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.

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.

Particle exchange heat engines are a novel class of cyclic heat engines that are all-electrical, contain no moving parts and can therefore be scaled down to nanometer size. At the center of their operation is the manipulation of a particle flow between a hot and a cold reservoir through energy filtering mechanisms, where their efficiency depends primarily on the sharpness of the energy filter. In this study, we investigate the efficiency enhancement of such engines by utilizing ultra-sharp transmission resonances formed by magnetic impurities interacting with superconductors, known as Yu-Shiba-Rusinov bound states. To this end, we couple a neutral and stable diradical molecule to superconducting break-junction electrodes, and study its thermoelectric properties at ultra-low temperatures. By driving the molecular heat engine through a phase transition from a Kondo state into the Yu-Shiba-Rusinov regime, we observe a five fold increase in the thermoelectric power factor. This observation could pave the way for practical applications such as cryogenic waste heat recovery and efficient spot-cooling for future quantum computing architectures.

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.

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.

Biotite crystals are phyllosilicate trioctahedral micas with the general chemical formula K(Mg,Fe)₃AlSi₃O₁₀(OH)₂ that form a solid-solution series with iron-poor phlogopite and iron-rich annite endmembers. With a wide band gap energy and a layered structure with free surface charges, biotite nanosheets can be readily obtained by cleavage methods and used as dielectrics in nanodevice fabrication for the next generation of electronics and energy harvesting. Here, a comprehensive study of biotite samples with different iron concentrations and oxidation states is presented. Structural, optical, magneto-optical, and magnetic characterizations were performed using several experimental techniques, including state-of-the-art synchrotron-based techniques, to correlate the iron chemistry (content and oxidation state) with the macroscopic properties of both minerals. The study reveals a nanoscale-homogeneous Fe distribution via synchrotron X-ray fluorescence mapping, defect-mediated optical transitions modulated by Fe³⁺/Fe²⁺ ratios, and temperature-dependent magnetic transitions from paramagnetism to competing ferro−/antiferromagnetic interactions. Furthermore, the use of these biotite crystals as substrates for ultrathin heterostructures incorporating monolayer (ML) MoSe₂ is explored by magneto photoluminescence at cryogenic temperatures. The results show that the presence of iron impurities in different oxidation states significantly impacts the valley properties for ML-MoSe₂. Overall, these findings offer a comprehensive interpretation of the physical properties of bulk biotites in a correlative approach, serving as a robust reference for future studies aiming to explore biotites in their ultrathin form.

Organic radicals are promising candidates for molecular spintronics due to their intrinsic magnetic moment, their low spin-orbit coupling, and their weak hyperfine interactions. Using a mechanically controlled break junction setup at both room and low temperatures (6 K), we analyze the difference in charge transport between two nitronyl nitroxide radicals (NNR): one with a backbone in the para configuration, the other with a backbone in the meta configuration. We find that para-NNR displays a Kondo resonance at 6 K, while meta-NNR does not. Additionally, the observed Kondo peak in the differential conductance has a roughly constant width independent of the conductance, consistent with a scenario where the molecule is coupled asymmetrically to the electrodes.

van der Waals heterostructures (vdWHs) composed of transition-metal dichalcogenides (TMDs) and layered magnetic semiconductors offer great opportunities to manipulate the exciton and valley properties of TMDs. Here, we present magneto-photoluminescence (PL) studies in a WSe₂monolayer (ML) on a CrSBr crystal, an anisotropic layered antiferromagnetic semiconductor. Our results reveal the unique behavior of each of the ML-WSe₂PL peaks under a magnetic field that is distinct from the pristine case. An intriguing feature is the clear enhancement of the PL intensity that we observe each time the external magnetic field tunes the energy of an exciton in CrSBr into resonance with one of the optical states of WSe₂. This result suggests a magnetic field-controlled resonant energy transfer (RET) beyond other effects reported in similar structures. Our work provides deep insight into the importance of different mechanisms in magnetic vdWHs and underscores its great potential for light harvesting and emission enhancement of two-dimensional materials.

Graphene has garnered significant interest in optoelectronics due to its unique properties, including broad wavelength absorption and high mobility. However, its weak stability in ambient conditions requires encapsulation for practical applications. In this study, we investigate graphene CVD-grown field-effect transistors fabricated on Si/SiO2 wafers, encapsulated with aluminum oxide (Al2O3) of different thicknesses. We measure and analyze their optoelectronic response across wavelengths from near-ultraviolet to near-infrared. We find that, while having a negligible role in the photogating process, the Al2O3 layer leads to stable and reproducible transferring curves operating in ambient conditions for over a month, with stable responsivities up to 1.5 A W−1 at the shortest wavelength. Moreover, the transferring curves are stable at elevated temperatures up to 107 ∘C. We also show that the sample performance can be tuned by changing the thickness of the SiO2 and Al2O3 layer which brings further perspectives in developing robust sample technologies, especially in the ultraviolet region where the responsivity increases. Aluminum oxide encapsulated graphene-based photodetectors can thus be interesting for applications in air and at elevated temperatures.

