Giant nonreciprocity of surface acoustic waves enabled by the magnetoelastic interaction

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Science Advances  04 Dec 2020:
Vol. 6, no. 49, eabc5648
DOI: 10.1126/sciadv.abc5648


Nonreciprocity, the defining characteristic of isolators, circulators, and a wealth of other applications in radio/microwave communications technologies, is generally difficult to achieve as most physical systems incorporate symmetries that prevent the effect. In particular, acoustic waves are an important medium for information transport, but they are inherently symmetric in time. In this work, we report giant nonreciprocity in the transmission of surface acoustic waves (SAWs) on lithium niobate substrate coated with ferromagnet/insulator/ferromagnet (FeGaB/Al2O3/FeGaB) multilayer structure. We exploit this structure with a unique asymmetric band diagram and expand on magnetoelastic coupling theory to show how the magnetic bands couple with acoustic waves only in a single direction. We measure 48.4-dB (power ratio of 1:69,200) isolation that outperforms current state-of-the-art microwave isolator devices in a previously unidentified acoustic wave system that facilitates unprecedented size, weight, and power reduction. In addition, these results offer a promising platform to study nonreciprocal SAW devices.


Nonreciprocal microwave transmission devices such as isolators and circulators have an important role in the front-end of most radio frequency (RF) systems and test and measurement equipment. These devices allow RF propagation in one direction and block propagation in the opposite direction. From an application point of view, the ideal attributes of an isolator device should include low insertion loss (allow full transmission from port 1 to port 2) and high isolation (block transmission from port 2 to port 1). This type of device can be thought of as a diode for RF energy. Current state-of-the-art isolators and circulators use a transversely magnetized ferrite junction to direct the incoming microwave energy and thus allowing travel in the direction of the magnetizing field. In 1971, Lewis (1) proposed an alternative form of acoustic isolator device concept using a layered surface acoustic wave (SAW) delay line with ZnO/YIG on GGG substrate. While acoustic isolator device concepts have largely been ignored for decades, these concepts are the subject of very recent theoretical investigations generating substantial interest in the scientific community (24). In general, nonreciprocal propagation of SAWs is nontrivial to achieve and has been observed in nonmagnetic metal (aluminum) and some semiconductor heterostructures (5). However, the nonreciprocity magnitude is not sufficient for real-world application relevance. On the other hand, spin wave nonreciprocity has been an active area of research interest in the community, resulting in numerous reports in the last decade or so (610). The theoretical framework that explains spin wave nonreciprocity is either based on frequency displacement in the ferromagnetic layer or is based on interband magnonic transitions in a system with lack of time-reversal symmetry (6, 9, 11).

Recently, the community has been investigating device physics using magnetoelastic interactions of spin and acoustic waves. This is based on traveling SAWs coupling into the magnetostrictive ferromagnetic thin film in the SAW propagation path. The most common materials system studied on this subject is Ni on lithium niobate (LiNbO3), which has been shown to have reciprocal transmission behavior due to polycrystallinity of the Ni film. This leads to larger Gilbert damping coefficient resulting in wider line widths in the magnetization response (12). Several device concepts such as magnetically tunable phase shifters and resonators were reported in the 1970s using magnetoelastic interactions. The recent resurgence of study in magnetoelastic interactions using SAWs is being termed as acoustically driven ferromagnetic resonance (ADFMR) (1315).

SAW-based frequency filters, delay lines, and sensors are mature technologies and have several applications in the RF frequency (low megahertz up to 2.5 GHz) regime. Ultralow loss, temperature-compensated SAW filters are essential elements in military and consumer communication devices such as cell phones and tablets. Acoustic transmission is advantageous because the propagation speeds and wavelengths are typically several orders of magnitude lower than for electromagnetic waves, and therefore, scaling down is easily achieved.

In this work, we demonstrate giant nonreciprocity of SAWs through the magnetoelastic interaction and operation of a magnetoelastic magnetic field–dependent microwave isolator. We use a ferromagnetic/dielectric heterostructure in a traditional SAW delay line filter geometry that achieves record-high RF isolation and nonreciprocal behavior, thereby opening a new avenue to explore next-generation size, weight, and power-friendly microwave isolator and circulator devices. A device schematic is shown in Fig. 1. The physical mechanism of the proposed isolator is based on the coupling between acoustic waves in LiNbO3 substrate and spin waves in an adjacent multilayer magnetic film. The configuration of the multilayer film allows for a strongly nonreciprocal dispersion law of spin waves, while ADFMR effectively attenuates acoustic waves in one direction and practically does not affect their propagation in the opposite direction. The combination of these two features leads to a much better achievable isolation compared to typical single-layered ADFMR isolators (12, 14, 15).

Fig. 1 Schematic of device design and experimental setup for measurement.

