Large ME coupling coefficient in the NPR device

The resonant bodies of the NEMS ME resonators were a 500 nm AlN thin film supporting a [Fe 7 Ga 2 B 1 (45 nm)/Al 2 O 3 (5 nm)] × 10 (hereafter termed FeGaB) thin-film ME heterostructures fully suspended on a Si substrate, where AlN and FeGaB (see Supplementary Note 1 for magnetic properties characterization) serve as the piezoelectric and magnetostrictive element of the ME heterostructure, respectively. The use of a NEMS resonator with an ultra-thin (thickness, T = 500 nm) AlN thin film enables efficient on-chip acoustic transduction with ultra-low energy dissipation25, 26. In this work, the demonstrated ME antennas span a wide range of frequencies from 60 MHz to 2.5 GHz, which are realized by a geometric design of resonating plates that exhibit different mode of vibrations (Supplementary Note 6).

The strong ME coupling at VHF frequencies was demonstrated through a ME NPR with an in-plane contour mode of vibration (by means of d 31 piezoelectric coefficient)27. In particular, a perpendicular electric field on the piezoelectric AlN layer induces actuation in the plane of the device. Figure 1a presents the schematic of the measurements and the structure of ME NPR which has a rectangular resonating plate consisting of a single-finger bottom Pt electrode and a thin-film FeGaB/AlN heterostructure. All the NEMS ME resonators in this work were fabricated using CMOS (complementary metal-oxide-semiconductor) compatible microfabrication processes (see Method and Supplementary Note 2). The scanning electron microscopy (SEM) image of the NPR ME resonator is shown in Fig. 1b. The length (L) and width (W) of the FeGaB/AlN active resonant body are 200 and 50 µm, respectively. The ME nanoplate FeGaB/AlN is fully released from the Si substrate but mechanically supported and electrically contacted by the two AlN/Pt anchors for optimized ME coupling with a minimum substrate clamping effect. To study the electromechanical properties of the ME NPR, the electrical admittance curve was characterized by using a network analyzer, as shown in Fig. 1c. The admittance spectrum at resonance can be fitted to the Butterworth–van Dyke model27, which yields an electromechanical resonance frequency (f r,NPR ) of 60.68 MHz, a high-quality factor (Q) of 930 and electromechanical coupling coefficient (k t 2) of 1.35% indicating a high electromechanical transduction efficiency and low loss (Supplementary Note 3). This f r,NPR corresponds to the contour mode of vibration excited in AlN, which can be analytically expressed as \({f_{{\rm{r,NPR}}}} \propto \frac{1}{{2{W_0}}}\sqrt {\frac{E}{\rho }} \), where W 0 is the width of the resonator pitch, E and ρ are the equivalent Young’s modulus and equivalent density of the FeGaB/AlN resonator, respectively28, 29. Finite element analysis (FEA) on the admittance curve of the device with the same geometry is shown in the Fig. 1d, which is in good agreement with Fig. 1c. At the resonance frequency of 60.56 MHz, the in-plane displacement distribution shown in Fig. 1d inset indicates a contour extensional mode of vibration, in which the bulk of the device structure expands in its plane. It is also notable that the Q-factor of this ME resonator is much higher than the conventional low frequency ME heterostructures in previous reports10, 30,31,32,33.

Fig. 1 ME NPR device with gigantic ME coupling. a Schematic representation of the magnetoelectric (ME) nanoplate resonator (NPR) and the induced ME voltage measurement setup by using a high-frequency lock-in amplifier (HFLIA). The RF magnetic field (H RF ) is generated by a RF coil. b Scanning electron microscopy (SEM) images of the fabricated the ME NPR. The red and blue areas show the suspended single nanoplate with FeGaB/AlN ME heterostructure and AlN anchors. The yellow area presents the RF ground-signal-ground electrode. c Admittance curve and Butterworth–van Dyke model fitting of the ME NPR with a resonance frequency (f r ) of 60.68 MHz, quality factor (Q) of 930 and electromenchanical coupling coefficient (k t 2) of 1.35%. The inset shows the schematic of the cross-section of the ME heterostructure. d Finite element analysis (FEA) of ME NPR for the admittance amplitude. The inset shows the in-plane displacement of the nanoplate at resonance peak position and its coordinate system. e Admittance curve of a non-magnetic control sample which has a same device design as ME NPR. The inset shows the schematic of the device cross-section. f, ME coupling coefficient (left axis) and the induced ME voltage (right axis) versus the frequency of H RF excitation. g FEA of ME NPR for the induced ME voltage. The inset shows the in-plane displacement excited by H RF . h Induced voltage versus the frequency of H RF excitation for the non-magnetic device. The inset illustrates the zoomed-in view of the resonance peak area (red circle) Full size image

