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Acoustic spin pumping in magnetoelectric bulk acoustic wave resonator
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21. A least-square fit to the data-set #2 in Fig. 1 of Ref. 19 with function yields αG ≈ 5.1 ⋅ 10−5 and ΔH0 ≈ 0.19 Oe, where the latter is the inhomogeneous broadening and γ is the gyromagnetic ratio.
23. The field was calculated by using the relation E = U/d, where U is the measured voltage, d = 0.168 mm is the length of the Pt stripe segment located underneath the BAW transducer (see Fig. 1(b)).
26. Note that in YIG gr scales linearly with tF while tF < 200 nm, and saturates at higher tF (see for example Ref. 27).
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28. Here b2 is the magnetoelastic coupling constant, b2 = B2/Ms ≈ 3 ⋅ 104 erg/(cm3 ⋅ G) for (Ga, Sc)-YIG (see Ref. 29); kMER is the wave vector corresponding MER, kMER ≈ 3 ⋅ 104 cm−1; u is an elastic displacement; as follows from Fig. 1(c); ρ ≈ 5.17 g/cm3, vt ≈ 3.9 ⋅ 105 cm/s, are YIG density and transversal velocity, respectively.
29.Y. A. Filimonov, Doctoral Thesis, Moscow, 2008 (in Russian).
30. We put here nm, see Ref. 26. Rw/L = 37 Ω ⋅ 0.375 mm/0.5 mm ≈27.8 Ω, see Ref. 5.
31. μV/mm, see Fig. 2(b), , see Ref. 3, , see Ref. 5.
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We present the generation and detection of spin currents by using magnetoelastic resonance excitation in a magnetoelectric composite high overtone bulk acoustic wave (BAW) resonator (HBAR) formed by a Al-ZnO-Al-GGG-YIG-Pt structure. Transversal BAW drives magnetization oscillations in YIG film at a given resonant magnetic field, and the resonant magneto-elastic coupling establishes the spin-current generation at the Pt/YIG interface. Due to the inverse spin Hall effect (ISHE) this BAW-driven spin current is converted to a dc voltage in the Pt layer. The dependence of the measured voltage both on magnetic field and frequency has a resonant character. The voltage is determined by the acoustic power in HBAR and changes its sign upon magnetic field reversal. We compare the experimentally observed amplitudes of the ISHE electrical field achieved by our method and other approaches to spin current generation that use surface acoustic waves and microwave resonators for ferromagnetic resonance excitation, with the theoretically expected values.
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