Heat transport by acoustic phonons in two-dimensional (2D) materials is fundamentally different from that in 3D crystals because the out-of-plane phonons propagate in a unique way that strongly depends on tension and bending rigidity. Here, using optomechanical techniques, we experimentally demonstrate that the heat transport time in freestanding graphene membranes is significantly higher than the theoretical prediction, and decreases by as much as 33% due to an electrostatically induced tension of 0.07 N/m. Using phonon scattering and Debye models, we explain these observations by the tension-enhanced acoustic impedance match of flexural phonons at the boundary of the graphene membrane. Thus, we experimentally elucidate the tunability of phononic heat transport in 2D materials by tension, and open a route towards electronic devices and circuits for high-speed control of temperature at the nanoscale.

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.

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.

CoPS₃ stands out in the family of the van der Waals antiferromagnets XPS₃ (X = Mn, Ni, Fe, and Co) due to the unquenched orbital momentum of the magnetic Co²⁺ ions, which is known to facilitate the coupling of spins to both electromagnetic waves and lattice vibrations. Here, using a time-resolved magneto-optical pump-probe technique, we experimentally study the ultrafast laser-induced dynamics of mutually correlated spins and lattice. It is shown that a femtosecond laser pulse acts as an ultrafast heater and, thus, results in the melting of the antiferromagnetic order. At the same time, the resonant pumping of the ⁴T_1g → ⁴T_2g electronic transition in Co²⁺ ions effectively changes their orbital momentum, giving rise to a mechanical force that moves the ions in the direction parallel to the orientation of their spins, thus generating a coherent B_g phonon mode at the frequency of about 4.7 THz.

In van der Waals (vdW) materials, the electron mean free path (MFP) is largely influenced by the discrete states in the unoccupied band structure. So far, the influence of these states has only been measured in graphene, while all measurements on other vdW materials lack energy resolution. Here, we present reflection and transmission spectra of freestanding, few-layered molybdenum disulfide (MoS2) samples in the 0-55 eV electron range. Our measurements reveal states of enhanced electron transmissivity above the vacuum level, that correspond to the (unoccupied) density of states. We also show a full quantum-mechanical calculation that confirms a good understanding of the elastic scattering in MoS2. A model is developed to extract the inelastic MFP spectrum, which is a measure of the inelastic scattering cross section. As MoS2 is a complicated system of different atomic planes, we expect that our methods generalize well to other van der Waals materials and heterostacks thereof.

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.

Antiferromagnetic materials feature intrinsic ultrafast spin dynamics, making them ideal candidates for future magnonic devices operating at THz frequencies. A major focus of current research is the investigation of optical methods for the efficient generation of coherent magnons in antiferromagnetic insulators. In magnetic lattices endowed with orbital angular momentum, spin-orbit coupling enables spin dynamics through the resonant excitation of low-energy electric dipoles such as phonons and orbital resonances which interact with spins. However, in magnetic systems with zero orbital angular momentum, microscopic pathways for the resonant and low-energy optical excitation of coherent spin dynamics are lacking. Here, we consider experimentally the relative merits of electronic and vibrational excitations for the optical control of zero orbital angular momentum magnets, focusing on a limit case: the antiferromagnet manganese phosphorous trisulfide (MnPS3), constituted by orbital singlet Mn2+ ions. We study the correlation of spins with two types of excitations within its band gap: a bound electron orbital excitation from the singlet orbital ground state of Mn2+ into an orbital triplet state, which causes coherent spin precession, and a vibrational excitation of the crystal field that causes thermal spin disorder. Our findings cast orbital transitions as key targets for magnetic control in insulators constituted by magnetic centers of zero orbital angular momentum.

Two-dimensional magnetic materials with strong magnetostriction are attractive systems for realizing strain-tuning of the magnetization in spintronic and nanomagnetic devices. This requires an understanding of the magneto-mechanical coupling in these materials. In this work, we suspend thin Cr₂Ge₂Te₆ layers and their heterostructures, creating ferromagnetic nanomechanical membrane resonators. We probe their mechanical and magnetic properties as a function of temperature and strain by observing magneto-elastic signatures in the temperature-dependent resonance frequency near the Curie temperature, T_C. We compensate for the negative thermal expansion coefficient of Cr₂Ge₂Te₆ by fabricating heterostructures with thin layers of WSe₂ and antiferromagnetic FePS₃, which have positive thermal expansion coefficients. Thus we demonstrate the possibility of probing multiple magnetic phase transitions in a single heterostructure. Finally, we demonstrate a strain-induced enhancement of T_C in a suspended Cr₂Ge₂Te₆-based heterostructure by 2.5 ± 0.6 K by applying a strain of 0.026% via electrostatic force.