Under the excitation of H RF with an amplitude about 60 nT (provided by a RF coil along the length direction of the resonator, see Supplementary Note 4), the induced ME voltage output of the NPR device was measured by using an UHF lock-in amplifier (UHFLI), as shown in Fig. 1f. A clear resonance peak is shown in the ME voltage spectrum at 60.7 MHz with a peak amplitude (U) of 180 μV. The amplitude of the peak is very sensitive to the excitation frequency exhibiting a Q-factor that is similar to the admittance curve in Fig. 1c. The experimentally measured output ME voltage spectrum (Fig. 1f) agrees well with the FEA results of the ME voltage spectrum with a peak amplitude of 196 μV as shown in Fig. 1g (Method). Figure 1g inset shows the simulated in-plane displacement of the ME resonator excited by the H rf at its resonance frequency, indicating a contour mode of vibration. The same mode of vibration excited by magnetic field and electric field demonstrates that the strain-mediated ME coupling is dominating. A high ME coupling coefficient of α ME = ∂U/(∂H rf ∙T) = 6 kV Oe−1 cm−1 can be obtained at the f r,NPR , where23, 34. It is notable this ME coupling coefficient is obtained without any DC bias magnetic field, and the value is comparable to recent reported values with optimum bias magnetic field at much lower electromechanical resonance frequencies of kHz35.

As a comparison, a non-magnetic single-finger NPR has also been tested as a control sample to confirm that the strain-mediated ME coupling is responsible for the observed voltage output under the H RF excitation. For the non-magnetic resonator, a Cu thin film of 500 nm was deposited on AlN plate (Fig. 1e inset) to replace the ferromagnetic FeGaB layer as the top electrode. As shown in Fig. 1e, the Cu/AlN based NPR exhibits a similar admittance behavior (both f r and Q) as the ME NPR (Fig. 1c). Figure 1h shows the H RF induced voltage spectrum of the resonator with a Cu/AlN heterostructure. With the same H RF excitation as the ME resonator (H rf = 60 nT), the induced voltage of the Cu/AlN resonator at its electromechanical resonance frequency of 64.7 MHz is very low, about two orders of magnitude smaller than the induced voltage in the FeGaB/AlN ME NPR (Fig. 1c). Note that the induced voltage spectrum profile of the Cu/AlN NPR is highly antisymmetric near its resonance frequency, which is totally different from the symmetric ME voltage spectrum (Fig. 1f) but similar to its admittance spectrum (Fig. 1e). This antisymmetric line shape can be attributed to a weak inductive coupling effect between the device ground loop and EM wave, which could also exist in the FeGaB/AlN NPR device. However, the symmetric ME voltage spectrum in the FeGaB/AlN NPR indicates that the inductive coupling effect has an extremely low efficiency compared to the ME coupling. Thus, the strong resonance peak induced by the H RF in FeGaB/AlN NPR device is resulted from the presence of the ME coupling, in which FeGaB films with high-permeability36, 37 couples to RF excitation magnetic field very effectively.

The ME NPR with multi-finger interdigitated electrodes, which we have demonstrated recently17, were found to have negligibly small ME voltage in the same measurement setup, that is over three orders of magnitude smaller at the electromechanical resonance compared to the single-plate ME NPR. This phenomenon has been confirmed through COMSOL simulations (Supplementary Note 5). Single-finger ME resonators produces high ME output voltage as the uniform RF excitation magnetic fields can couple strongly to single nanoplate. While the negligibly ME voltage output in multi-finger ME resonators is due to the fact that, the uniform H RF do not couple efficiently to the multi-finger NPRs which produce nonuniform RF strain fields and nonuniform magnetization fields.

