Research ArticleAPPLIED PHYSICS

High-frequency magnetoacoustic resonance through strain-spin coupling in perpendicular magnetic multilayers

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Science Advances  18 Sep 2020:
Vol. 6, no. 38, eabb4607
DOI: 10.1126/sciadv.abb4607
  • Fig. 1 Measurement protocol.

    (A) Illustration of the ultrafast TR-MOKE measurements (left) on the [Co/Pd]n multilayer with numbers in parentheses denoting layer thicknesses in nanometers (right). In the TR-MOKE measurement, in the absence of an external magnetic field Hext, the magnetostrictive effect can be measured, in which the acoustic strain wave induces the magnetization oscillation. The magnetization of the [Co/Pd]n multilayer is tilted to the angle (θ) when Hext > 0 is applied with the angle (θH = 80°). The TR-MOKE signals will include the signal from spin precession and acoustic strain wave. By fitting the data, we can separate them and identify their coupling. The figure in the right plane of the top shows the [Co/Pd]n multilayered structure used in our work. (B) The magnetic hysteresis (M-H) loops of the [Co(0.8 nm)/Pd(1.5 nm)]11 multilayer with a magnetic anisotropy field Hk,eff of ~6.5 kOe.

  • Fig. 2 Ultrafast measurement results.

    (A) The experimental and fitted TR-MOKE signals and (B) the experimental TDTR signals as a function of Hext (10 to 29 kOe). It is clearly seen that TDTR signals do not change in the whole region of Hext, while TR-MOKE signals show different oscillation patterns with external fields. For Hext < 18 kOe or Hext > 24 kOe, magnetization precession presents a damped oscillation, while for 18 kOe < Hext < 24 kOe, it shows a resonance phenomenon. (C and D) Fourier transform of the TR-MOKE signals with Hext = 14 kOe and 21 kOe, respectively, from which two peaks (FMR and strain) can be found. For Hext = 14 kOe, the two peaks are separate; however, the two peaks are overlapping when Hext = 21 kOe. a.u., arbitrary units.

  • Fig. 3 High-frequency magnetoacoustic resonance.

    (A) The frequency of the [Co(0.8 nm)/Pd(1.5 nm)]11 multilayer as a function of Hext. Two frequencies of spin precession (mode 1, open black circles; mode 2, open red diamonds) are derived by fitting the experimental data of TR-MOKE. The figure also includes the frequency of acoustic waves measured from TDTR (blue stars). The anticrossing point of mode 1 and mode 2 occurs at the resonance field (Hext ≈ 21 kOe), where the frequencies of modes 1 and 2 split and open a gap Δf. We assign the strain mode as the one with field-independent frequencies that are nearly identical to the acoustic wave frequencies from TDTR. The frequency of the FMR mode increases linearly with Hext. The relationship between γ and g is given by γ = g. γe/ge where ge and γe are the g-factor and gyromagnetic ratio for an electron. (B) The individual Mz amplitudes of modes 1 and 2 from both the experiment and the theory as a function of Hext for the [Co(0.8 nm)/Pd(1.5 nm)]11 multilayer. There exists an apparent amplification of both modes due to the coupling between these two modes near the anticrossing point. (C) A zoomed-in frequency plot of the resonance region from the experiment and the theory. The experimental error bars (~3 GHz) are based on the FFT resolution (~3 GHz). (D) A zoomed-in amplitude plot of the resonance region from the experiment and the theory. The experimental error bars represent the standard error from mathematical fitting of the measurement data based on Eq. 1.

  • Fig. 4 Time-dependent magnetization dynamics.

    (A and B) The experimental and simulated TR-MOKE signal of the [Co(0.8 nm)/Pd(1.5 nm)]11 multilayer with Hext = 21 kOe, respectively. The strain used to produce the simulated signal is 0.5%. (C) The oscillation amplitude versus Hext for different strain amplitudes (0.1, 0.2, and 0.5%). (D and E) The time evolution of the out-of-plane magnetization (Mz) versus the time delay when a square strain pulse is applied. The pulse amplitude is 0.5%, the time period is 2.0 ns, and the pulse length is 1.0 ns. The simulated spin precession coupled with a 0.5% strain pulse under an Hext of 21 kOe (D) and 24 kOe (E), respectively. When the strain pulse is on, the system gets excited rapidly to an enhanced large-angle precession with a rise time of ~100 ps under Hext = 21 kOe, but not 24 kOe. When the strain pulse is off, the system at these Hext values shows relaxation behavior. (F) Strain-assisted switching for [Co(0.8 nm)/Pd(1.5 nm)]11 with Hext = 1 kOe. When strain is absent in the system (strain amplitude of 0%), switching does not occur (shown by the black line). When strain (strain amplitude of 0.5%) is applied, switching occurs (shown by the red line).

Supplementary Materials

  • Supplementary Materials

    High-frequency magnetoacoustic resonance through strain-spin coupling in perpendicular magnetic multilayers

    De-Lin Zhang, Jie Zhu, Tao Qu, Dustin M. Lattery, R. H. Victora, Xiaojia Wang, Jian-Ping Wang

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