Electrical Generation and Detection of Terahertz Signal Based on Spin-Wave Emission From Ferrimagnets

Zhifeng Zhu, Kaiming Cai, Jiefang Deng, Venkata Pavan Kumar Miriyala, Hyunsoo Yang, Xuanyao Fong, and Gengchiau Liang

Phys. Rev. Applied 13, 034040 – Published 16 March 2020

Abstract

Terahertz (THz) signals, mainly generated by photonic or electronic approaches, are being sought for various applications, whereas the development of magnetic source might be a necessary step to harness the magnetic nature of electromagnetic radiation. We show that the relativistic effect on the current-driven domain-wall motion induces THz spin-wave emission in ferrimagnets. The required current density increases dramatically in materials with strong exchange interaction and rapidly exceeds $10^{12} A m^{- 2}$ , leading to the device breakdown and thus the lack of experimental evidence. By translating the collective magnetization oscillations into voltage signals, we propose a three-terminal device for the electrical detection of THz spin wave. Through material engineering, a wide frequency range from 264 GHz to 1.1 THz and uniform continuous signals with improved output power can be obtained. As a reverse effect, the spin wave generated in this system is able to move the ferrimagnetic domain wall. Our work provides guidelines for the experimental verification of THz spin wave, and could stimulate the design of THz spintronic oscillators for wideband applications as well as the all-magnon spintronic devices.

Received 13 September 2019
Revised 18 December 2019
Accepted 26 February 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.034040

Physics Subject Headings (PhySH)

Dzyaloshinskii-Moriya interaction Spin dynamics Spin waves Spintronics Ultrafast magnetic effects

Ferrimagnets Optical sources & detectors

Terahertz techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhifeng Zhu ^1,2,*, Kaiming Cai ¹, Jiefang Deng¹, Venkata Pavan Kumar Miriyala ¹, Hyunsoo Yang¹, Xuanyao Fong¹, and Gengchiau Liang^1,†

¹Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore
²School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China

^*a0132576@u.nus.edu
^†elelg@nus.edu.sg

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Vol. 13, Iss. 3 — March 2020

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Figure 1
Illustration and condition for the spin-wave emission. (a) Schematic view of the THz spin wave generated in the FIM/W bilayer, where the red and blue color in the FIM layer distinguish the up and down domain, respectively. The length and width of W and FIM are 400 and 40 nm, respectively. The current moves the Néel wall along the +x direction. The spin wave is initiated at the DW and vanishes in −x direction. The precession frequency of each spin is identified in THz range. (b) The DW velocity as a function of J_c. The dashed line separates regions without (region 1) and with (region 2) spin wave. (c) The spatial profile of magnetization at J_c = 4 × 10¹¹ A m⁻² and A_ex = 5 meV, where the DW is located at 148 nm. The DW moves to the right as marked by the brown arrow. (d) Critical current density for the spin-wave emission as a function of exchange constant.
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Figure 2
Electrical detection of the THz signal. (a) Schematics of the three-terminal structure. The length and width of both $Mg O$ and FM layer are 40 nm. The FM layer has in-plane easy axis along the +y direction. The bias tee is a three-port diplexer consisting of a capacitor and an inductor. I_c = 160 µA and I_MTJ = 16 µA are used in this study unless otherwise stated. (b) Simulation workflow. The current distribution is calculated using the distributed resistance model, and then the average current passing through the W layer is input to the atomistic spin model to get the magnetization dynamics. At each time step, the MTJ resistance (R_M) is updated based on the magnetization of the FIM layer (m_FIM), followed by the recalculation of current distribution. This process forms a closed loop and free running to get the time evolution of magnetizations. The number of segmentation nA = 10, nB = 10, n = 13, which gives 0.03% difference in I_HA compared to n = 193 (cf. Note 5 in Ref. [43]). Refer to Note 4 in Ref. [43] for the notation of parameters. (c) Time evolution of m_y and ΔV_o, defined as V_o–252.465 mV, at I_c = 160 µA and I_MTJ = 16 µA. m_y is obtained by averaging spins under the MTJ. The reduction of oscillation amplitude is induced by the loss of energy input when the DW moves away. (d) The frequency spectrum for the time region starting from 97.26 ps, marked by the black dot, to 200 ps. The main frequency is originated from spin wave at 437 GHz and a smaller SOT-induced precession with negligible amplitude appears at 213 GHz, shown as the inset.
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Figure 3
Relativistic effect on the domain-wall motion. (a) v_DW as a function of J_c at A_ex = 5 meV for systems with (dashed line) and without (solid line) the Lorentz contraction. (b) v_DW as a function of A_ex with I_c = 160 µA and I_MTJ = 16 µA. Results from the atomistic model are shown as blue dots. Analytical results based on Eqs. (1) and (2) are plotted as the solid and dashed line, respectively. A_ex above 8 meV is not considered since the J_SW is above 10¹² A m⁻², which can easily lead to device breakdown. (c) v_DW as a function of J_c at different A_ex. Dashed lines define the critical current density, above which the spin waves are emitted. The effect of FLT is studied in the sample with A_ex = 5 meV, where the black squares denote v_DW with β = 1.1.
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Figure 4
Parametric effect on the oscillator performance. (a) Numerical results of f as a function of A_ex with I_c = 160 µA and I_MTJ = 16 µA. The maximum frequency is 1.1 THz at A_ex = 8 meV. (b,c), Time evolution (b) and frequency spectrum (c) of V_o in samples with different damping constant at I_c = 160 µA and I_MTJ = 16 µA. The curves are vertically offset for clarity, i.e., 36 µV in (b) and 3.4 µV in (c). V_o becomes more uniform and maintains for a longer time when the damping constant is reduced. f remains nearly unchanged for different α, i.e., f = 437, 442, and 428 GHz for α = 0.015, 0.012, and 0.01, respectively. A substantial f_SOT appears at 209 GHz for α = 0.01.
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