(A) Schematic cross-sectional representation of the magnetoelastic isolator device. The geometry of the device is similar to the standard ADFMR device (15). The multilayer thin-film stack in this study is FeGaB/Al2O3/FeGaB thin film. (B) Schematic top view representation of the isolator device including measurement setup.


Figure 2 shows the conventional angle-dependent magnetic field sweep versus transmission magnitude plot from the ADFMR device driven at 1435 MHz. Resonance field, line width, and contrast are quantitatively similar to that observed in a single-layer FeGaB device (16). Here, the growth field HG was applied at 60° relative to +z (see inset). In all prior reports of ADFMR in Ni, broad absorption resonances occurred in all four quadrants with even and odd symmetries. Notable distinctions of our measurement include the following: (i) breaking even symmetry, with lobes occurring only in quadrants II and IV; (ii) extremely narrow line width, indicating low damping and therefore high-frequency selectivity; (iii) acoustic wave absorption much larger than any previously reported results; and (iv) high nonreciprocity in opposite SAW travel directions.

Fig. 2 Nonreciprocal SAW transmission in FeGaB/Al2O3/FeGaB multilayer stack with growth field HG at 60°.

ADFMR plot with 1435-MHz SAWs traveling in (A) +z-direction (forward) and (B) −z-direction (reverse). Absorption (blue on color scale) occurs at ADFMR resonance, which we observe in directions perpendicular to the growth field. (C) Field sweeps at ϕ = 150° for forward (blue) and reverse (orange) SAW propagation. (D) Field sweeps at ϕ = 330° for forward (blue) and reverse (orange) SAW propagation. The difference between forward and reverse sweeps at a common static field condition is the isolation.

In Fig. 2, red indicates maximum transmission (far from magnetic resonance) of approximately −55 dB. This is the insertion loss of the device, and there are several known reasons for high insertion loss. Insertion loss increases with frequency due to interactions with thermally excited elastic waves and energy lost to air adjacent to the surface (air loading) (17). In addition, operating the device at higher-order harmonics and impedance mismatch also contribute to higher insertion loss, but these can be minimized through careful engineering of the interdigital transducers (IDTs), which is outside the scope of the current work. In our prior work, we have reported the transmission behavior as a function of operating frequency for a similar device using a Ni thin film as the ferromagnetic material (15).

Resonant absorption of SAWs by spin waves in the magnetic material appears as blue on the color scale, and we observe none of this interaction along the growth field axis 60° (quadrant I) and 240° (quadrant III). Interactions only exist in the perpendicular directions 150° (quadrant II) and 330° (quadrant IV). Minimum transmission was −115 dB, which occurred at H = 9 Oe, ϕ = 150° for forward propagating SAWs, and H = 11 Oe, ϕ = 330° for reverse propagating SAWs. This minimum transmission value is 60 dB lower than the insertion loss (99.9999% power absorption), which is remarkable in its own right as the highest reported ADFMR-related absorption value to date. These conditions of maximum acoustic-spin interaction are highlighted by the line cuts in Fig. 2 (C, orange, and D, blue). Reversing the SAW propagation direction under the same field conditions results in the other line cuts in Fig. 2 (C, blue, and D, orange), which are nearly flat in comparison, indicating almost zero interaction between the SAWs and the magnetic layer.

The isolation (i.e., the difference between forward and reverse transmission) measured at both resonant angles is 48.4 dB. This represents substantially higher isolation performance compared to state-of-the-art commercial single-stage isolator devices, which are typically 18- to 20-dB isolation performance. In addition, the size and weight benefits are substantial compared to the state of the art. To give a perspective on the size and weight benefits, the size of commercial isolator packages ranges from approximately 40 to 75 mm, whereas the size of our proposed integrated device is less than 8 mm, which translates to about 5 to 10 times advantage in physical size. Similarly, the weight of our integrated device package would be about 10 to 20 times less. There is a second resonance at higher field (H = 35 Oe, ϕ = 150°) that also exhibits notable nonreciprocity, albeit with much lower isolation than the low-field resonance. Results were qualitatively similar with a driving SAW frequency of 863 MHz but with a lower isolation of about 10 dB (see the Supplementary Materials). Within the last year, other ADFMR studies reported isolation performance of 2 dB at 3.45 GHz (18) and 11 dB at 1.85 GHz (19).

When HG = 0° or 90°, the nonreciprocity minimizes or completely disappears. Here, absorption occurs at small angles from the z axis, but along the z axis, ADFMR is prohibited because there exists no x component for the microwave driving field produced by the Rayleigh waves, which is a necessary condition for FMR.

