We report on the first observation of microvolt-scale inverse spin Hall effect (ISHE) dc voltage driven by an acoustic spin pumping (ASP) in a bulk acoustic wave (BAW) resonator formed by a Al-ZnO-Al-YIG(1)-GGG-YIG(2)-Pt structure. When 2 mW power is applied to an Al-ZnO-Al transducer, the voltage VISHE ∼ 4 μV in the Pt film is observed as a result of resonant ASP from YIG(2) to Pt in the area ∼ 170 μm. The results of frequency and magnetic field mapping of VISHE(f,H) together with reflectivity of the resonator show an obvious agreement between the positions of the voltage maxima and BAW resonance frequencies fn(H) on the (f, H) plane. At the same time a significant asymmetry of the VISHE(fn(H)) value in reference to the magnetoelastic resonance (MER) line fMER(H) position is revealed, which is explained by asymmetry of the magnetoelastic waves dispersion law.

Interest in the magnetoelastic (ME) coupling between spin waves (SW) and acoustic waves (AW) in ferromagnets renewed recently in the fields of microwave electronics, magnonics, and spintronics.1–11 In particular, much attention is given to acoustically driven (AD) excitation of magnetic oscillations in artificial multiferroic structures due to strain mediated coupling between the microwave electric field in a piezoelectric layer and magnetization in a ferromagnetic layer.6–11 

In the field of microwave spintronics, acoustic spin pumping (ASP) is the generation of spin-polarized electron currents in normal metal from AD magnetization precession in an attached magnetic material.12–14 In ferrimagnetic insulator yttrium iron garnet (YIG)/paramagnetic metal (platinum, Pt) bilayers, a pure spin current generation not accompanied by charge current was discovered and then investigated in numerous works.15 In the case of piezoelectric generation of AW using rf electric (rather than magnetic) fields in such YIG/Pt heterosystems, there are great opportunities for low power consumption spintronic devices free from energy dissipation due to ohmic losses.

More recently, the generation of pure spin current from YIG to Pt detected by inverse spin Hall effect (ISHE) under magnetic dynamics excitation in a composite magnetoelectric high overtone bulk acoustic wave resonator (HBAR)16–20 was demonstrated for the first time.21 According to our estimates, the excitation of AD magnetic oscillations under double resonance conditions (magnetoelastic resonance (MER) in a YIG film and a high-quality BAW resonance of the whole structure) sufficiently exceeds surface AW method efficiency. Indeed, the measured ISHE signal didn’t exceed several tens of nanovolts for 5 mW power supplied to the transducer and 168 μm effective length of spin current generation along the Pt stripe.21–23 

In this paper we report on the observation of considerably larger HBAR-driven ISHE voltage. The maximum voltage obtained is an order of magnitude higher than the one mentioned above. The spin pumping efficiency enhancement is achieved by using YIG films with sufficiently high magnetoelastic constant, the increase in the efficiency of BAW resonances excitation and proper HBAR mode selection. The latter is possible due to frequency and magnetic field mapping of ISHE voltage and HBAR resonance positions in a wide range of frequencies and fields. As a result of mapping, nontrivial asymmetry in the behavior of the voltage signal localized in the (f,H) plane on the lines of resonant frequencies fn (H) was found. We explain this asymmetry by the contribution of non-uniform exchange to the ME dispersion law. As a result, the frequency of MER is higher than the frequency of ferromagnetic resonance (FMR). The character of AD magnetic oscillations is cardinally different on the frequencies lying above and below the ME gap. In the first case, short SW with wavenumbers higher than those of AW are excited. In the second case, quasi-uniform precession takes place.

The resonator structure under investigation is schematically shown in the insertion in Fig. 1. It contains a gadolinium-gallium garnet (GGG) substrate with (111) orientation and two La, Ga-substituted YIG epitaxial films on both sides of the substrate characterized by lower (in relation to pure YIG) saturation magnetization 4πMs 800-900 G. A BAW transducer consisting of a piezoelectric film (ZnO) sandwiched between thin-film Al electrodes is deposited on one side of the YIG-GGG-YIG structure. For the excitation of the primarily transverse BAW with elastic displacement u parallel to the crystallographic direction [110] in the YIG film plane, a textured ZnO film with inclination of piezoelectric c-axis is deposited by magnetron sputtering according to the original technology.24 

FIG. 1.

