Measuring the magnon phase in a hybrid magnon-photon system

Yue Zhao, Ledong Wang, Jianshu Xue, Qi Zhang, Yufeng Tian, Shishen Yan, Lihui Bai, Michael Harder, Qingjie Guo, and Ya Zhai

Phys. Rev. B 105, 174405 – Published 9 May 2022

Abstract

Hybrid magnon-photon systems are a promising candidate for quantum information applications, with the potential to store and transfer both amplitude and phase information. For the photon subsystem, both amplitude and phase can be detected via microwave transmission. However, for the magnon subsystem, current techniques, such as spin pumping, are only sensitive to the amplitude. Measurements of the magnon phase remain elusive. Here, we demonstrate electrical detection of the magnon phase in a hybrid magnon-photon system using spin rectification. Spin rectification can be used to characterize typical hybrid features, such as the distorted microwave frequency-magnetic field dispersion and the resonance linewidth evolution. With spin rectification we also observe the phase difference between high-frequency and low-frequency coupled modes, which allows us to identify the relative magnon phase in a straightforward manner. This unique phase-sensitive technique could play an important role in integrated magnon-photon hybrid devices, in particular at low cooperativity.

Received 16 February 2022
Revised 15 April 2022
Accepted 26 April 2022

DOI:https://doi.org/10.1103/PhysRevB.105.174405

Physics Subject Headings (PhySH)

Spin dynamics Spin-phonon coupling

Ferromagnets

Cavity resonators Electrical techniques Landau-Lifschitz-Gilbert equation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yue Zhao, Ledong Wang, Jianshu Xue, Qi Zhang, Yufeng Tian, Shishen Yan ^*, and Lihui Bai ^†

School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China

Michael Harder

Department of Physics, British Columbia Institute of Technology, 3700 Willingdon Avenue, Burnaby, British Columbia, Canada V5G 3H2

Qingjie Guo and Ya Zhai

Department of Physics, Southeast University, 210096 Nanjing, China

^*shishenyan@sdu.edu.cn
^†lhbai@sdu.edu.cn

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Vol. 105, Iss. 17 — 1 May 2022

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Images

Figure 1
(a) Schematic illustration of the coplanar superconducting cavity-Py system. The cavity is made of a 500-nm-thick DyBCO layer deposited on a MgO substrate. The fundamental resonance frequency of the cavity was 4.1642 GHz. Open gaps of 0.5 mm enabled coupling between the cavity and the signal lines. The 80-nm-thick Py layer deposited on a MgO substrate, was placed on the top of the signal line of the cavity. (b) The FMR absorption spectrum of the Py layer at $ω / 2 π = 4.2 GHz$ . (c) The red line (right) is the transmission spectra, $S_{21}$ , of the unloaded cavity (top) and the phase of the microwave current, $ϕ_{j_{z^{'}}}$ (bottom), at 77 K with no magnetic field. When the Py (80 nm)/MgO sample is placed on the cavity signal line, $S_{21}$ and $ϕ_{j_{z^{'}}}$ shift to the blue curve (left).
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Figure 2
The spin rectification voltage is sensitive to the magnon phase in a hybrid magnon-photon system. (a) Row data of $V_{S R} - ω$ spectrum at 38 mT and 16 mT without offset. The experimentally detected spin rectification voltage (b) and theoretical prediction (c) were plotted in a same frame of $ω$ -H dispersion. [(d),(e)] Schematic illustration of the magnetization precession $m_{x}$ respecting to the microwave magnetic field $h_{x^{'}}$ and $j_{z^{'}}$ for the high-frequency mode and the low-frequency mode respectively. In the low-frequency (high-frequency) mode the magnon phase, $ϕ_{m_{x}}$ , is in-phase (out-of-phase by $π$ ) with the phase of the microwave current, $ϕ_{j_{z^{'}}}$ . The insets in (d) and (e) illustrate the $m_{x}$ and $j_{z^{'}}$ in the $x^{'} - z^{'}$ plane where the Py layer is located.
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Figure 3
(a) Row data of $V_{S R} - ω$ spectrum at 16 mT and $- 16 mT$ without offset for the high-frequency mode. (b) Row data of $V_{S R} - ω$ spectrum at 38 mT and $- 38 mT$ without offset for the low-frequency mode. [(c),(d)] Spin rectified voltage from the high-frequency and low-frequency modes, respectively, plotted as a function of the magnetic field and microwave frequency. [(e),(f)] The magnetization precession image under a static magnetic field reversal, from the high-frequency and low-frequency modes. The insets in (e) and (f) illustrate the $m_{x}$ and $j_{z}$ in the $x^{'} - z^{'}$ plane where the Py layer is located.
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Figure 4
(a) Microwave transmission and (c) spin rectified voltage as a function of microwave frequency and in-plane magnetic field at 77 K. (b) The microwave transmission amplitude $| S_{21} |_{\max}^{2}$ and (d) the magnitude of the spin rectified voltage $| V_{S R, \max} |$ extracted from (a) and (c), and plotted as a function of the magnetic field and microwave frequency, respectively.
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Figure 5
The dispersion spectra of the hybrid system extracted from (a) the spin rectified voltage, $V_{S R}$ , and (c) the microwave transmission, $| S_{21} {(ω) |}^{2}$ . [(b),(d)] Normalized linewidth of the hybrid modes determined from the $V_{S R}$ and $| S_{21} {(ω) |}^{2}$ spectra, respectively. Solid blue and red lines in (a), (b), (c) and (d) are calculated using Eq. (1).
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