We investigate the dipolar-exchange spin wave spectrum in thin ferromagnetic bilayers with in-plane magnetization, incorporating interlayer exchange coupling and intra- and interlayer dipolar interactions. In the continuum approximation, we analyze the nonreciprocity of propagating magnetic stray fields emitted by spin waves as a function of the relative orientation of the layer magnetizations that are observable by magnetometry of synthetic antiferromagnets or weakly coupled type-A van der Waals antiferromagnetic bilayers as a function of an applied magnetic field.

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.

Surface plasmons are collective electron excitations in metallic systems, and the associated electromagnetic wave usually has the transverse-magnetic polarization. On the other hand, spin waves are spin excitations perpendicular to the equilibrium magnetization and are usually circularly polarized in a ferromagnet. The direct coupling of these two modes is challenging due to the difficulty of matching electromagnetic boundary conditions at the interface of magnetic and nonmagnetic materials. Here, we overcome this challenge by utilizing the linearly polarized spin waves in antiferromagnets (AFM) and show that a strong coupling between AFM magnons and surface plasmons can be realized in a hybrid two-dimensional (2D) material/AFM structure, featuring a clear anticrossing spectrum at resonance. The coupling strength, characterized by the gap of anticrossing at resonance, can be tuned by electric gating on 2D materials and probed by measuring the two reflection minima in the reflection spectrum. Further, as a potential application, we show that plasmonic modes can mediate the coupling of two well-separated AFMs over several micrometers, featuring symmetric and antisymmetric hybrid modes. Our results may open a platform to study antiferromagnetic spintronics and its interplay with plasmonic photonics.

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.

We propose a hybrid quantum system consisting of a magnetic particle inductively coupled to two superconducting transmon qubits, where qubit-qubit interactions are mediated via magnons. We show that the system can be tuned into three different regimes of effective qubit-qubit interactions, namely, a transverse (XX+YY), a longitudinal (ZZ), and a nontrivial ZX interaction. In addition, we show that an enhanced coupling can be achieved by employing an ellipsoidal magnet, carrying anisotropic magnetic fluctuations. We propose a scheme for realizing two-qubit gates, and simulate their performance under realistic experimental conditions. We find that iswap and cz gates can be performed in this setup with an average fidelity ≤99%, while an icnot gate can be applied with an average fidelity ≤88%. Our proposed hybrid circuit architecture offers an alternative platform for realizing two-qubit gates between superconducting qubits and could be employed for constructing qubit networks using magnons as mediators.

Surface plasmons in two-dimensional (2D) electron systems have attracted great attention for their promising light-matter applications. However, the excitation of a surface plasmon, in particular, transverse-electric (TE) surface plasmon, remains an outstanding challenge due to the difficulty to conserve energy and momentum simultaneously in the normal 2D materials. Here we show that the TE surface plasmons ranging from gigahertz to terahertz regime can be effectively excited and manipulated in a hybrid dielectric, 2D material, and magnet structure. The essential physics is that the surface spin wave supplements an additional freedom of surface plasmon excitation and thus greatly enhances the electric field in the 2D medium. Based on widely used magnetic materials like yttrium iron garnet and manganese difluoride, we further show that the plasmon excitation manifests itself as a measurable dip in the reflection spectrum of the hybrid system while the dip position and the dip depth can be well controlled by an electric gating on the 2D layer and an external magnetic field. Our findings should bridge the fields of low-dimensional physics, plasmonics, and spintronics and open a novel route to integrate plasmonic and spintronic devices.

The shot noise in tunneling experiments reflects the Poissonian nature of the tunneling process. The shot-noise power is proportional to both the magnitude of the current and the effective charge of the carrier. Shot-noise spectroscopy thus enables us, in principle, to determine the effective charge q of the charge carriers of that tunnel. This can be used to detect electron pairing in superconductors: In the normal state, the noise corresponds to single electron tunneling (q=1e), while in the paired state, the noise corresponds to q=2e. Here, we use a newly developed amplifier to reveal that in typical mesoscopic superconducting junctions, the shot noise does not reflect the signatures of pairing and instead stays at a level corresponding to q=1e. We show that transparency can control the shot noise, and this q=1e is due to the large number of tunneling channels with each having very low transparency. Our results indicate that in typical mesoscopic superconducting junctions, one should expect q=1e noise and lead to design guidelines for junctions that allow the detection of electron pairing.

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.

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.

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.

Quantum sensing has developed into a main branch of quantum science and technology. It aims at measuring physical quantities with high resolution, sensitivity, and dynamic range. Electron spins in diamond are powerful magnetic field sensors, but their sensitivity in the microwave regime is limited to a narrow band around their resonance frequency. Here, we realize broadband microwave detection using spins in diamond interfaced with a thin-film magnet. A pump field locally converts target microwave signals to the sensor-spin frequency via the non-linear spin-wave dynamics of the magnet. Two complementary conversion protocols enable sensing and high-fidelity spin control over a gigahertz bandwidth, allowing characterization of the spin-wave band at multiple gigahertz above the sensor-spin frequency. The pump-tunable, hybrid diamond-magnet sensor chip opens the way for spin-based gigahertz material characterizations at small magnetic bias fields.