Frequency dependences of the DC voltage signal (the blue curve) and voltage reflection coefficient modulus |S11(f)| (the red curve) simultaneously measured at the constant magnetic field H =744 Oe. The schematic images of the structure with the Pt stripe and the main vectors are shown in the insertion. The layer thicknesses: Al electrodes – 150-200 nm, ZnO – 2 μm, GGG – 480 μm, YIG – 38 μm, Pt – 12 nm. The top and the bottom electrodes are patterned by optical lithography being overlapped in the area of diameter l =168 μm with adjacent contact pads.

FIG. 1.

Frequency dependences of the DC voltage signal (the blue curve) and voltage reflection coefficient modulus |S11(f)| (the red curve) simultaneously measured at the constant magnetic field H =744 Oe. The schematic images of the structure with the Pt stripe and the main vectors are shown in the insertion. The layer thicknesses: Al electrodes – 150-200 nm, ZnO – 2 μm, GGG – 480 μm, YIG – 38 μm, Pt – 12 nm. The top and the bottom electrodes are patterned by optical lithography being overlapped in the area of diameter l =168 μm with adjacent contact pads.

Close modal

A thin Pt strip of 12 nm thickness is attached to the surface of the bottom YIG film underneath the acoustic resonator aperture (see ins. Fig. 1). In this geometry, the transverse BAW electrically excited and detected by the transducer drives magnetization oscillations in YIG films.16–20 For the best ME interaction, a magnetic field H is applied also in the [110] direction.20 These AD oscillations establish a spin current js||x from YIG into the Pt strip perpendicular to the interface. To obtain the best conditions for ASP detection via the ISHE, the stripe is formed so that its long side is perpendicular to H. In this case, the ISHE electric field EISHE is parallel to the long side of the stripe.

The measurements are conducted by a specially designed microwave board-probe connected to an S-parameter network analyzer. The voltage across the platinum strip in the magnetic field of the given orientation is recorded using a conventional lock-in technique.23 On the first stage the voltage complex reflection coefficient S11(f) of the transducer is measured in a wide frequency range in the absence of magnetic field to determine the region for effective excitation of the transverse BAW. The excitation efficiency is determined by the depth of the spectrum dips δSn = |S11(f)| - |S11(fn)|. As a result, a region near 3 GHz containing a considerable number of resonant frequencies fn with 3.2 MHz spacing apart and δSn0.1 is chosen for further measurements in the magnetic field. For comparison, a similar nonmagnetic HBAR structure with yttrium aluminum garnet (YAG) substrate is also measured.

In Fig. 1 the red curve represents |S11(f)| dependence measured at a constant magnetic field H = 744 Oe. In the central region of 30 MHz (region III) the resonances are not observed. As it was shown in previous studies, such a behavior occurs near the crossover of uncoupled dispersion laws of spin and acoustic waves: fSW(qcr) = fAW(qcr), where fSW(q) = γ{Heff(q)[Heff(q)+4πMeff]}½ = {fH(q)[fH(q)+fM)]}½, fAW(q) = qv/2π, q is a wavenumber, v is a transverse AW velocity in YIG, Heff(q) and 4πMeff are the effective magnetic field and saturation magnetization, γ ≈ 2.8 MHz/Oe is the gyromagnetic ratio, qcr is the crossover wavenumber.16–20 The frequency width of MER region is determined as a minimal repulsion of coupled ME waves branches. In the MER region AW energy effectively transfers to the magnetic system which leads, first, to a decrease in Q-factor of the resonances and their frequency shifts and further to complete disappearance of the regular resonance structure. Meanwhile, in I and II regions adjoining below and above the MER, the resonances strictly manifest themselves. But as it is shown below, their frequencies are shifted relative to the case of non-resonant field.

The dc voltage signal on the Pt stripe (the blue curve in Fig. 1) is measured simultaneously with |S11(f)| under Prf = 2 mW power applied to the transducer. In region III where resonances are absent the resonant character of the voltage is also absent. For the given magnetic field maximal voltage ∼ 4μV is observed on the frequency of 3.139 GHz which is approximately 35 MHz less than the crossover frequency.

