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Magnomechanical systems provide a promising route for exploring coherent hybrid magnon-phonon interactions and hybrid information processing, but their realization has so far been limited by weak magnon-phonon coupling in conventional bulk platforms. We show that a suspended membrane of a two-dimensional van der Waals ferromagnet with in-plane magnetization and out-of-plane mechanical oscillations exhibits large magnomechanical coupling dominated by magnetoelastic interactions. The parametric single magnon-phonon coupling rate scales linearly with pre-strain and can reach hundreds of Hertz to low kiloHertz in suspended membranes of van der Waals ferromagnets such as CrGeTe_3 under experimentally realistic conditions. This rate exceeds typical values reported for YIG spheres by more than three orders of magnitude. Our results demonstrate that suspended membranes of van der Waals magnets provide a robust and highly tunable platform for magnomechanics.
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-plan
Achieving magnon-photon hybridization in the microwave regime is essential for integrating magnetic excitations with superconducting circuits. While this has been extensively demonstrated in bulk magnetic systems, realizing it in two-dimensional van der Waals materials remains challenging due to their reduced magnetic volume and increased dissipation. Here, magnon-photon hybridization is observed in exfoliated flakes of the van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$, with thicknesses down to 30 nm. The resulting magnon polaritons-hybrid excitations of cavity photons and magnons-are evidenced by reproducible avoided crossings across six devices, enabled by a low-impedance superconducting resonator design. The coupling strength follows the expected square-root dependence on thickness, and extrapolation of this scaling indicates that hybridization in the monolayer limit is within reach.
We combine polarized infrared magneto-transmission and Faraday angle rotation measurements to map the collective excitations of the van der Waals antiferromagnet FePS$_3$. Below the Néel temperature ($T_\mathrm{N} \approx 118~\mathrm{K}$), the phonon spectrum becomes strongly anisotropic, reflecting the underlying zigzag antiferromagnetic order. In contrast, a prominent excitation at $122~\mathrm{cm}^{-1}$ ($15$~meV) is polarization-independent, hardens on cooling, and splits linearly with magnetic field, identifying its magnetic origin. From absolute transmission and Faraday rotation, we reconstruct the circular optical conductivities and reveal a pronounced dichroism of the field-split excitations. The upper branch near $129~\mathrm{cm}^{-1}$ exhibits a reduced dichroic response, consistent with hybridization with a nearby infrared phonon. Several phonon modes exhibit sizable Faraday rotation, providing evidence for spin-phonon coupling and demonstrating that lattice vibrations acquire magnetic-field-dependent optical activity. In addition, additional excitations appear in the infrared spectra and a broad mid-infrared feature near $900~\mathrm{cm}^{-1}$ emerges only below $T_\mat
Charged domain walls (CDW) in ferroelectrics are emerging as functional interfaces with potential applications in nonvolatile memory, logic, and neuromorphic computing. However, CDWs in conventional ferroelectrics are vertical, buried, or electrically inaccessible interfaces that prevent their use in functional devices. Here, we overcome these challenges by stacking two opposite polar domains of van der Waals ferroelectric $α$-In$_2$Se$_3$ to generate artificial head-head (H-H) CDWs and use edge contact to fabricate charged domain wall-based field-effect transistors (CDW-FET). We relate the atomic structure to the temperature-dependent electrical and magneto-transport of the CDW-FET. CDW-FETs exhibit a metal-to-insulator transition with decreasing temperature and enhanced conductance and field-effect mobility compared to single domain $α$-In$_2$Se$_3$. We identify two regimes of transport: variable range hopping due to disorder in the band edge below 70 K and thermally activated interfacial trap-assisted transport above 70 K. The CDW-FETs show room-temperature resistance down to 3.1 k$Ω$ which is 2-9 orders of magnitude smaller than the single CDW in thin-film ferroelectrics. These
Here, we use atomic resolution scanning transmission electron microscopy (STEM) and first principles calculations to study the atomic and electronic structure of strongly charged domain walls in $α$-In$_2$Se$_3$. STEM imaging and density functional theory (DFT) show that head-to-head (HH) domain walls contain a layer of nonpolar $β$-In$_2$Se$_3$, whereas tail-to-tail (TT) domain walls are atomically abrupt. We apply 4D STEM and multislice electron ptychography to map ferroelectric domains in 2D and 3D, showing that nearly $180^\circ$ domain walls exhibit complex, curved 3D structures that differ from ideal $180^\circ$ structures. Band structure calculations show localized conducting states within a $\sim$ 1 nm thick layer at both HH and TT domain walls, such as a midgap state at the $β$ layer of the HH domain wall. These properties make strongly charged domain walls in $α$-In$_2$Se$_3$ excellent candidates for realizing 2D electron or hole gases and domain wall engineering in van der Waals ferroelectrics.