Optical photons are ideal carriers for long-distance transmission, while state-of-the-art quantum processors, such as supercon-ducting qubits, operate at microwave frequencies. An important requirement for networked quantum computation is therefore the ability to coherently convert the quantum information from microwave to optical frequencies and vice-versa. We theoretically address a scheme to achieve this via an intermediate conversion to magnons that enhances the weak direct magneto-optical coupling. We wish to demonstrate the feasibility of such a scheme by employing the magnetoelastic coupling between the modes of a magnetic vortex (vortex breathing mode, VBM) and that of the lattice (elastic breathing mode, EBM), which requires no additional external bias field. In our setup all but the opto-mechanical coupling can be made resonant. We propose an alternative Mumax3 simulation post-processing procedure for semi-classical normalization, where we use regression analysis of the the internal energy dependency on excitation amplitude in a limit cycle motion. We provide estimates for direct resonant coupling between the VBM and the EBM.

We theoretically predict and experimentally observe the onset of weak-link physics in the dynamical response of transition-edge sensors (TESs). We develop a theoretical framework based on a Fokker-Planck description that incorporates both the TESs electrical response, stemming from Josephson phenomena, and the electrothermal effects due to coupling to a thermal bath. Our measurements of a varying dynamic resistance are in excellent agreement with our theory, thereby establishing weak-link phenomena as the main mechanism underlying the operation of TESs. Furthermore, our description enables the calculation of power spectral densities, paving the way for a more thorough investigation of the unexplained "excess noise"in long diffusive junctions and TESs reported in recent experiments.

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.

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.

Superconductors are materials with zero electrical resistivity and the ability to expel magnetic fields, which is known as the Meissner effect. Their dissipationless diamagnetic response is central to magnetic levitation and circuits such as quantum interference devices. In this work, we used superconducting diamagnetism to shape the magnetic environment governing the transport of spin waves-collective spin excitations in magnets that are promising on-chip signal carriers-in a thin-film magnet. Using diamond-based magnetic imaging, we observed hybridized spin-wave-Meissner-current transport modes with strongly altered, temperature-tunable wavelengths and then demonstrated local control of spin-wave refraction using a focused laser. Our results demonstrate the versatility of superconductor-manipulated spin-wave transport and have potential applications in spin-wave gratings, filters, crystals, and cavities.

We discuss spin-wave transport in anisotropic ferromagnets with an emphasis on the zeros of the band edges as a function of a magnetic field. An associated divergence of the magnon spin should be observable by enhanced magnon conductivities in nonlocal configurations, especially in two-dimensional ferromagnets.

We propose a scheme for generating and controlling entangled coherent states (ECSs) of magnons, i.e., the quanta of the collective spin excitations in magnetic systems, or phonons in mechanical resonators. The proposed hybrid circuit architecture comprises a superconducting transmon qubit coupled to a pair of magnonic yttrium iron garnet spherical resonators or mechanical beam resonators via flux-mediated interactions. Specifically, the coupling results from the magnetic/mechanical quantum fluctuations modulating the qubit inductor, formed by a superconducting quantum interference device. We show that the resulting radiation-pressure interaction of the qubit with each mode can be employed to generate maximally entangled states of magnons or phonons. In addition, we numerically demonstrate a protocol for the preparation of magnonic and mechanical Bell states with high fidelity including realistic dissipation mechanisms. Furthermore, we have devised a scheme for reading out the prepared states using standard qubit control and resonator field displacements. In this paper, we demonstrate an alternative platform for quantum information using ECSs in hybrid magnonic and mechanical quantum networks.

Atomically engineered artificial lattices are a useful tool for simulating complex quantum phenomena, but have so far been limited to the study of Hamiltonians where electron-electron interactions do not play a role. However, it is precisely the regime in which these interactions do matter where computational times lend simulations a critical advantage over numerical methods. Here, we propose a platform for constructing artificial matter that relies on the confinement of field-emission resonances, a class of vacuum-localized discretized electronic states. We use atom manipulation of surface vacancies in a chlorine-terminated Cu(100) surface to reveal square patches of the underlying metal, thereby creating atomically precise potential wells that host particle-in-a-box modes. By adjusting the dimensions of the confining potential, we can access states with different quantum numbers, making these patches attractive candidates as quantum dots or artificial atoms. We demonstrate that the lifetime of electrons in these engineered states can be extended and tuned through modification of the confining potential, either via atomic assembly or by changing the tip-sample distance. We also demonstrate control over a finite range of state filling, a parameter which plays a key role in the evolution of quantum many-body states. We model the transport through the localized state to disentangle and quantify the lifetime-limiting processes, illustrating the critical dependence of the electron lifetime on the properties of the underlying bulk band structure. The interplay with the bulk bands gives rise to negative differential resistance, leading to possible applications in engineering custom atomic-scale resonant tunnelling diodes, which exhibit similar current-voltage characteristics.