To clarify the origin of the voltage, the frequency dependences of VISHE(f) and |S11(f)| are measured for a set of magnetic fields in the range 0.1÷1 kOe. The measurements make possible 3D images of VISHE(f,H) and |S11(f,H)|. The fragment of VISHE(f,H) is shown in Fig. 2(a). For comparison, the positions of three resonances fn,n±1 (reflectivity minima) on the (f,H) plane are represented on the color plot (Fig. 2(b)) of VISHE(f,H) by red points. As one can see the voltage is observed only in the (f,H) domain where the resonant frequency undergoes shift and splits into two branches near the fMER(H) line. There is a one-to-one correspondence between the VISHE maxima localizations and the fn(H) positions on the (f,H) plane. The pattern shown in Fig. 2(b) replicates in a wide frequency range along the fMER(H) line. Such a behavior of HBAR resonances is attributed to AD magnetization precession in YIG under MER condition.17–20 The fitting via formula fMER(H) = fSW(qcr) leads to the following parameters: 4πMeff ∼ 950 G and Heff(qcr) = HH with δH∼14 Oe. Hereafter, the elastic and ME parameters for pure YIG are used. Assuming that 4πMeff = 4πMs+|Ha|, Heff(q) = H+Hex(q) (where Ha ≈ - (50 ÷ 70 Oe) and Hex(q) = Dq2 are the anisotropy and the exchange fields)25–27 and that Hex(qcr) ≈ δH, one can obtain exchange stiffness constant D ≈ 5×10-9 cm2 Oe typical for YIG and magnetization 4πMs ≈ 900 G typical for (La,Ga)YIG.

FIG. 2.

(a) DC voltage on Pt stripe versus frequency and field for the main sample with YIG/Pt system (insertion in Fig. 1). (b), (c) Color maps of DC voltage: (b) – for 3D image shown in (a), (c) – for control sample with YAG (440 μm)/Pt(12 nm) system. The red points correspond to the positions of HBARs resonances.

FIG. 2.

(a) DC voltage on Pt stripe versus frequency and field for the main sample with YIG/Pt system (insertion in Fig. 1). (b), (c) Color maps of DC voltage: (b) – for 3D image shown in (a), (c) – for control sample with YAG (440 μm)/Pt(12 nm) system. The red points correspond to the positions of HBARs resonances.

Close modal

The same measurements in the reversal field display that only the voltage sign change takes place. The measurements of control HBAR without magnetic layers demonstrate the absence of both the shift of resonant frequencies and the voltage signal on Pt stripe (see Fig. 2(c)). The same applies to the main resonator when it was excited at the frequencies of longitudinal BAW. The absence of the voltage in this case at the power level up to 5mW shows that heating signal is negligible or absent in our experiment.13 Thus, all of the above proves that the voltage is created by ASP and ISHE.

Let us now discuss that in contrast to the resonance branches fn(H) behavior in Fig. 2(b), the maximal voltage dependence VISHE(fn(H)) is asymmetrical in reference to fMER(H) line. Above the line the localization of VISHE(fn(H)) corresponds to the positions of resonances fn(H) (the left branches) and the 3D image of VISHE(f,H) represents continuous ridges along the resonance localization line in the (f,H) plane. Below fMER(H) line the VISHE(fn(H)) dependence displays an additional localization when fn(H) = fFMR(H)= fMER(H-14 Oe), where fFMR(H)= fSW(q=0) is a frequency of FMR.