Conventional deep learning models embed data in Euclidean space $\mathbb{R}^d$, a poor fit for strictly hierarchical objects such as taxa, word senses, or file systems. We introduce van der Put Neural Networks (v-PuNNs), the first architecture whose neurons are characteristic functions of p-adic balls in $\mathbb{Z}_p$. Under our Transparent Ultrametric Representation Learning (TURL) principle every weight is itself a p-adic number, giving exact subtree semantics. A new Finite Hierarchical Approximation Theorem shows that a depth-K v-PuNN with $\sum_{j=0}^{K-1}p^{\,j}$ neurons universally represents any K-level tree. Because gradients vanish in this discrete space, we propose Valuation-Adaptive Perturbation Optimization (VAPO), with a fast deterministic variant (HiPaN-DS) and a moment-based one (HiPaN / Adam-VAPO). On three canonical benchmarks our CPU-only implementation sets new state-of-the-art: WordNet nouns (52,427 leaves) 99.96% leaf accuracy in 16 min; GO molecular-function 96.9% leaf / 100% root in 50 s; NCBI Mammalia Spearman $ρ= -0.96$ with true taxonomic distance. The learned metric is perfectly ultrametric (zero triangle violations), and its fractal and information-theo
For the development of nanoscale electronics and photonics using atomically thin two-dimensional (2D) materials, it is important to realize van der Waals (vdW) interfaces with low thermal resistance, to minimize performance reduction caused by heat accumulation. However, characterizing the thermal interface resistance between vdW materials is still a challenge. Here, we introduce a novel optomechanical methodology to characterize the thermal transport across interfaces in 2D heterostructures. We first determine the specific heat and thermal conductivity as the function of temperature for the upper and lower material layers separately and then extract the thermal boundary conductance (TBC) of the heterostructure from its thermal time constant. We obtain a TBC of $2.41 \pm 1.03$ and $4.14 \pm 1.74$~\si{MW m^{2} K^{-1}} for FePS$_3$/WSe$_2$ and MoS$_2$/FePS$_3$ interfaces, respectively, which are comparable to values reported in the literature. Moreover, they agree with a Debye model including the acoustic impedance mismatch of flexural phonons. This work enables efficient thermal management down to the nanoscale and offers new insights into energy dissipation in vdW heterostructures.
Spintronics is concerned with replacing charge current with current of spin, the electron's intrinsic angular momentum. In magnetic insulators, spin currents are carried by magnons, the quanta of spin-wave excitations on top of the magnetically ordered state. Magnon spin currents are especially promising for information technology due to their low intrinsic damping, non-reciprocal transport, micrometer wavelengths at microwave frequencies, and strong interactions that enable signal transduction. In this perspective, we give our view on the progress and challenges towards realizing magnon spintronics based on atomically thin Van der Waals magnets, a recently discovered class of magnetic materials of which the tunability and versatility has attracted a great deal of ongoing research.
The layered metamagnet CrSBr offers a rich interplay between magnetic, optical and electrical properties that can be extended down to the two-dimensional (2D) limit. Despite the extensive research regarding the long-range magnetic order in magnetic van der Waals materials, short-range correlations have been loosely investigated. By using Small-Angle Neutron Scattering (SANS) we show the formation of short-range magnetic regions in CrSBr with correlation lengths that increase upon cooling up to ca. 3 nm at the antiferromagnetic ordering temperature (TN ~ 140 K). Interestingly, these ferromagnetic correlations start developing below 200 K, i.e., well above TN. Below TN, these correlations rapidly decrease and are negligible at low-temperatures. The experimental results are well-reproduced by an effective spin Hamiltonian, which pinpoints that the short-range correlations in CrSBr are intrinsic to the monolayer limit, and discard the appearance of any frustrated phase in CrSBr at low-temperatures within our experimental window between 2 and 200 nm. Overall, our results are compatible with a spin freezing scenario of the magnetic fluctuations in CrSBr and highlight SANS as a powerful t
