$\textit{In situ}$ electric-field control of ferromagnetic resonance in the low-loss organic-based ferrimagnet V[TCNE]$_{x\sim 2}$

We demonstrate indirect electric-field control of ferromagnetic resonance (FMR) in devices that integrate the low-loss, molecule-based, room-temperature ferrimagnet vanadium tetracyanoethylene (V[TCNE]$_{x \sim 2}$) mechanically coupled to PMN-PT piezoelectric transducers. Upon straining the V[TCNE]$_x$ films, the FMR frequency is tuned by more than 6 times the resonant linewidth with no change in Gilbert damping for samples with $\alpha = 6.5 \times 10^{-5}$. We show this tuning effect is due to a strain-dependent magnetic anisotropy in the films and find the magnetoelastic coefficient $|\lambda_S| \sim (1 - 4.4)$ ppm, backed by theoretical predictions from DFT calculations and magnetoelastic theory. Noting the rapidly expanding application space for strain-tuned FMR, we define a new metric for magnetostrictive materials, $\textit{magnetostrictive agility}$, given by the ratio of the magnetoelastic coefficient to the FMR linewidth. This agility allows for a direct comparison between magnetostrictive materials in terms of their comparative efficacy for magnetoelectric applications requiring ultra-low loss magnetic resonance modulated by strain. With this metric, we show V[TCNE]$_x$ is competitive with other magnetostrictive materials including YIG and Terfenol-D. This combination of ultra-narrow linewidth and magnetostriction in a system that can be directly integrated into functional devices without requiring heterogeneous integration in a thin-film geometry promises unprecedented functionality for electric-field tuned microwave devices ranging from low-power, compact filters and circulators to emerging applications in quantum information science and technology.