Nanomechanical resonances of two-dimensional (2D) materials are sensitive probes for condensedmatter physics, offering new insights into magnetic and electronic phase transitions. Despite extensive research, the influence of the spin dynamics near a phase transition on the nonlinear dynamics of 2D membranes has remained largely unexplored. Here, we investigate nonlinear magneto-mechanical coupling to antiferromagnetic order in suspended FePS3-based heterostructure membranes. By monitoring the motion of these membranes as a function of temperature, we observe characteristic features in both nonlinear stiffness and damping close to the Néel temperature TN. We account for these experimental observations with an analytical magnetostriction model in which these nonlinearities emerge from a coupling between mechanical and magnetic oscillations, demonstrating that magneto-elasticity can lead to nonlinear damping. Our findings thus provide insights into the thermodynamics and magneto-mechanical energy dissipation mechanisms in nanomechanical resonators due to the material’s phase change and magnetic order relaxation.

Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degree-of-freedom models have been used to account for experimentally observed nonlinear effects, it is shown that these models quickly deviate from experimental findings when multiple modes influence the nonlinear response. Here, we present a nonlinear reduced-order modeling methodology based on finite-element method simulations for capturing the global nonlinear dynamics of nanomechanical resonators. Our physics-based approach obtains the quadratic and cubic nonlinearities of resonators over a wide frequency range that spans 70 MHz. To qualitatively validate our approach, we perform experiments on a graphene nanodrum driven optothermally and show that the model can replicate diverse ranges of nonlinear phenomena, including multistability, parametric resonance, and different internal resonances without considering any empirical nonlinear fitting parameters. By providing a direct link between microscopic geometry, material parameters, and nonlinear dynamic response, we clarify the physical significance of nonlinear parameters that are obtained from fitting the dynamics of nanomechanical systems, and provide a route for designing devices with desired nonlinear behavior.

Micro and nanomechanical resonators are essential to the state-of-the-art communication, data processing, timekeeping, and sensing systems. The discovery of graphene and other two-dimensional (2D) materials has been a profound source of inspiration for the next generation of these devices, owing to their exceptional mechanical, electrical, and thermal properties. However, alongside their advantages, the atomically thin nature of these resonators also presents its own unique challenges, as the dynamic response of these resonators rapidly becomes nonlinear, where nonlinear coupling and dissipation processes manifest. To unleash the full potential of these resonators, a comprehensive understanding of the emerging nonlinear phenomena is crucial. In this pursuit, this thesis studies nonlinear dissipation pathways in 2D material resonators that arise from the coupling of their internal mechanical modes to each other as well as to theirmicroscopic physics. The thesis consists of six chapters.

Nonlinearities are inherent to the dynamics of two-dimensional materials. Phenomena-like intermodal coupling already arise at amplitudes of only a few nanometers, and a range of unexplored effects still awaits to be harnessed. Here, we demonstrate a route for generating mechanical frequency combs in graphene resonators undergoing symmetry-breaking forces. We use electrostatic force to break the membrane's out-of-plane symmetry and tune its resonance frequency toward a one-to-two internal resonance, thus achieving strong coupling between two of its mechanical modes. When increasing the drive level, we observe splitting of the fundamental resonance peak, followed by the emergence of a frequency comb regime. We attribute the observed physics to a nonsymmetric restoring potential and show that the frequency comb regime is mediated by Neimark bifurcation of the periodic solution. These results demonstrate that mechanical frequency combs and chaotic dynamics in 2D material resonators can emerge near internal resonances due to symmetry-breaking.

Mechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.

Diamagnetic levitation offers stable confinement of an object from its environment at zero power, and thus is a promising technique for developing next generation unclamped resonant sensors. In this work, we realize a resonant weighing scale using a graphite plate that is diamagnetically levitating over a checkerboard arrangement of permanent magnets. We characterize the bending vibrations of the levitating object using laser Doppler vibrometry and use microgram glass beads to calibrate the responsivity of the sensor's resonance frequency to mass changes. The sensor is used for real-time measurement of the evaporation rate of nano-litre droplets with high-accuracy. By analyzing the resonator's frequency stability, we show that the millimeter graphite sensor can reach mass resolutions down to 4.0 ng, relevant to biological and chemical sensing concepts.

Diamagnetic levitation is a promising technique for realizing resonant sensors and energy harvesters since it offers thermal and mechanical isolation from the environment at zero power. To advance the application of diamagnetically levitating resonators, it is important to characterize their dynamics in the presence of both magnetic and gravitational fields. Here we experimentally actuate and measure rigid body modes of a diamagnetically levitating graphite plate. We numerically calculate the magnetic field and determine the influence of magnetic force on the resonance frequencies of the levitating plate. By analyzing damping mechanisms, we conclude that eddy current damping dominates dissipation in mm-sized plates. We use finite element simulations to model eddy current damping and find close agreement with experimental results. We also study the size-dependent Q-factors (Qs) of diamagnetically levitating plates and show that Qs above 100 million are theoretically attainable by reducing the size of the diamagnetic resonator down to microscale, making these systems of interest for next generation low-noise resonant sensors and oscillators.