Given a split simply connected and connected algebraic group scheme $\mathbb G$ over $\mathbb Z$ and a split parabolic subgroup scheme $\mathbb P\subset \mathbb G$, this paper constructs semi-orthogonal decompositions of the bounded derived category $D^b(\mathrm {rep}( \mathbb P))$ of noetherian representations of $\mathbb P$ with each semi-orthogonal component being equivalent to the bounded derived category $D^b(\mathrm {rep}( \mathbb G))$ of noetherian representations of $\mathbb G$. The semi-orthogonal components of those decompositions are stable under the monoidal action of $D^b(\mathrm {rep}( \mathbb G))$ on $D^b(\mathrm {rep}( \mathbb P))$. The decompositions depend on an arbitrarily chosen total order on the Weyl group that refines the Bruhat order. The semi-orthogonal decompositions are also compatible with the Bruhat order on cosets of the Weyl group of $\mathbb P$ in the Weyl group of $\mathbb G$. Their construction builds upon the foundational results on $\mathbb B$-modules from the works of Mathieu, Polo, and van der Kallen, and upon properties of the Steinberg basis of the $ \mathbb T$-equivariant $K$-theory of $ \mathbb G/\mathbb B$. As a corollary, we obtain full e
Polarization dependent x-ray absorption spectroscopy was used to study the magnetic ground state and the orbital occupation in bulk-phase VI$_3$ van der Waals crystals below and above the ferromagnetic and structural transitions. X-ray natural linear dichroism and X-ray magnetic circular dichroism spectra acquired at the V $L_{2,3}$ edges are compared against multiplet cluster calculations within the frame of the ligand field theory to quantify the intra-atomic electronic interactions at play and evaluate the effects of symmetry reduction occurring in a trigonally distorted VI$_6$ unit. We observed a non zero linear dichroism proving the presence of an anisotropic charge density distribution around the V$^{3+}$ ion due to the unbalanced hybridization between the Vanadium and the ligand states. Such hybridization acts as an effective trigonal crystal field, slightly lifting the degeneracy of the $t_{2g}^2$ ground state. However, the energy splitting associated to the distortion underestimates the experimental band gap, suggesting that the insulating ground state is stabilized by Mott correlation effects rather than via a Jahn-Teller mechanism. Our results clarify the role of the dis
We study the complexity of satisfiability problems in probabilistic and causal reasoning. Given random variables $X_1, X_2,\ldots$ over finite domains, the basic terms are probabilities of propositional formulas over atomic events $X_i = x_i$, such as $P(X_1 = x_1)$ or $P(X_1 = x_1 \vee X_2 = x_2)$. The basic terms can be combined using addition (yielding linear terms) or multiplication (polynomial terms). The probabilistic satisfiability problem asks whether a joint probability distribution satisfies a Boolean combination of (in)equalities over such terms. Fagin et al. (1990) showed that for basic and linear terms, this problem is NP-complete, making it no harder than Boolean satisfiability, while Mossé et al. (2022) proved that for polynomial terms, it is complete for the existential theory of the reals. Pearl's Causal Hierarchy (PCH) extends the probabilistic setting with interventional and counterfactual reasoning, enriching the expressiveness of languages. However, Mossé et al. (2022) found that satisfiability complexity remains unchanged. Van der Zander et al. (2023) showed that introducing a marginalization operator to languages induces a significant increase in complexity.
Van der Waals materials provide a versatile toolbox for the emergence of new quantum phenomena and the fabrication of functional heterostructures. Among them, the trihalide VI3 stands out for its unique magnetic and structural landscape. Here we investigate the spin and orbital magnetic degrees of freedom in the layered ferromagnet VI3 by means of temperature-dependent x-ray absorption spectroscopy and x-ray magnetic circular and linear dichroism. We detect localized electronic states and reduced magnetic dimensionality, due to electronic correlations. We furthermore provide experimental evidence of (a) an unquenched orbital magnetic moment (up to 0.66(7)) in the ferromagnetic state, and (b) an instability of the orbital moment in proximity of the spin reorientation transition. Our results support a coherent picture where electronic correlations give rise to a strong magnetic anisotropy and a large orbital moment, and establish VI3 as a prime candidate for the study of orbital quantum effects.