For the explanation of the asymmetry, the solutions for the ME wave dispersion equation (F2-Q2)(F2- F2SW(Q)) = ζ’Q2FH(Q) FM are presented in Fig. 3. Here, all the reduced frequencies F, FM, H, SW and the wavenumber Q are normalized on the fFMR and the wavenumber q0=2πfFMR/v, (F=f/fFMR, Q=q/q0), and ζ’= 3×10-3/4π is a dimensionless ME coupling constant. For fFMR ∼ 3 GHz (F=1), MER area III is of 30 MHz and corresponds to region III in Fig. 1. Then areas I and II correspond to regions I and II in Fig. 1, respectively. When the exciting frequencies lie in area II, both SW and u have two wavenumbers: QSWII and QAWII ∼1< QSWII. If the frequencies lie in area I, the wavenumbers are QSWI and QAWI ∼1>QSW I. However, the amplitudes of the partial SW with QSW I, II considerably exceed those for the SW with QAW I, II.17,28 Conversely, the magnitude of u is determined by the partial waves with QAW I, II. It may be assumed that out of the MER region an effective magnetic field hME(fn)δSn∂u/∂x, with δSn∼An=1/(F2 - Fn2) linearly excites magnetization m(x,n) = Anmk(x)IkPk as a superposition of standing SW eigenmodes mk(x) with wavenumbers QSW k=πk/(dq0).20,29 The factors Pk∼1/[F2-F2SW(QSWk)] and Ik∼1/(Q2AWn - Q2SWk) are connected with magnetic permeability and overlapping integral. So, flattening of SW dispersion in region I originates two opposite effects. On the one hand, with distance from the MER region in area I the value |Ik| diminishes faster than in area II. On the other hand, when Fn1, SW eigenfrequencies determined by Pk are concentrated near the bottom of the dispersion curve. So a great number of SW eigenmodes fall into the width of HBAR resonance. For spatial distributions of the elastic deformation and SW eigenmodes depicted schematically on the right panels, the overlapping integrals differ by an order of magnitude. However, the number of summable modes in area I exceeds the one for area II also by an order of magnitude. This compensates the smallness of Ik and the excitation efficiency begins to grow. If fn(H) < fFMR(H), then QSW I becomes imaginary and m(x,n) reduces sharply. So, the excitation of quasi-magnetic oscillations in areas I and II may have both different efficiencies and different decrease rates with detuning from the MER area, as it takes place in the experiment.

FIG. 3.

(the left panel) Dispersion diagram for ME waves (the solid lines) and uncoupled SW F=FSW(Q) and AW F=Q (the dashed green and red lines) in reduced coordinates. Only the solutions for propagating waves without dissipation, i.e. when Q is real are shown. (the right panels) Spatial distributions of SW k-th eigenmode and elastic deformation across the YIG film thickness in the areas I and II.

FIG. 3.

(the left panel) Dispersion diagram for ME waves (the solid lines) and uncoupled SW F=FSW(Q) and AW F=Q (the dashed green and red lines) in reduced coordinates. Only the solutions for propagating waves without dissipation, i.e. when Q is real are shown. (the right panels) Spatial distributions of SW k-th eigenmode and elastic deformation across the YIG film thickness in the areas I and II.

Close modal

In the case F∼1, nonlinear AD FMR in both YIG films is also possible. The preliminary measurements show that with Prf decrease the VISHE(fn(H)) in regions I and II also decrease but at different rates and become equal at Prf ≈ 0.5 mW. Nevertheless, the asymmetry of the signal form VISHE(f,H) is still the same as it is shown in Fig. 2(a).

In summary, we have demonstrated a considerably larger ASP via the composite HBAR than previously reported one.21 Simultaneous (f,H) mapping of VISHE(f,H) and |S11| has shown a one-to-one correspondence between the localization of voltage maxima and the positions of HBAR resonant frequencies fn(H) on the (f,H) plane. Meanwhile, the VISHE(fn(H)) dependences demonstrate a quite different behavior depending on whether these voltage maxima are localized above or below the MER line frequency. This asymmetry is attributed to the dispersion of ME waves in which occurrence for a non-uniform exchange field is important. At AW frequencies fn(H) higher than the MER line, the quasi-magnetic modes with wavenumbers more than 5×104 cm-1 are excited, whereas at fn(H) lower than the MER line frequency, the wavenumbers of excited modes are essentially smaller. Thus we assume that the combination of sensitive spectroscopic HBAR technique30,31 with electrical detection of magnetic dynamics by ISHE is of interest for the study of SW dispersion and damping due to back action from an acoustically driven SW on resonant properties of the HBAR and also due to the detection of spin current in Pt.

This work was supported by grants 16-07-01210 and 17-07-01498 from the Russian Foundation for Basic Research. We are grateful to Marina Temiryazeva for AFM investigations of YIG films surfaces.

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