From the line cuts in Fig. 3 (C and D), we do observe small nonreciprocity. Small absorption of SAWs occurred even if the anisotropy axis was oriented nonoptimally. The absorption happens because the magnetic state of the bilayers became canted under the external magnetic field, and some portion the magnetoelastic driving field can interact with the magnetic material. Nonetheless, this is negligible compared to the giant nonreciprocity shown in Fig. 2. Figures 2 and 3 are shown on the same scale for ease of comparison.

Fig. 3 SAW transmission in FeGaB/Al2O3/FeGaB multilayer stack with growth field HG at 90°.

ADFMR plot with 1435-MHz SAWs traveling in (A) +z-direction (forward) and (B) −z-direction (reverse). Absorption (blue on color scale) occurs at ADFMR resonance, close to 0° and 180° in this case. (C) Field sweeps at ϕ = 174° for forward (blue) and reverse (orange) SAW propagation. (D) Field sweeps at ϕ = 354° for forward (blue) and reverse (orange) SAW propagation.

This observed giant nonreciprocity in transmission is attributed to two primary effects. (i) There is a drastic difference between the damping of oscillations in acoustic and magnetic systems. Since oscillations in a magnetic system decay very fast, even weak coupling to an acoustic system momentarily drains the energy from acoustic oscillations, i.e., when the magnetic system becomes connected to the acoustic system, acoustic waves decay at a much higher rate. (ii) Coupling between the two systems (spin waves and acoustic waves) is resonant. This means that for effective interaction, spin waves and acoustic waves must simultaneously have equal frequencies and wavelengths. The dispersion spectra of spin waves in bilayers are nonreciprocal, meaning that for the same frequency, spin waves propagating in the opposite directions have different wavelengths. This difference allows for effective damping of acoustic waves traveling in one direction while keeping the acoustic waves traveling in the opposite direction practically unaffected. We validate this fact with the proposed theory in the next section.


The interaction between acoustic waves and spin waves in magnetostrictive materials can be understood with the classical weakly coupled oscillator framework (20, 21). Within this framework, the acoustic waves and spin waves interact with each other, producing coupled magnetoelastic waves (modes). In the approximation of weak coupling between the magnetic and acoustic waves, the dispersion law for magnetoelastic waves can be written asωkme=12(ωka+ωksw)±(ωkaωksw)24+κ2(1)where ωka is the dispersion of the acoustic wave, ωksw is the dispersion of the spin wave, and κk is the scalar parameter defining how the coupling modifies the dispersion characteristics of the SAWs and ultimately changes the propagation behavior (4). In particular, as shown in Eq. 1, the strongest interaction between the waves happens when the frequencies of acoustic and spin waves are close to each other for the same wave number, k. In this case, the first part under the square root vanishes, and the frequencies of the magnetoelastic modes differ by the value of κ, which leads to the modification of dispersion law.

For the giant nonreciprocity effect, the dispersion of spin waves in bilayers (11) is asymmetric with respect to wave number k, i.e. ωkswωksw. For the magnetoelastic waves, this means that if the resonance condition at a particular frequency and the direction of travel can be satisfied, then the reversal of k changes the frequency of spin wave modes, the resonance condition is no longer satisfied, and the interaction vanishes.

In Fig. 4A, we demonstrate the calculated dispersion laws for acoustic waves and spin waves in a LiNbO3 substrate with a magnetic bilayer placed on the top. The magnetic bilayers are oriented in the antiferromagnetic fashion and biased with an external magnetic field of 10 Oe, which is less than saturation (see insets). Note that the curves cross each other at nonsymmetric points with respect to k = 0. Two dispersion curves for the spin waves and SAWs cross at 1.435 GHz for the negative values of wave number (backward propagation), while they are gapped for forward propagation. The consequence of this crossing is the modification of the acoustic dispersion law and the enhanced absorption of backward propagating (with k < 0) waves.

Fig. 4 Theoretical behavior of the nonreciprocal ADFMR device concept.

(A) Dispersion of spin waves in a bilayer and SAWs in the substrate for applied magnetic field of 11.5 Oe. (B) Linear loss for the magnetoelastic wave as a function of the applied magnetic field calculated for forward and backward propagation for HG = 60°. The inset shows the configuration of the SAW propagation, applied magnetic field, and crystalline anisotropy. (C) Same as (B) for HG = 90°.

The modification of the dispersion law also modifies the losses for acoustic waves, the quantity we observe in the experiment. Considering the magnetic layer to be much thinner than the acoustic wavelength, we can use an approximate formula for the lossesLoss4.34 Im(ωkme)/(cR) [dB/m](2)where cR is the Rayleigh SAW velocity.

The dependence of the magnetoelastic wave spectrum ωkme on the direction of travel governs the operating principle of the magnetic SAW isolator—the direction selectivity of the SAW damping. Here, we calculate the losses for two cases, when the easy axis is oriented 60° (HG = 60°) from the direction of travel, and when it is perpendicular to the direction of travel (HG = 90°), see Fig. 4 (B and C). For the 60° case, the nonreciprocity is large, i.e., the value of damping is very different for counter-propagating waves; however, for the 90° case, the interaction is barely present. This behavior qualitatively agrees with the experimental data. The detailed derivation of the magnetoelastic coupling coefficient is given in the Supplementary Materials.

