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.

The unique properties of two-dimensional (2D) materials bring great promise to improve sensor performance and realise novel sensing principles. However, to enable their high-volume production, wafer-scale processes that allow integration with electronic readout circuits need to be developed. In this perspective, we review recent progress in on-chip 2D material sensors, and compare their performance to the state-of-the-art, with a focus on results achieved in the Graphene Flagship programme. We discuss transfer-based and transfer-free production flows and routes for complementary metal-oxide-semiconductor integration and prototype development. Finally, we give an outlook on the future of 2D material sensors, and sketch a roadmap towards realising their industrial and societal impact.

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.

Fundamental research on two-dimensional (2D) magnetic systems based on van der Waals materials has been rapidly gaining traction since their recent discovery. With the increase of recent knowledge, it has become clear that such materials have also a strong potential for applications in devices that combine magnetism with electronics, optics, and nanomechanics. Nonetheless, many challenges still lay ahead. Several fundamental aspects of 2D magnetic materials are still unknown or poorly understood, such as their often-complicated electronic structure, optical properties, magnetization dynamics, and magnon spectrum. To elucidate their properties and facilitate integration in devices, advanced characterization techniques and theoretical frameworks need to be developed or adapted. Moreover, developing synthesis methods which increase critical temperatures and achieve large-scale, high-quality homogeneous thin films is crucial before these materials can be used for real-world applications. Therefore, the field of 2D magnetic materials provides many challenges and opportunities for the discovery and exploration of new phenomena, as well as the development of new applications. This Roadmap presents the background, challenges, and potential research directions across key topics in the field, including fundamentals, synthesis, characterization, and applications. We hope that this work can provide a strong starting point for young researchers in the field and provide a general overview of the key challenges for more experienced researchers.

This thesis discusses several studies on magnetic two-dimensional (2D) materials, focusing on their nanomechanical properties and the behavior of resonance frequencies in response to temperature changes. These studies employ nanomechanical resonators, specifically suspended membranes (drum resonators) of 2D magnetic materials. The frequency response of these resonators is measured using optical excitation combined with an interferometric setup, allowing identification of resonance frequencies. By altering the temperature of the resonators, the resonance frequency shifts as the strain within the 2D material changes. This strain change is partially magnetostrictive in origin due to changes in the magnetic order within the materials, offering a method to study these magnetic characteristics...

Magnetostrictive coupling has recently attracted interest as a sensitive method for studying magnetism in two-dimensional (2D) materials by mechanical means. However, its application in high-frequency magnetic actuators and transducers requires rapid modulation of the magnetic order, which is difficult to achieve with external magnets, especially when dealing with antiferromagnets. Here, we optothermally modulate the magnetization in antiferromagnetic 2D material membranes of metal phosphor trisulfides (MPS₃), to induce a large high-frequency magnetostrictive driving force. From the analysis of the temperature-dependent resonance amplitude, we provide evidence that the force is due to a thermo-magnetostrictive effect, which significantly increases near the Neél temperature, due to the strong temperature dependence of the magnetization. By studying its angle dependence, we find the effect is observed to follow anisotropic magnetostriction of the crystal lattice. The results show that the thermo-magnetostrictive effect results in a strongly enhanced thermal expansion force near the critical temperature of magnetostrictive 2D materials, which can enable more efficient actuation of nano-magnetomechanical devices and can also provide a route for studying the high-frequency coupling among magnetic, mechanical, and thermodynamic degrees of freedom down to the 2D limit.

The temperature dependent order parameter provides important information on the nature of magnetism. Using traditional methods to study this parameter in two-dimensional (2D) magnets remains difficult, however, particularly for insulating antiferromagnetic (AF) compounds. Here, we show that its temperature dependence in AF MPS₃ (M(II) = Fe, Co, Ni) can be probed via the anisotropy in the resonance frequency of rectangular membranes, mediated by a combination of anisotropic magnetostriction and spontaneous staggered magnetization. Density functional calculations followed by a derived orbital-resolved magnetic exchange analysis confirm and unravel the microscopic origin of this magnetization-induced anisotropic strain. We further show that the temperature and thickness dependent order parameter allows to deduce the material’s critical exponents characterising magnetic order. Nanomechanical sensing of magnetic order thus provides a future platform to investigate 2D magnetism down to the single-layer limit.

Semiconducting van der Waals magnets exhibit a rich physical phenomenology with different collective excitations, as magnons or excitons, that can be coupled, thereby offering new opportunities for optoelectronic, spintronic, and magnonic devices. In contrast with the well-studied van der Waals magnets CrI₃ or Fe₃GeTe₂, CrPS₄ is a layered metamagnet with a high optical and magnon transport anisotropy. Here, the structural anisotropy of CrPS₄ above and below the magnetic phase transition is investigated by fabricating nanomechanical resonators. A large anisotropy is observed in the resonance frequency of resonators oriented along the crystalline a- and b-axis, indicative of a lattice expansion along the b-axis, boosted at the magnetic phase transition, and a rather small continuous contraction along the a-axis. This behavior in the mechanical response differs from that previously reported in van der Waals magnets, as FePS₃ or CoPS₃, and can be understood from the quasi-1D nature of CrPS₄. The results pinpoint CrPS₄ as a promising material in the field of low-dimensional magnetism and show the potential of mechanical resonators for unraveling the in-plane structural anisotropy coupled to the magnetic ordering that, in a broader context, can be extended to studying structural modifications in other 2D materials and van der Waals heterostructures.

The temperature dependent order parameter provides important information on the nature of magnetism. Using traditional methods to study this parameter in two-dimensional (2D) magnets remains difficult, however, particularly for insulating antiferromagnetic (AF) compounds. We show that its temperature dependence in AF MPS3 (M(II) = Fe, Co, Ni) can be probed via the anisotropy in the resonance frequency of rectangular membranes, mediated by a combination of anisotropic magnetostriction and spontaneous staggered magnetization. Density functional calculations followed by a derived orbital-resolved magnetic exchange analysis confirm and unravel the microscopic origin of this magnetization inducing anistropic strain. We further show that the temperature and thickness dependent order parameter allows to deduce the material's critical exponents characterising magnetic order. Nanomechanical sensing of magnetic order thus provides a future platform to investigate 2D magnetism down to the single-layer limit.

Suspended piezoelectric thin films are key elements enabling high-frequency filtering in telecommunication devices. To meet the requirements of next-generation electronics, it is essential to reduce device thickness for reaching higher resonance frequencies. Here, the high-quality mechanical and electrical properties of graphene electrodes are combined with the strong piezoelectric performance of the free-standing complex oxide, BaTiO₃ (BTO), to create ultrathin piezoelectric resonators. It is demonstrated that the device can be brought into mechanical resonance by piezoelectric actuation. By sweeping the DC bias voltage on the top graphene electrode, the BTO membrane is switched between the two poled ferroelectric states. Remarkably, ferroelectric hysteresis is also observed in the resonance frequency, magnitude and Q-factor of the first membrane mode. In the bulk acoustic mode, the device vibrates at 233 GHz. This work demonstrates the potential of combining van der Waals materials with complex oxides for next-generation electronics, which not only opens up opportunities for increasing filter frequencies, but also enables reconfiguration by poling, via ferroelectric memory effect.