A promising approach to attain long-distance coherent spin propagation is accessing topological spin-polarized edge states in graphene. Achieving this without external magnetic fields necessitates engineering graphene band structure, obtainable through proximity effects in van der Waals heterostructures. In particular, proximity-induced staggered potentials and spin-orbit coupling are expected to form a topological bulk gap in graphene with gapless helical edge states that are robust against disorder. In this work, we detect the spin-polarized helical edge transport in graphene at zero external magnetic field, allowed by the proximity of an interlayer antiferromagnet, CrPS4. We show the coexistence of the quantum spin Hall (QSH) states and magnetism in graphene, where the induced spin-orbit and exchange couplings also give rise to a large anomalous Hall (AH) effect. The detection of the QSH states at zero external magnetic field, together with the AH signal that persists up to room temperature, opens the route for practical applications of magnetic graphene in quantum spintronic circuitries.

Helical molecules have been proposed as candidates for producing spin-polarized currents, even at room conditions, due to their chiral asymmetry. However, describing their transport mechanism in single molecular junctions is not straightforward. In this work, we show the synthesis of two novel kinds of dithia[11]helicenes to study their electronic transport in break junctions among a series of three helical molecules: dithia[n]helicenes, with n = 7, 9, and 11 molecular units. Our experimental measurements and clustering-based analysis demonstrate low conductance values that remain similar across different applied voltages and molecules. Additionally, we assess the length dependence of the conductance for each helicene, revealing an exponential decay characteristic of off-resonant transport. This behavior is primarily attributed to the misalignment between the energy levels of the molecule-electrodes system. The length dependence trend described above is supported by ab initio calculations, further confirming an off-resonant transport mechanism.

The high susceptibility of ultrathin two-dimensional (2D) material resonators to force and temperature makes them ideal systems for sensing applications and exploring thermomechanical coupling. Although the dynamics of these systems at high stress has been thoroughly investigated, their behavior near the buckling transition has received less attention. Here, we demonstrate that the force sensitivity and frequency tunability of 2D material resonators are significantly enhanced near the buckling bifurcation. This bifurcation is triggered by compressive displacement that we induce via thermal expansion of the devices, while measuring their dynamics via an optomechanical technique. We understand the frequency tuning of the devices through a mechanical buckling model, which allows to extract the central deflection and boundary compressive displacement of the membrane. Surprisingly, we obtain a remarkable enhancement of up to 14× the vibration amplitude attributed to a very low stiffness of the membrane at the buckling transition, as well as a high frequency tunability by temperature of more than 4.02$\%$ K−1. The presented results provide insights into the effects of buckling on the dynamics of free-standing 2D materials and thereby open up opportunities for the realization of 2D resonant sensors with buckling-enhanced sensitivity.

Heat-to-charge conversion efficiency of thermoelectric materials is closely linked to the entropy per charge carrier. Thus, magnetic materials are promising building blocks for highly efficient energy harvesters as their carrier entropy is boosted by a spin degree of freedom. In this work, we investigate how this spin-entropy impacts heat-to-charge conversion in the A-type antiferromagnet CrSBr. We perform simultaneous measurements of electrical conductance and thermocurrent while changing magnetic order using the temperature and magnetic field as tuning parameters. We find a strong enhancement of the thermoelectric power factor at around the Néel temperature. We further reveal that the power factor at low temperatures can be increased by up to 600% upon applying a magnetic field. Our results demonstrate that the thermoelectric properties of 2D magnets can be optimized by exploiting the sizable impact of spin-entropy and confirm thermoelectric measurements as a sensitive tool to investigate subtle magnetic phase transitions in low-dimensional magnets.

Multicellular cable bacteria display an exceptional form of biological conduction, channeling electric currents across centimeter distances through a regular network of protein fibers embedded in the cell envelope. The fiber conductivity is among the highest recorded for biomaterials, but the underlying mechanism of electron transport remains elusive. Here, we performed detailed characterization of the conductance from room temperature down to liquid helium temperature to attain insight into the mechanism of long-range conduction. A consistent behavior is seen within and across individual filaments. The conductance near room temperature reveals thermally activated behavior, yet with a low activation energy. At cryogenic temperatures, the conductance at moderate electric fields becomes virtually independent of temperature, suggesting that quantum vibrations couple to the charge transport through nuclear tunneling. Our data support an incoherent multistep hopping model within parallel conduction channels with a low activation energy and high transfer efficiency between hopping sites. This model explains the capacity of cable bacteria to transport electrons across centimeter-scale distances, thus illustrating how electric currents can be guided through extremely long supramolecular protein structures.