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.

Through rational chemical design, and thanks to the hybrid nature of metal-organic frameworks (MOFs), it is possible to prepare molecule-based 2D magnetic materials stable at ambient conditions. Here, we illustrate the versatility of this approach by changing both the metallic nodes and the ligands in a family of layered MOFs that allows the tuning of their magnetic properties. Specifically, the reaction of benzimidazole-type ligands with different metal centers (MII = Fe, Co, Mn, Zn) in a solvent-free synthesis produces a family of crystalline materials, denoted as MUV-1(M), which order antiferromagnetically with critical temperatures that depend on M. Furthermore, the incorporation of additional substituents in the ligand results in a novel system, denoted as MUV-8, formed by covalently bound magnetic double layers interconnected by van der Waals interactions, a topology that is very rare in the field of 2D materials and unprecedented for 2D magnets. These layered materials are robust enough to be mechanically exfoliated down to a few layers with large lateral dimensions. Finally, the robustness and crystallinity of these layered MOFs allow the fabrication of nanomechanical resonators that can be used to detect-through laser interferometry-the magnetic order in thin layers of these 2D molecule-based antiferromagnets.

Coupled nanomechanical resonators made of two-dimensional materials are promising for processing information with mechanical modes. However, the challenge for these systems is to control the coupling. Here, we demonstrate strong coupling of motion between two suspended membranes of the magnetic 2D material FePS3. We describe a tunable electromechanical mechanism for control over both the resonance frequency and the coupling strength using a gate voltage electrode under each membrane. We show that the coupling can be utilized for transferring data between drums by amplitude modulation. Finally, we also study the temperature dependence of the coupling and how it is affected by the antiferromagnetic phase transition characteristic of this material. The presented electrical coupling of resonant magnetic 2D membranes holds the promise of transferring mechanical energy over a distance at low electrical power, thus enabling novel data readout and information processing technologies.

The charge density wave (CDW) state in van der Waals systems shows interesting scaling phenomena as the number of layers can significantly affect the CDW transition temperature, T_CDW. However, it is often difficult to use conventional methods to study the phase transition in these systems due to their small size and sensitivity to degradation. Degradation is an important parameter, which has been shown to greatly influence the superconductivity in layered systems. Since the CDW state competes with the onset of superconductivity, it is expected that T_CDW will also be affected by the degradation. Here, we probe the CDW phase transition by the mechanical resonances of suspended 2H-TaS₂ and 2H-TaSe₂ membranes and study the effect of disorder on the CDW state. Pristine flakes show the transition near the reported values of 75 K and 122 K, respectively. We then study the effect of degradation on 2H-TaS₂, which displays an enhancement of T_CDW up to 129 K after degradation in ambient air. Finally, we study a sample with local degradation and observe that multiple phase transitions occur at 87 K, 103 K, and 118 K with a hysteresis in temperature in the same membrane. The observed spatial variations in the Raman spectra suggest that variations in crystal structure cause domains with different transition temperatures, which could result in the hysteresis. This work shows the potential of using nanomechanical resonance to characterize the CDW in suspended 2D materials and demonstrates that the degradation can have a large effect on transition temperatures.

Van der Waals magnets provide an ideal playground to explore the fundamentals of low-dimensional magnetism and open opportunities for ultrathin spin-processing devices. The Mermin-Wagner theorem dictates that as in reduced dimensions isotropic spin interactions cannot retain long-range correlations, the long-range spin order is stabilized by magnetic anisotropy. Here, using ultrashort pulses of light, we control magnetic anisotropy in the two-dimensional van der Waals antiferromagnet NiPS₃. Tuning the photon energy in resonance with an orbital transition between crystal field split levels of the nickel ions, we demonstrate the selective activation of a subterahertz magnon mode with markedly two-dimensional behavior. The pump polarization control of the magnon amplitude confirms that the activation is governed by the photoinduced magnetic anisotropy axis emerging in response to photoexcitation of ground state electrons to states with a lower orbital symmetry. Our results establish pumping of orbital resonances as a promising route for manipulating magnetic order in low-dimensional (anti)ferromagnets.

