Magnetoelastic conversion in integrated YIG nanostructures

Motivated by the recent proposal of two-step transduction from microwave to optical domain using magnetic and elastic intermediate stages arXiv:2205.05088, we consider the coupling between resonant magnetic and elastic modes within a simple axially-symmetric nanodevice designed to host high-quality-factor acoustic modes: A suspended YIG ring structure supported by a central stem, fabricated from a continuous single-crystal film. We study the modes of the system with our custom finite element solvers. We identify the lowest order ``breathing'' mode of a magnetic vortex and the lowest order elastic breathing mode as having the largest mode overlap. For this pair of modes, the external out-of-plane magnetic bias field is critical for bringing them into resonance; however, we show that at the same time it also affects the strength of the coupling. To counteract this, we optimize the radius of the ring at fixed thickness. For the 100 nm-thick film the resonant coupling is maximized at $g/2π= 8\text{MHz}$ at $R\approx1.7μ\text{m}$, indicating that the overlap integral approaches the idealized limit assumed in previous order-of-magnitude estimates. Our results pave the way for the design of tunable frequency-conversion devices based on magnetoelastics.