We further gain insight into the magnetization dependence of the single-finger ME NPR shown in Fig. 1 by examining its ME coupling strength at different bias magnetic fields. The induced ME voltage spectrum was measured with DC bias magnetic fields swept from −5 to 5 mT along the resonator length direction (as shown in the inset of Fig. 2b). Figure 2a shows the α ME as a function of the DC bias magnetic field H DC and the frequency of H RF . At zero bias magnetic field μ 0 H DC = 0, the α ME is maximized at the f r,NPR of 60.7 MHz, which is in good agreement with Fig. 1f. At μ 0 H DC = ±5 mT, f r,NPR is shifted to 60.72 MHz as shown in the dashed curve of Fig. 2a. This can be attributed to the ΔE effect17, that is the bias magnetic field modifies the Young’s modulus of FeGaB and thus leads to varied f r,NPR of the resonator17, 31, 38. Moreover, a hysteretic behavior of the α ME (at f r,NPR ) was observed by sweeping the DC magnetic field back and force, with the maximum value of 6 kV cm−1 Oe−1 at ±0.5 mT (Fig. 2b). This is consistent with the strain-mediated ME coupling mechanism and the magnetic hysteresis of the FeGaB/AlN nanoplate (Supplementary Note 1). The magnetic field dependence of α ME in the ME NPR provides another direct evidence that the observed interaction between EM wave and acoustic resonance results from the ME coupling.

Fig. 2 Bias magnetic field and frequency dependence. a Magnetoelectric (ME) coupling coefficient α ME of ME NPR as functions of DC bias magnetic field H DC (x-axis) and the frequency of RF magnetic field (y-axis). The dashed curve exhibits the resonance frequency (highest intensity at each frequency sweep) versus the bias magnetic field. The bias magnetic field was swept from −5 to 5 mT. b The hysteresis loop of α ME obtained by sweeping the magnetic field back and force at f = 60.7 MHz. The inset shows the schematic representation of the ME NPR with the external bias magnetic field applied along its length direction. c Induced ME voltage as a function of magnetic field at excitation frequency of 60.7 MHz (red) and 1 MHz (blue) Full size image

It is important to note that the strong α ME at zero bias magnetic field directly leads to robust self-biased ME sensors. This is drastically different from conventional ME heterostructures with electromechanical resonance frequencies in the kilohertz frequency range, which show near zero ME coupling at zero bias magnetic field32, 39,40,41. This difference can be attributed to the edge curling wall42, 43 under self-bias condition for the magnetic/non-magnetic multilayers (FeGaB/Al 2 O 3 ) used as the magnetostrictive layer in ME antennas. The detection limit of the NPR ME antennas for sensing weak H RF under zero bias magnetic field was also characterized as shown in Fig. 2c, where the induced voltage is plotted as a function of H RF at two different excitation frequencies. At the resonance frequency of 60.7 MHz (red), the linear curve scatters at 40 pT with a limit detection voltage of 0.1 µV, indicating a detection limit of 40 pT for the NPR ME sensor. While at the off-resonance frequency of 1 MHz (blue), the induced voltage randomly distributes around the 0.1 µV, showing no sensitivity to 1 MHz magnetic field excitation with the amplitude of 10−11–10−7 T.

It is notable that ME NPR antenna arrays with multiple frequency bands from MHz to GHz can be integrated in one wafer by designing the ME NPR with different lateral dimensions (or W), since the f r,NPR is inversely proportional to W 27. This allows the broadband ME NPR antenna arrays on the same wafer, which compensates for the narrowband operation frequencies of ME antennas. The resonance frequencies as well as the Q-factors of various NPR (including FBAR) devices fabricated on one wafer are summarized in Supplementary Note 6 as a function of W.

FBAR ME antennas

We further designed, fabricated, and tested ME antennas that operate at GHz based on the thickness resonance mode of FeGaB/AlN thin-film FBAR devices. The antenna radiation property of the ME FBAR based antennas was tested in a far-field configuration at GHz range in an anechoic chamber. As shown in Fig. 3a, b, the active element of ME FBAR antenna is a suspended FeGaB/AlN ME circular disk with a diameter of 200 µm. This FBAR ME antenna exhibits a thickness extensional mode of vibration as shown in the schematic representation of Fig. 3a. A calibrated linear polarization standard horn antenna and a ME FBAR based antenna are connected to the port 1 and port 2 of a network analyzer, respectively for antenna gain measurements (see Methods). Different from ME NPR, the electromechanical resonance frequency of the ME FBAR (f r,FBAR ) is defined by the thickness of the circular resonating disk and can be expressed by \({f_{{\rm{r,FBAR}}}} \propto \frac{1}{{2T}}\sqrt {\frac{E}{\rho }} \). The f r,FBAR was found to be 2.53 GHz by measuring the reflection coefficient (S 22 ) of the FBAR device as shown in Fig. 3c, which also exhibits a peak return loss of 10.26 dB and a Q-factor of 632. Figure 3c inset shows the simulated out-of-plane displacement of the FBAR indicating a thickness extensional mode of vibration (see Supplementary Note 7 for the simulated S 22 ). The receiving and transmitting behavior of ME antennas corresponds to the S 21 and S 12 parameters, respectively, as shown in Fig. 3d. Clearly S 12 and S 21 curves nearly overlap with each other. These S-parameters (S 21 , S 12 and S 22 ) for the ME FBAR were obtained at zero bias magnetic field for the ME FBAR. The antenna gain for the ME FBAR is measured to be −18 dBi at f r,FBAR through gain comparison method (Methods). It is not trivial to simulate the ME antenna radiation in the framework of a three-dimensional (3D) device. While by using a 1D model, one may not be able to capture the real physics which contain many boundary conditions and anisotropic materials parameters. For example, the magnetic FeGaB layer in the ME antenna shows a highly anisotropic Young’s modulus with a ΔE effect of 160 GPa along the in-plane magnetic hard axis direction, which is very hard to incorporate into any existing model.