Oxide heterointerfaces constitute a rich platform for realizing novel functionalities in condensed matter. A key aspect is the strong link between structural and electronic properties, which can be modified by interfacing materials with distinct lattice symmetries. Here, we determine the effect of the cubic-tetragonal distortion of SrTiO₃ on the electronic properties of thin films of SrIrO₃, a topological crystalline metal hosting a delicate interplay between spin-orbit coupling and electronic correlations. We demonstrate that below the transition temperature at 105 K, SrIrO₃ orthorhombic domains couple directly to tetragonal domains in SrTiO₃. This forces the in-phase rotational axis to lie in-plane and creates a binary domain structure in the SrIrO₃ film. The close proximity to the metal-insulator transition in ultrathin SrIrO₃ causes the individual domains to have strongly anisotropic transport properties, driven by a reduction of bandwidth along the in-phase axis. The strong structure-property relationships in perovskites make these compounds particularly suitable for static and dynamic coupling at interfaces, providing a promising route towards realizing novel functionalities in oxide heterostructures.

The reduced dimensionality of two-dimensional (2D) materials results in characteristic types of magnetically and electronically ordered phases. However, only few methods are available to study this order, in particular in ultrathin insulating antiferromagnets that couple weakly to magnetic and electronic probes. Here, we demonstrate that phase transitions in thin membranes of 2D antiferromagnetic FePS₃, MnPS₃ and NiPS₃ can be probed mechanically via the temperature-dependent resonance frequency and quality factor. The observed relation between mechanical motion and antiferromagnetic order is shown to be mediated by the specific heat and reveals a strong dependence of the Néel temperature of FePS₃ on electrostatically induced strain. The methodology is not restricted to magnetic order, as we demonstrate by probing an electronic charge-density-wave phase in 2H-TaS₂. It thus offers the potential to characterize phase transitions in a wide variety of materials, including those that are antiferromagnetic, insulating or so thin that conventional bulk characterization methods become unsuitable.

Complex oxide thin films and heterostructures exhibit a variety of electronic phases, often controlled by the mechanical coupling between film and substrate. Recently it has become possible to isolate epitaxially grown single-crystalline layers of these materials, enabling the study of their properties in the absence of interface effects. In this work, we use this technique to create nanomechanical resonators made out of SrTiO₃ and SrRuO₃. Using laser interferometry, we successfully actuate and measure the motion of the nanodrum resonators. By measuring the temperature-dependent mechanical response of the SrTiO₃ resonators, we observe signatures of a structural phase transition, which affects both the strain and mechanical dissipation in the resonators. Here, we demonstrate the feasibility of integrating ultrathin complex oxide membranes for realizing nanoelectromechanical systems on arbitrary substrates and present a novel method of detecting structural phase transitions in these exotic materials.

The high flexibility, impermeability and strength of graphene membranes are key properties that can enable the next generation of nanomechanical sensors. However, for capacitive pressure sensors, the sensitivity offered by a single suspended graphene membrane is too small to compete with commercial sensors. Here, we realize highly sensitive capacitive pressure sensors consisting of arrays of nearly ten thousand small, freestanding double-layer graphene membranes. We fabricate large arrays of small-diameter membranes using a procedure that maintains the superior material and mechanical properties of graphene, even after high-temperature annealing. These sensors are readout using a low-cost battery-powered circuit board, with a responsivity of up to 47.8 aF Pa⁻¹ mm⁻², thereby outperforming the commercial sensors.

Porous, atomically thin graphene membranes have interesting properties for filtration and sieving applications. Here, graphene membranes are used to pump gases through nanopores using optothermal forces, enabling the study of gas flow through nanopores at frequencies above 100 kHz. At these frequencies, the motion of graphene is closely linked to the dynamic gas flow through the nanopore and can thus be used to study gas permeation at the nanoscale. By monitoring the time delay between the actuation force and the membrane mechanical motion, the permeation time-constants of various gases through pores with diameters from 10–400 nm are shown to be significantly different. Thus, a method is presented for differentiating gases based on their molecular mass and for studying gas flow mechanisms. The presented microscopic effusion-based gas sensing methodology provides a nanomechanical alternative for large-scale mass-spectrometry and optical spectrometry based gas characterisation methods.

Despite theoretical predictions that graphene should be impermeable to all gases, practical experiments on sealed graphene nanodrums show small leak rates. Thus far, the exact mechanism for this permeation has remained unclear, because different potential leakage pathways have not been studied separately. Here, we demonstrate a sealing method that consists of depositing SiO₂ across the edge of suspended multilayer graphene flakes using electron beam-induced deposition. By sealing, leakage along the graphene-SiO₂ interface is blocked, which is observed to result in a reduction in permeation rate by a factor of 10⁴. The experiments thus demonstrate that gas flow along the graphene-SiO₂ interface tends to dominate the leak rate in unsealed graphene nanodrums. Moreover, the presented sealing method enables the study of intrinsic gas leakage through graphene membranes and can enable hermetic graphene membranes for pressure sensing applications.