For the case when the anisotropy axis is oriented at HG = 60° to the direction of SAW propagation and the SAW excitation frequency is ω/(2π) = 1.435 GHz, the dependence of the losses is plotted in Fig. 4B. Note the large peak situated around the value of 10 Oe for the applied magnetic field. The maximum absorption of the SAWs happens when the SAW dispersion curve crosses the dispersion curve of spin waves.

The results in Fig. 4B show that, theoretically, at 10 Oe applied magnetic field, the forward loss is around 0.4 dB/mm (indicating near full transmission), whereas the backward loss is about 7.5 dB/mm. Taking the difference between forward and backward losses, 7.1 dB/mm, and multiplying by the 2.2-mm length of the multilayer stack, the calculated isolation performance is around 15.6 dB. When the growth field is applied at 90° (Fig. 4C), the calculated isolation performance is only about 0.2 dB, nearly negligible in comparison with the 60° case.

Experimentally, in our measurements for HG = 60°, the difference between forward and backward propagation is the isolation performance of the device, which is a remarkably high isolation of 48.4 dB. We suspect that since the resonance fields are very low in these multilayer stacks, assumptions of the film properties will have strong influence on the theoretical prediction of the device performance, particularly the assumption of gyromagnetic ratio and the Gilbert damping constant. This may explain the difference between the theoretical value and our experimental result.

Nevertheless, these results are particularly interesting for the development of next-generation frequency-agile tunable isolator and circulator devices because of the high isolation performance. One obvious concern to address in the near term is the high insertion loss, which can be mitigated by advanced SAW IDT design techniques taking care to impedance match at the desired operating frequency.


In this work, we use split-finger IDT design, generating Rayleigh waves using single crystal y-cut LiNbO3 substrate. Favorable SAW propagation is along the z axis between two pairs of IDTs for the delay line filter geometry as shown in the schematic representation of the device in Fig. 1. Split-finger design minimizes the destructive interference caused by reflection from the IDTs and thereby allows the device operation at higher odd harmonics of the fundamental frequency. The nominal designed fundamental frequency f1 is around 291 MHz; however, most of the reported measurements are at higher harmonic f3, f5, and f7 = 873, 1455, and 2037 MHz, respectively. IDTs have 60 finger pairs with the minimum electrode separation λ/8 = 1.5 μm. The delay line spacing between two IDT pairs is 3 mm. IDT patterning for metal liftoff was completed using negative tone liftoff photoresist NR9-1000Py and a Karl Suss MA6 mask aligner contact lithography system. The Al electrode thickness is 70 nm, deposited using e-beam evaporation. Details on the SAW device design, fabrication, and its impact on ADFMR performance are discussed in our prior work (15).

In the spacing between the IDTs, a multilayer thin-film stack of FeGaB/Al2O3/FeGaB is deposited via sputtering and lithographically patterned (22) with a width of 500 μm along x and a length of 2200 μm along z. The film stack is deposited in the presence of external magnetic field. A schematic figure of in situ magnetic field orientation with respect to the SAW k-vector is shown in the Supplemental Materials.

For measurements, a signal generator (Keysight N5171B) delivered pulsed RF with 20 dBm power to the ADFMR device, and the amplified output was measured using a spectrum analyzer (Keysight N9000A). We observed that this input power remained in the linear regime, where the characteristics of the results are not power dependent. At higher powers, nonlinear behavior may occur. Time gating was used to isolate the signal transmitted via SAWs, which is delayed by about 1 μs compared to the electromagnetic radiative signal because of the slower velocity of SAWs. A vector electromagnet was used to sweep the angle ϕ and magnitude H of the magnitizing field. The magnitude was swept from high (50 Oe) to low (0 Oe) to ensure consistency in hysteretic behavior. To measure the nonreciprocal transmission behavior of the device, the generator and analyzer were interchanged between input and output ports in two separate measurement sweeps. A vector network analyzer was used to calibrate the transmission values.


Supplementary material for this article is available at

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.


Acknowledgments: Funding: This work was supported by the Air Force Office of Scientific Research (AFOSR) Award No. FA955020RXCOR074. Author contributions: P.J.S., M.R.P., and N.X.S. formulated the experiment and conceived this study; P.J.S. fabricated the devices; A.M. deposited the films; D.A.B. performed the ADFMR measurements; and I.L. developed the theory. P.J.S., I.L., and D.A.B. wrote the manuscript. N.X.S. and M.R.P. planned and supervised the project. All authors discussed the results and reviewed and edited the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.

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