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Abstract Nanoelectromechanical systems (NEMS) incorporating atomic or molecular layer van der Waals materials can support multimode resonances and exotic nonlinear dynamics. Here we investigate nonlinear coupling of closely spaced modes in a bilayer (2L) molybdenum disulfide (MoS₂) nanoelectromechanical resonator. We model the response from a drumhead resonator using equations of two resonant modes with a dispersive coupling term to describe the vibration induced frequency shifts that result from the induced change in tension. We employ method of averaging to solve the equations of coupled modes and extract an expression for the nonlinear coupling coefficient (λ) in closed form. Undriven thermomechanical noise spectral measurements are used to calibrate the vibration amplitude of mode 2 (a₂) in the displacement domain. We drive mode 2 near its natural frequency and measure the shifted resonance frequency of mode 1 (f_1s) resulting from the dispersive coupling. Our model yieldsλ = 0.027 ± 0.005 pm⁻² · μs⁻²from thermomechanical noise measurement of mode 1. Our model also captures an anomalous frequency shift of the undriven mode 1 due to nonlinear coupling to the driven mode 2 mediated by large dynamic tension. This study provides a direct means to quantifyingλby measuring the thermomechanical noise in NEMS and will be valuable for understanding nonlinear mode coupling in emerging resonant systems. 

Nanoelectromechanical systems (NEMS) enabled by two-dimensional (2D) magnetic materials are promising candidates for exploring ultrasensitive detection and magnetostrictive phenomena, thanks to their high mechanical stiffness, high strength, and ultralow mass. The resonance modes of such vibrating membrane NEMS can be probed optically and also manipulated mechanically via electrostatically induced strain. Electrostatic frequency tuning of 2D magnetic NEMS resonators is, thus, an important means of investigating magneto-mechanical coupling mechanisms. Toward realizing magneto-mechanical coupled devices, we build circular drumhead iron phosphorus trisulfide (FePS3) NEMS resonators with different diameters (3–7 μm). Here, we report on experimental demonstration of tunable antiferromagnet FePS3 drumhead resonators with the highest fractional frequency tuning range up to Δf/f0 = 32%. Combining experimental results and analytical modeling of the resonance frequency scaling, we attain quantitative understanding of the elastic behavior of FePS3, including the transition from “membrane” to “plate” regime, with built-in tension (γ) ranging from 0.1 to 2 N/m. This study not only offers methods for investigating mechanical properties of ultrathin membranes of magnetic 2D materials but also provides important guidelines for designing future high-performance magnetic NEMS resonators.