The Fréchet distance is a distance measure between trajectories in $\Bbb{R}^d$ or walks in a graph $G$. Given constant-time shortest path queries, the Discrete Fréchet distance $D_G(P, Q)$ between two walks $P$ and $Q$ can be computed in $O(|P| \cdot |Q|)$ time using a dynamic program. Driemel, van der Hoog, and Rotenberg [SoCG'22] show that for weighted planar graphs this approach is likely tight, as there can be no strongly-subquadratic algorithm to compute a $1.01$-approximation of $D_G(P, Q)$ unless the Orthogonal Vector Hypothesis (OVH) fails. Such quadratic-time conditional lower bounds are common to many Fréchet distance variants. However, they can be circumvented by assuming that the input comes from some well-behaved class: There exist $(1+\varepsilon)$-approximations, both in weighted graphs and in $\Bbb{R}^d$, that take near-linear time for $c$-packed or $κ$-straight walks in the graph. In $\Bbb{R}^d$ there also exists a near-linear time algorithm to compute the Fréchet distance whenever all input edges are long compared to the distance. We consider computing the Fréchet distance in unweighted planar graphs. We show that there exist no strongly-subquadratic $1.25$-approx
This activity was created within the framework of the "Space for Education" project, which ams at experiencing physical principles on the basis of topics related to space travel. It enables the students to investigate the power supply of the International Space Station. If available, they determine the current parameters of the electrical system from the telemetry of the ISS in real time. Otherwise, they can use archive data attached to the working documents. From this, they calculate the electrical power provided by the solar cells. Additional materials at: https://www.haus-der-astronomie.de/raum-fuer-bildung ----- Diese Aktivität wurde im Rahmen des Projekts "Raum für Bildung" erstellt, welches physikalische Prinzipien anhand der Raumfahrt erlebbar macht. Sie ermöglicht den Schülerinnen und Schülern, die Stromversorgung der Internationalen Raumstation zu untersuchen. Falls vorhanden, ermitteln sie die augenblicklichen Parameter des elektrischen Systems aus der Telemetrie der ISS in Echtzeit. Ansonsten können sie Archivdaten nutzen, die den Arbeitsunterlagen beigefügt sind. Hieraus berechnen sie die von den Solarzellen zur Verfügung gestellte elektrische Leistung. Weitere Material
This activity was created within the framework of the "Space for Education" project, which ams at experiencing physical principles on the basis of topics related to space travel. Artificial satellites are suitable as application-oriented examples to explain the effect of gravity on their orbits. This working material deals with the orbit of the International Space Station (ISS) around the Earth. In simple calculations and representations, the students learn how the orbits of artificial satellites are created and which characteristic velocities occur. They compare their ISS results with those of geostationary satellites and discover applications of this particular orbit. Additional materials at: https://www.haus-der-astronomie.de/raum-fuer-bildung ----- Diese Aktivität wurde im Rahmen des Projekts "Raum für Bildung" erstellt, welches physikalische Prinzipien anhand der Raumfahrt erlebbar macht. Künstliche Satelliten eignen sich als anwendungsnahe Beispiele, um die Wirkung der Gravitation auf ihre Bahn näher zu erläutern. Dieses Arbeitsmaterial behandelt dazu exemplarisch den Orbit der Internationalen Raumstation (ISS) um die Erde. In einfachen Rechnungen und Darstellungen erfahren d
Magnetic van der Waals materials provide an ideal playground for exploring the fundamentals of low-dimensional magnetism and open new 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 order is stabilized by magnetic anisotropy. Here, using ultrashort pulses of light, we demonstrate all-optical control of magnetic anisotropy in the two-dimensional van der Waals antiferromagnet NiPS$_3$. 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 sub-THz two-dimensional magnon mode. The pump polarization control of the magnon amplitude confirms that the activation is governed by the instantaneous magnetic anisotropy axis emergent in response to photoexcitation of orbital states with a lowered symmetry. Our results establish pumping of orbital resonances as a universal route for manipulating magnetic order in low-dimensional (anti)ferromagnets.
Initially, we make a detailed historical survey of van der Waals forces, collecting the main references on the subject. Then, we review a method recently proposed by Eberlein and Zietal to compute the dispersion van der Waals interaction between a neutral but polarizable atom and a perfectly conducting surface of arbitrary shape. This method has the advantage of relating the quantum problem to a corresponding classical one in electrostatics so that all one needs is to compute an appropriate Green function. We show how the image method of electrostatics can be conveniently used together with the Eberlein and Zietal mehtod (when the problem admits an image solution). We then illustrate this method in a couple of simple but important cases, including the atom-sphere system. Particularly, in our last example, we present an original result, namely, the van der Waals force between an atom and a boss hat made of a grounded conducting material.
The current attempt is aimed to honor the first centennial of Johannes Diderik van der Waals (VDW) awarding Nobel Prize in Physics. The VDW theory of ordinary fluids is reviewed in the first part of the paper, where special effort is devoted to the equation of state and the law of corresponding states. In addition, a few mathematical features involving properties of cubic equations are discussed, for appreciating the intrinsic beauty of the VDW theory. A theory of astrophysical fluids is shortly reviewed in the second part of the paper, grounding on the tensor virial theorem for two-component systems, and an equation of state is formulated with a convenient choice of reduced variables. Additional effort is devoted to particular choices of density profiles, namely a simple guidance case and two cases of astrophysical interest. The related macroisothermal curves are found to be qualitatively similar to VDW isothermal curves below the critical threshold and, for sufficiently steep density profiles, a critical macroisothermal curve exists, with a single horizontal inflexion point. Under the working hypothesis of a phase transition (assumed to be gas-stars) for astrophysical fluids, sim