[Paper Review] Nonlinear dynamics and magneto-elasticity of nanodrums near the phase transition

Makars Šiškins, Ata Keşkekler+7 more|arXiv (Cornell University)|Sep 18, 2023

Mechanical and Optical Resonators4 citations

TL;DR

This study investigates nonlinear magneto-elastic coupling in suspended FePS₃-based 2D heterostructure membranes near the Néel temperature (T_N), revealing that magnetic order relaxation induces nonlinear damping and stiffness changes. Using laser interferometry and a magnetostriction model, the authors demonstrate that magneto-elastic interactions generate a previously unexplored source of nonlinear dissipation in nanomechanical resonators near second-order phase transitions.

ABSTRACT

Nanomechanical resonances of two-dimensional (2D) materials are sensitive probes for condensed-matter physics, offering new insights into magnetic and electronic phase transitions. Despite extensive research, the influence of the spin dynamics near a second-order 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 FePS$_3$-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 $T_{ m{N}}$. 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.

Motivation & Objective

• To explore the influence of spin dynamics near a second-order phase transition on nonlinear mechanical dynamics in 2D nanodrums.
• To investigate how antiferromagnetic order in FePS₃-based heterostructures affects nonlinear stiffness and damping near T_N.
• To develop and validate a magnetostriction-based analytical model explaining nonlinear damping arising from magneto-mechanical coupling.
• To demonstrate that nanomechanical resonators can serve as intrinsic probes of magnetic phase transitions without external magnetic fields.
• To identify magneto-elasticity as a novel source of nonlinear energy dissipation in 2D membrane resonators.

Proposed method

• Fabricated freestanding FePS₃-based heterostructure membranes (9.5 ± 0.6 nm thick) suspended over 1.5 µm circular cavities in Si/SiO₂ substrates.
• Employed laser interferometry with a vector network analyzer to measure mechanical resonance frequency and amplitude as a function of temperature.
• Used a nonlinear Duffing oscillator model with mass-normalized coefficients to fit experimental resonance peaks and extract nonlinear stiffness and damping.
• Developed a magnetostriction model based on Landau theory, incorporating coupling between mechanical displacement and magnetic order parameter L.
• Derived a kinetic equation for the dynamic magnetic order parameter L_ω, leading to a nonlinear damping coefficient ξ_nl proportional to τ and system parameters.
• Applied harmonic balance to the coupled mechanical-magnetic system to derive the amplitude-frequency response equation (Eq. 14), including nonlinear stiffness and damping terms.

Experimental results

Research questions

• RQ1 How does the nonlinear stiffness of FePS₃-based nanodrums evolve near the Néel temperature T_N?
• RQ2 What is the origin of the observed nonlinear damping enhancement near T_N in antiferromagnetic 2D membranes?
• RQ3 To what extent can magneto-elastic coupling explain the temperature-dependent nonlinear dynamics in these nanomechanical resonators?
• RQ4 Can the magnetic phase transition in FePS₃ be probed via mechanical nonlinearities without external magnetic fields?
• RQ5 What is the role of magnetostriction in generating nonlinear dissipation mechanisms in 2D nanodrums?

Key findings

• Nonlinear stiffness and damping exhibit characteristic anomalies near the Néel temperature T_N, with a sharp increase in nonlinear damping coefficient ξ_nl.
• The resonance frequency ω₀ shows a non-monotonic temperature dependence, with a derivative peak at T_N, indicating strong coupling to magnetic order.
• The experimental data are well-fit by a theoretical model incorporating magnetostriction, with the nonlinear damping arising from the relaxation of the magnetic order parameter L.
• The model predicts that nonlinear damping emerges from the coupling between mechanical oscillations and the time-dependent relaxation of the magnetic order parameter via magnetostriction.
• The effective nonlinear damping coefficient scales with τ = 1/(2κa(T*ₙ − T)), showing a divergence-like behavior near T_N, consistent with experimental observations.
• The re-normalized resonance frequency ω₀² = (1/m)(k₁ + λL₀²(Ec₃)/(2r²)) confirms that magnetic order directly modifies the mechanical stiffness.