The angularly resolved power absorption measurements shown in Fig. 2 were performed using a custom-built setup that allowed for RF transmission measurements of a sample as it was rotated in relation to a fixed electromagnet (12). A signal generator was used to output an RF wave tuned to the first, third, and fifth harmonics of the IDTs (287, 861, and 1429 MHz, respectively), and a spectrum analyzer was used to measure the resulting output from the devices. Data shown in the figure were normalized to the transmitted power in the presence of a large (150 mT) applied field to remove the variation in device insertion loss when operating at different frequencies (12).

Because of the harmonic operation of the IDTs, device efficiency was dramatically reduced at higher operating frequencies. As a result of this low efficiency, the electromagnetic wave generated by the IDTs became comparable in amplitude to the acoustic signal at high harmonics. To obtain an accurate measurement of the magnetoelastic portion of the interaction, we leveraged the difference in wave speeds between acoustic and electromagnetic waves. Since acoustic waves travel ~100,000 times slower than electromagnetic waves, the two signals can be differentiated by using a time-gating technique (9, 11, 12, 22).

The signal generator output was turned on for 700 ns and then turned off for 1300 ns (generating a 700-ns pulse with a period of 2 μs). Given the distance between the transducers and the speed of sound in the substrate, the acoustic propagation time was estimated to be approximately 800 ns. Thus, by only sampling the output signal after 800 ns had passed from the start of the pulse, it was ensured that only the acoustic component of the transmitted signal was being measured.

The electrical transmission data shown in Fig. 4 were obtained differently to allow for simultaneous measurement with the continuous-wave (CW) NV optical measurements. A +18-dBm microwave signal was modulated at low frequency and applied to the ADFMR devices. The output signal was routed to a Krytar 303BK power diode, whose output was connected to a lock-in amplifier tuned to the low-frequency modulation of the RF source. Because of the CW nature of the RF excitation, it was impossible to differentiate between the acoustic and electromagnetic waves. This explains the discrepancy between the power absorption shown at 1429 MHz in Figs. 2 and 4, as the data in Fig. 4 have an offset from the contribution of the electromagnetic wave (that is, not strongly modulated by the ferromagnetic film).

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