The addition of a lateral alkyl chain is a well-known strategy to reduce π-stacked ensembles of molecules in solution, with the intention to minimize the interactions between the molecules’ backbones. In this paper, we study whether this concept generalizes to single-molecule junctions by using a combination of mechanically controllable break junction (MCBJ) measurements and clustering-based data analysis with two small series of model compounds decorated with various bulky groups. The systematic study suggests that introducing alkyl side chains also favors the formation of electrode-molecule configurations that are not observed in their absence, thereby inducing broadening of the conductance peak in the one-dimensional histograms. Thus, the introduction of alkyl chains in aromatic compounds for molecular electronics must be carefully designed and optimized for the specific purpose, balancing between increased solubility and the possibility of additional junction configurations.

Heat transport in two dimensions is fundamentally different from that in three dimensions. As a consequence, the thermal properties of 2D materials are of great interest, from both scientific and application points of view. However, few techniques are available for the accurate determination of these properties in ultrathin suspended membranes. Here, we present an optomechanical methodology for extracting the thermal expansion coefficient, specific heat, and thermal conductivity of ultrathin membranes made of 2H-TaS₂, FePS₃, polycrystalline silicon, MoS₂, and WSe₂. The obtained thermal properties are in good agreement with the values reported in the literature for the same materials. Our work provides an optomechanical method for determining the thermal properties of ultrathin suspended membranes, which are difficult to measure otherwise. It provides a route toward improving our understanding of heat transport in the 2D limit and facilitates engineering of 2D structures with a dedicated thermal performance.

Open-shell polycyclic aromatic hydrocarbons (PAHs) represent promising building blocks for carbon-based functional magnetic materials. Their magnetic properties stem from the presence of unpaired electrons localized in radical states of π character. Consequently, these materials are inclined to exhibit spin delocalization, form extended collective states, and respond to the flexibility of the molecular backbones. However, they are also highly reactive, requiring structural strategies to protect the radical states from reacting with the environment. Here, we demonstrate that the open-shell ground state of the diradical 2-OS survives on a Au(111) substrate as a global singlet formed by two unpaired electrons with antiparallel spins coupled through a conformational-dependent interaction. The 2-OS molecule is a “protected” derivative of the Chichibabin’s diradical, featuring a nonplanar geometry that destabilizes the closed-shell quinoidal structure. Using scanning tunneling microscopy (STM), we localized the two interacting spins at the molecular edges, and detected an excited triplet state a few millielectronvolts above the singlet ground state. Mean-field Hubbard simulations reveal that the exchange coupling between the two spins strongly depends on the torsional angles between the different molecular moieties, suggesting the possibility of influencing the molecule’s magnetic state through structural changes. This was demonstrated here using the STM tip to manipulate the molecular conformation, while simultaneously detecting changes in the spin excitation spectrum. Our work suggests the potential of these PAHs as all-carbon spin-crossover materials.

Quantum interference plays an important role in charge transport through single-molecule junctions, even at room temperature. Of special interest is the measurement of the destructive quantum interference dip itself. Such measurements are especially demanding when performed in a continuous mode of operation. Here, we use mechanical modulation experiments at ambient conditions to reconstruct the destructive quantum interference dip of conductance versus displacement. Simultaneous measurements of the Seebeck coefficient show a sinusoidal response across the dip without sign change. Calculations that include electrode distance and energy alignment variations explain both observations quantitatively, emphasizing the crucial role of thermal fluctuations for measurements under ambient conditions. Our results open the way for establishing a closer link between break-junction experiments and theory in explaining single-molecule transport phenomena, especially when describing sharp features in the transmission.

The recent discovery of cable bacteria has greatly expanded the known length scale of biological electron transport, as these multi-cellular bacteria are capable of mediating electrical currents across centimeter-scale distances. To enable such long-range conduction, cable bacteria embed a network of regularly spaced, parallel protein fibers in their cell envelope. These fibers exhibit extraordinary electrical properties for a biological material, including an electrical conductivity that can exceed 100 S cm ⁻¹. Traditionally, long-range electron transport through proteins is described as a multi-step hopping process, in which the individual hopping steps are described by Marcus electron transport theory. Here, we investigate to what extent such a classical hopping model can explain the conductance data recorded for individual cable bacterium filaments. To this end, the conductive fiber network in cable bacteria is modelled as a set of parallel one-dimensional hopping chains. Comparison of model simulated and experimental current(I)/voltage(V) curves, reveals that the charge transport is field-driven rather than concentration-driven, and there is no significant injection barrier between electrodes and filaments. However, the observed high conductivity levels (>100 S cm ⁻¹) can only be reproduced, if we include much longer hopping distances (a > 10 nm) and lower reorganisation energies (λ < 0.2 eV) than conventionally used in electron relay models of protein structures. Overall, our model analysis suggests that the conduction mechanism in cable bacteria is markedly distinct from other known forms of long-range biological electron transport, such as in multi-heme cytochromes.