Terahertz magnon frequency comb

Xianglong Yao, Zhejunyu Jin, Zhenyu Wang, Zhaozhuo Zeng, and Peng Yan

Phys. Rev. B 108, 134427 – Published 19 October 2023

Abstract

Magnon frequency comb (MFC), the spin-wave spectra composing of equidistant coherent peaks, is attracting much attention in magnonics. A terahertz (THz) MFC, combining the advantages of the THz and MFC technologies, is highly desired because it would significantly advance the MFC applications in ultrafast magnonic metrology, sensing, and communications. Here, we show that the THz MFC can be generated by nonlinear interactions between spin waves and skyrmions in antiferromagnets [Z. Jin et al., Phys. Rev. Lett. 131, 166704 (2023)]. It is found that the strength of the three-wave mixing between propagating magnons and breathing skyrmions follows a linear dependence on the driving frequency and the MFC signal can be observed over a broad driving frequency range. Our results extend the working frequency of MFC to the THz regime, which would have potential applications in ultrafast spintronic devices and promote the development of nonlinear magnonics in antiferromagnets.

Received 18 September 2023
Accepted 6 October 2023

DOI:https://doi.org/10.1103/PhysRevB.108.134427

Physics Subject Headings (PhySH)

Magnons Skyrmions

Antiferromagnets Nonlinear waves

Landau-Lifschitz-Gilbert equation Micromagnetic modeling Terahertz techniques

Condensed Matter, Materials & Applied PhysicsNonlinear Dynamics

Authors & Affiliations

Xianglong Yao, Zhejunyu Jin, Zhenyu Wang^*, Zhaozhuo Zeng, and Peng Yan ^†

School of Physics and State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, China

^*Present address: School of Physics and Electronics, Hunan University, Changsha 410082, China.
^†Corresponding author: yan@uestc.edu.cn

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Issue

Vol. 108, Iss. 13 — 1 October 2023

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Images

Figure 1
(a) Schematic diagram of an antiferromagnetic film hosting a skyrmion. (b) The dispersion relation of antiferromagnetic spin waves obtained by the FFT of the dynamical magnetization from micromagnetic simulations. The dashed black and red lines are the analytical formulas Eq. (3) and Eq. (4), respectively. (c) The FFT spectra of the antiferromagnetic film with (violet curve) and without (orange curve) a skyrmion (SK). The gray regions in (b) and (c) correspond to the band gap of spin waves. (d) The time evolution of the skyrmion center position ( $x_{s}$ , $y_{s}$ ) and radius ( $R_{s}$ ) under the driving field with frequency 0.095 THz.
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Figure 2
(a) Snapshot of the interaction between propagating magnons and skyrmion in AFM. The incident spin waves and breathing skyrmion are excited by the microwave fields $h_{1} sin (ω_{1} t) \hat{x}$ (black bar) and $h_{2} sin (ω_{2} t) \hat{z}$ (blue box), respectively. The red rectangle is the detection region. Black arrows label the Hall trajectory of magnons. (b) The spin-wave spectrum of the detection region in (a) when only the exciting field $h_{1} = 500$ mT is applied. (c) The spin-wave spectra as a function of the driving field amplitude ( $h_{1}$ ). The driving frequency is fixed at 1.3 THz. (d) The FFT spectrum at three representative fields $h_{1} = 0.02$ mT (top), 0.08 mT (middle), and 10 mT (bottom), respectively. In (c) and (d), the skyrmion breathing mode is excited by the second microwave field with amplitude $h_{2} = 5$ mT and frequency $ω_{2} / 2 π = 0.095$ THz.
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Figure 3
(a) The amplitudes of three main peaks at $ω_{k} = ω_{1}$ and $ω_{k} \pm ω_{r}$ as a function of the driving field amplitude ( $h_{1}$ ). The solid lines are the fitting curves with the parameter $g = 55.7$ MHz based on Eq. (5). (b) Analytical curves of the mode amplitudes, which are obtained by numerically solving Eq. (5) with parameters $ω_{k} / 2 π = 1.3$ THz, $ω_{r} / 2 π = ω_{2} / 2 π = 0.095$ THz, $h_{2} = 0$ mT, $α = 0.001$ , and $g = 55.7$ MHz.
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Figure 4
(a) The spin-wave spectrum as a function of the driving field frequency $ω_{1}$ . The driving field amplitude is fixed at $h_{1} = 30$ mT. (b) The FFT amplitudes of three modes at frequencies $ω_{1}$ (top), and $ω_{1} \pm ω_{r}$ (middle) as a function of the driving field frequency. The bottom panel in (b) shows the dependence of the coupling strength on the driving field frequency. Magenta dots are extracted from simulation results and the green line is the linear fitting.
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Figure 5
Schematic of experimental detection of nonlinear topological magnon spin Hall effect. THz magnons are excited by femtosecond laser (purple arrow) and scattered by breathing skyrmion (green arrows). Meanwhile, incident (black arrows) and nonlinear magnons (blue/red arrows) are scattered to different channels (gray background) due to the very different Hall angles. At the end of each channel, the accumulated magnons with different frequencies are detected through magneto-optical spectroscopy (blue arrows). Here, the Kerr rotation and Faraday rotation describe the rotation of the plane of polarization for reflected and transmitted laser, respectively. It is noted that left-handed magnons will be scattered to top right channels (not shown).
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Figure 6
The time-evolution of four magnon modes obtained from numerically solving Eq. (5). The exciting field of the incident magnon and skyrmion breathing modes are set as $h_{1} = 40$ mT, $ω_{1} / 2 π = ω_{k} / 2 π = 1.3$ THz, $h_{2} = 5$ mT, and $ω_{2} / 2 π = ω_{r} / 2 π = 0.095$ THz. The coupling strength is $g = 55.7$ MHz and the damping constant is $α = 0.001$ .
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