Fig. 3 ME FBAR antenna. a Schematic illustration of the magnetoelectric (ME) thin-film bulk acoustic wave resonators (FBAR) and the antenna measurement setup. The horn antenna and ME FBAR are connected to the S 1 and S 2 port of a network analyzer. b Scanning electron microscopy (SEM) images of the fabricated the ME FBAR. The red and blue areas show the suspended circular plate and AlN anchors. The yellow area presents the electrode. c Return loss curve (S 22 ) of ME FBAR. The inset shows the out-of-plane displacement of the circular disk at resonance peak position. d Transmission and receiving behavior (S 12 and S 21 ) of ME FBAR. e Return loss (S 22 ) curve of the non-magnetic Al/AlN control FBAR. f Transmission and receiving behavior (S 12 and S 21 ) of the non-magnetic Al/AlN control FBAR Full size image

A non-magnetic control device with 1000 nm Al/500 nm AlN has also been tested with the same experimental setups in order to rule out any artificial EM coupling to the ground loop of devices. In the non-magnetic control device, 1000 nm Al was used to replace the 500 nm thick FeGaB multilayer for achieving a device resonance frequency near 2.5 GHz. The loss mechanism of ME antennas is dominated by the mechanical resistance R m related to the different mechanical damping mechanisms of the magnetic and piezoelectric phases, which is much larger than the radiation resistance R r . The impedance matching is therefore dominated by R m , not R r . Therefore, impedance matching is no longer directly related to the radiation efficiency of ME antennas, which is different from conventional antennas. As shown in Fig. 3e, the Al/AlN control device exhibits a similar electromechanical property as FeGaB/AlN FBAR with similar S 22 but better impedance matching with an electromechanical resonance frequency of 2.50 GHz. However, no evident S 21 and S 12 resonance peak can be observed in the horn antenna measurements in Fig. 3f, except a very weak peak at 2.50 GHz with a peak amplitude just above the noise level, similar to the Cu/AlN NPR control sample shown in Fig. 1h. This suggests that the ME coupling effect dominates in the S 21 and S 12 measurement of the ME FBAR antenna.

The radiation behaviors of ME FBAR antenna was also tested by rotating the linearly polarized standard antenna as shown in Fig. 4. The standard antenna can be rotated along one of the three major axes of the ME antenna, the out-of-plane direction (Fig. 4a, b), the in-plane perpendicular to the ME antenna anchor direction (Fig. 4c, d) and the in-plane along the ME antenna anchor direction (Fig. 4e, f). In all the schematics of Fig. 4, the sinusoidal wave along 0° (or 180°) direction denotes the propagating H-field component of the incoming EM wave. All three polar gain charts in Fig. 4a, c, e show the similar shape of a sideways figure eight due to the magnetic anisotropy of the FeGaB/Al 2 O 3 multilayer in the circular resonating disk of the ME FBAR. As shown in Fig. 4a, the ME FBAR antenna has the highest gain when the H rf is perpendicular to the anchor direction of the antenna, and lowest gain when the H rf is parallel to the anchor direction. This is because the in-plane magnetic anisotropy of the FeGaB in the circular disk of the FBAR is along the width direction of the ME antenna, and the highest permeability and therefore strongest coupling between H rf and ME antenna is achieved along 0 or 180° direction in Fig. 4a. The other two rotation test configurations in Fig. 4c, e show similar behavior, in which the antenna gain shows its maximum value at 0° (or 180°).This is related to the shape anisotropy of the thin ferromagnetic layer. All the rotational antenna gain measurements at different configurations demonstrate that the high ME antenna gain originates from the strong magnetic coupling between the magnetic field component of the EM wave and the FeGaB of the FeGaB/AlN heterostructure in ME FBAR antennas.