We experimentally and theoretically demonstrate that nonlinear spin-wave dynamics can induce an effective resonant interaction between nonresonant magnon modes in a yttrium iron garnet disk. Under strong pumping near the ferromagnetic resonance mode, we observe a spectral splitting that emerges with increasing drive amplitude. This phenomenon is well captured by a theoretical framework based on the linearization of a magnon three-wave mixing Hamiltonian, which at high power leads to parametric Suhl instabilities. The access and control of nonlinear magnon-parametric processes enable the development of experimental platforms in an unexplored parameter regime for both classical and quantum computation protocols.

A quantitative understanding of the microscopic mechanisms responsible for damping in van der Waals nanomechanical resonators remains elusive. In this work, we investigate van der Waals magnets, where the thermal expansion coefficient exhibits an anomaly at the magnetic phase transition due to magnetoelastic coupling. Thermal expansion mediates the coupling between mechanical strain and heat flow and determines the strength of thermoelastic damping (TED). Consequently, variations in the thermal expansion coefficient are reflected directly in TED, motivating our focus on this mechanism. We extend existing TED models to incorporate anisotropic thermal conduction, a critical property of van der Waals materials. By combining the thermodynamic properties of the resonator material with the anisotropic TED model, we examine dissipation as a function of temperature. Our findings reveal a pronounced impact of the phase transition on dissipation, along with transitions between distinct dissipation regimes controlled by geometry and the relative contributions of in-plane and out-of-plane thermal conductivity. These regimes are characterized by the resonant interplay between strain and in-plane or through-plane heat propagation. To validate our theory, we compare it to experimental data of the temperature-dependent mechanical resonances of FePS3 resonators.