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Dimensional crossover in spin Hall oscillators

Andrew Smith, Kemal Sobotkiewich, Amanatullah Khan, Eric A. Montoya, Liu Yang, Zheng Duan, Tobias Schneider, Kilian Lenz, Jürgen Lindner, Kyongmo An, Xiaoqin Li, and Ilya N. Krivorotov
Phys. Rev. B 102, 054422 – Published 17 August 2020

Abstract

Auto-oscillations of magnetization driven by direct spin current have been previously observed in multiple quasi-zero-dimensional (0D) ferromagnetic systems such as nanomagnets and nanocontacts. Recently, it was shown that pure spin Hall current can excite coherent auto-oscillatory dynamics in quasi-one-dimensional (1D) ferromagnetic nanowires but not in quasi-two-dimensional (2D) ferromagnetic films. Here we study the 1D to 2D dimensional crossover of current-driven magnetization dynamics in wire-based Pt/Ni80Fe20 bilayer spin Hall oscillators via varying the wire width. We find that increasing the wire width results in an increase of the number of excited auto-oscillatory modes accompanied by a decrease of the amplitude and coherence of each mode. We also observe a crossover from a hard to a soft onset of the auto-oscillations with increasing wire width. The amplitude of auto-oscillations rapidly decreases with increasing temperature suggesting that interactions of the phase-coherent auto-oscillatory modes with incoherent thermal magnons play an important role in suppression of the auto-oscillatory dynamics. Our measurements set the upper limit on the dimensions of an individual spin Hall oscillator and elucidate the mechanisms leading to suppression of coherent auto-oscillations with increasing oscillator size.

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  • Received 5 May 2020
  • Accepted 3 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.054422

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsNonlinear Dynamics

Authors & Affiliations

Andrew Smith1, Kemal Sobotkiewich2, Amanatullah Khan1, Eric A. Montoya1, Liu Yang1, Zheng Duan1, Tobias Schneider3, Kilian Lenz3, Jürgen Lindner3, Kyongmo An2, Xiaoqin Li2, and Ilya N. Krivorotov1,*

  • 1Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
  • 2Department of Physics, Center for Complex Quantum Systems, University of Texas, Austin, Texas 78712, USA
  • 3Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, Bautzner Landstrasse 400, 01328 Dresden, Germany

  • *Corresponding author: ilya.krivorotov@uci.edu

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Vol. 102, Iss. 5 — 1 August 2020

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Images

  • Figure 1
    Figure 1

    (a) Schematic of Pt/Py/AlOx wire SHO device. Five devices with the wire width varying from 0.17 μm to 2.11 μm were studied. The active region length is 1.9 μm for all devices. Green arrows schematically show the electric current flow direction. (b) Scanning electron micrograph of the 0.51 μm wide SHO device. The magnetic field is applied in the plane of the sample at an angle θ with respect to the charge current flow direction. (c) Change in resistance of the five samples with different wire widths measured at 4.2 K for magnetic field applied at 5 off the y axis (θ=85). (d) Saturation field Hsat of the wire for magnetic field applied at θ=85 as a function of the wire width (solid line is a guide to the eye).

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  • Figure 2
    Figure 2

    (a) Power spectral density (PSD) of the microwave signal generated by the 1.07 μm wide Pt/Py/AlOx wire SHO at the bias current density Jdc=2.0×108cm2, bath temperature T=4.2 K, and magnetic field H=470 Oe applied at 5 from y axis θ=85. Three auto-oscillatory modes are excited. The non-Lorentzian peak line shapes are mainly due to standing waves in the microwave circuit. (b)–(f) Microwave emission spectra versus Jdc for five wires of different widths measured in fields exceeding Hsat by approximately 100 Oe and applied at θ=85. The logarithmic color scale represents the emitted power normalized to the maximum power Pmax. The wire widths and the applied field values are shown in the figures. The low-frequency edge mode is seen for narrower wires (0.17 μm and 0.34 μm wide). The higher-frequency bulk modes are observed in wider wires (0.34 μm, 0.53 μm, 1.07 μm, and 2.11 μm wide).

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  • Figure 3
    Figure 3

    (a) Integrated microwave power emitted by all bulk modes of the wire Pb versus bias current density Jdc. The data are shown for all four wires exhibiting bulk mode auto-oscillations. (b) Maximum value of the integrated microwave power emitted by all bulk modes of the wire Pbt as a function of the wire width. (c) Maximum integrated power of the largest-amplitude bulk mode Pbl as a function of the wire width.

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  • Figure 4
    Figure 4

    Brillouin light scattering characterization of auto-oscillatory modes of the 1.07 μm wide wire device at room temperature (T=300K). (a) Optical micrograph of the devices showing Pt/Py wire, Ti/Au leads, and laser spot of the BLS apparatus focused on one edge of the active region of the device. (b) BLS spectrum measured at the laser beam position at the edge of the active region shown in (a) for Jdc=9.77×107cm2 and H=495 Oe applied at θ=87. Spatially resolved BLS allows us to reveal the origin of the excitations: (c) Spatial profile of the BLS signal intensity at f=4.3GHz—the center frequency of the low-frequency peak (edge mode). The rectangle denotes the approximate location of the active region of the device. This BLS spectral mapping reveals that this auto-oscillatory mode is an edge spin wave mode of the wire. (d) Spatial profile of the BLS signal intensity at f=5.6GHz—the center frequency of the high-frequency peak (bulk mode). This BLS spectral mapping reveals that this auto-oscillatory mode is a bulk spin wave mode of the wire.

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  • Figure 5
    Figure 5

    Micromagnetic simulations of spin wave spectra in the 1.07 μm wide wire with HOe=36 Oe, H=470 Oe, and θ=85. (a) Simulated spin Hall oscillator microwave emission spectra at θSH=0.045 (global average FFT). (b) Simulated cell-by-cell FFT spectra mx2 at θSH=0.045 to be compared to BLS data. Note the scale of (b) is 2500× the scale of (a). Inset shows a zoom of 50× in amplitude. (c) Simulated spin wave eigenmode spectra (global average FFT).

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  • Figure 6
    Figure 6

    Micromagnetic simulations of spin wave spatial profiles in the 1.07 μm wide wire. Amplitude (top) and phase (bottom) spatial profiles are shown for the auto-oscillatory modes with frequencies (a) 4.47, (b) 4.61, (c) 5.16, (d) 5.23, (e) 5.51, and (f) 5.63. The amplitude scales for (a)–(c) are the same, while the scales for (d), (e), and (f) are 2×, 100×, and 10× larger, respectively. Amplitude (top) and phase (bottom) spatial profiles for spin wave eigenmodes with frequencies (g) 4.64, (h) 5.13, and (i) 5.18 GHz. Individual panel labels correspond to the peaks labeled ai in Fig. 5.

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  • Figure 7
    Figure 7

    Temperature and angular dependence of auto-oscillatory dynamics in the 0.53 μm wide wire device. (a) Critical current density Jc (blue circles) and integrated power Pbt (red squares) versus bath temperature measured at H=750 Oe and θ=85. (b) Critical current density (blue circles) and maximum emitted power Pbt (red squares) versus in-plane magnetic field angle θ measured at bath temperature of 56 K and magnetic field H=1900 Oe.

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