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.

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.

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.

Ultrafast scanning electron microscopy images carrier dynamics and carrier induced surface voltages using a laser pump electron probe scheme, potentially surpassing all-optical techniques in probe resolution and surface sensitivity. Current implementations have left a four order of magnitude gap between optical pump and electron probe resolution, which particularly hampers spatial resolution in the investigation of carrier induced local surface photovoltages. Here, we present a system capable of focusing the laser using an inverted optical microscope built into an ultrafast scanning electron microscopy setup to enable high numerical aperture pulsed optical excitation in conjunction with ultrafast electron beam probing. We demonstrate an order of magnitude improvement in optical pump resolution, bringing this to sub-micrometer length scales. We further show that temporal laser pump resolution can be maintained inside the scanning electron microscope by pre-compensating dispersion induced by the components required to bring the beam into the vacuum chamber and to a tight focus. We illustrate our approach using molybdenum disulfide, a two-dimensional transition metal dichalcogenide, where we measure ultrafast carrier relaxation rates and induced negative surface potentials between different flakes selected with the scanning electron microscope as well as on defined positions within a single flake.

Although 2D materials hold great potential for next-generation pressure sensors, recent studies revealed that gases permeate along the membrane-surface interface, necessitating additional sealing procedures. In this work, we demonstrate the use of free-standing complex oxides as self-sealing membranes that allow the reference cavity beneath to be sealed by a simple anneal. To test the hermeticity, we study the gas permeation time constants in nanomechanical resonators made from SrRuO3 and SrTiO3 membranes suspended over SiO2/Si cavities which show an improvement up to 4 orders of magnitude in the permeation time constant after annealing the devices. Similar devices fabricated on Si3N4/Si do not show such improvements, suggesting that the adhesion increase over SiO2 is mediated by oxygen bonds that are formed at the SiO2/complex oxide interface during the self-sealing anneal. Picosecond ultrasonics measurements confirm the improvement in the adhesion by 70% after annealing.

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.

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.

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.

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.

Paper holds the promise to replace silicon substrates in applications like internet of things or disposable electronics that require ultra-low-cost electronic components and an environmentally friendly electronic waste management. In the last years, spurred by the abovementioned properties of paper as a substrate and the exceptional electronic, mechanical and optical properties of van der Waals (vdW) materials, many research groups have worked towards the integration of vdW materials-based devices on paper. Recently, a method to deposit a continuous film of densely packed interconnects of vdW materials on paper by simply rubbing the vdW crystals against the rough surface of paper has been presented. This method utilizes the weak interlayer vdW interactions and allows cleaving of the crystals into micro platelets through the abrasion against the paper. Here, we aim to illustrate the general character and the potential of this technique by fabricating films of 39 different vdW materials (including superconductors, semi-metals, semiconductors, and insulators) on standard copy paper. We have thoroughly characterized their optical properties showing their high optical quality: one can easily resolve the absorption band edge of semiconducting vdW materials and even the excitonic features present in some vdW materials with high exciton binding energy. We also measured the electrical resistivity for several vdW materials films on paper finding exceptionally low values, which are in some cases, orders of magnitude lower than those reported for analogous films produced by inkjet printing. We finally demonstrate the fabrication of field-effect devices with vdW materials on paper using the paper substrate as an ionic gate.

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.

Paper has the potential to dramatically reduce the cost of electronic components. In fact, paper is 10 000 times cheaper than crystalline silicon, motivating the research to integrate electronic materials on paper substrates. Among the different electronic materials, van der Waals materials are attracting the interest of the scientific community working on paper-based electronics because of the combination of high electrical performance and mechanical flexibility. Up to now, different methods have been developed to pattern conducting, semiconducting and insulating van der Waals materials on paper but the integration of superconductors remains elusive. Here, the deposition of NbSe2, an illustrative van der Waals superconductor, on standard copy paper is demonstrated. The deposited NbSe2 films on paper display superconducting properties (e.g. observation of Meissner effect and resistance drop to zero-resistance state when cooled down below its critical temperature) similar to those of bulk NbSe2.

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.

Graphene quantum dots (QDs) are intensively studied as platforms for the next generation of quantum electronic devices. Fine tuning of the transport properties in monolayer graphene QDs, in particular with respect to the independent modulation of the tunnel barrier transparencies, remains challenging and is typically addressed using electrostatic gating. We investigate charge transport in back-gated graphene mechanical break junctions and reveal Coulomb blockade physics characteristic of a single, high-quality QD when a nanogap is opened in a graphene constriction. By mechanically controlling the distance across the newly formed graphene nanogap, we achieve reversible tunability of the tunnel coupling to the drain electrode by 5 orders of magnitude, while keeping the source-QD tunnel coupling constant. The break junction device can therefore become a powerful platform to study the physical parameters that are crucial to the development of future graphene-based devices, including energy converters and quantum calorimeters.

We fabricate paper-supported semiconducting devices by rubbing a layered molybdenum disulfide (MoS2) crystal onto a piece of paper, similar to the action of drawing/writing with a pencil on paper. We show that the abrasion between the MoS2 crystal and the paper substrate efficiently exfoliates the crystals, breaking the weak van der Waals interlayer bonds and leading to the deposition of a film of interconnected MoS2 platelets. Employing this simple method, which can be easily extended to other 2D materials, we fabricate MoS2-on-paper broadband photodetectors with spectral sensitivity from the ultraviolet (UV) to the near-infrared (NIR) range. We also used these paper-based photodetectors to acquire pictures of objects by mounting the photodetectors in a homebuilt single-pixel camera setup.

We report the Raman spectroscopy of C12/C13 graphene isotope superlattices (SLs) synthesized by chemical vapor deposition. At large periods the Raman spectrum corresponds to the sum of the bulk C12 and C13 contributions. However, at small periods we observe the formation of mixed C12/C13 modes for Raman processes that involve two phonons, which results in the tripling of the 2D and 2D′ Raman peaks. This tripling can be well understood in the framework of real-space Raman spectroscopy, where the two emitted phonons stem from different regions of the SL. The intensity of the mixed peak increases as the SL half-period approaches the mean free path of the photoexcited electron-hole pairs. By varying the SL period between 6 and 225 nm we have a direct measure of the photoexcited electron mean free path, which is found to be 18 nm for suspended graphene and 7 nm for graphene on SiO2 substrates.

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.

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.