phonon modes (continuous lines) are compared qualitatively. The details of the analytical equations are available in Ref. [14]. (b) The resonance frequency of the $n = 1$ , 2, 3, and 4 modes. The continuous lines correspond to a fit to Eq. (3) at $α = 4.7$ , $β_{0} = 5.9 GHz$ , $β_{1} = 37 GHz$ , and $γ = 15.0 GHz$ .
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