The recent discovery of type-II multiferroicity in monolayer NiI_2 indicated a new pathway for intrinsic magnetoelectric coupling in the two-dimensional limit. However, determining whether this phenomenon is a unique anomaly or a general, chemically tunable property of the material class remains unresolved. Here, we demonstrate the universality of type-II multiferroicity in the transition metal dihalides by visualizing the ferroelectric order in monolayer NiBr_2. Using scanning tunneling microscopy (STM), we resolve atomic-scale ferroelectric domains and confirm their magnetoelectric origin through reciprocal manipulation experiments: reorienting magnetic order via electric fields and suppressing the electric polarization with external magnetic fields. Furthermore, we find that the multiferroic state in NiBr_2 is energetically less robust than in its iodide counterpart, consistent with modified superexchange interactions and the reduced spin-orbit coupling. Our results establish the transition metal dihalides as a versatile platform where the stability of magnetoelectric phases can be engineered through chemical substitution.

Strong electronic correlations in narrow-band systems provide a promising route to realize emergent quantum phases. While ferroelectricity in van der Waals materials is typically associated with inversion symmetry breaking driven by lattice distortions, interlayer sliding, or moiré reconstruction, the possibility of generating ferroelectricity directly from electronic interactions remains largely unexplored. Here, using molecular beam epitaxy, scanning tunneling microscopy, and ab initio calculations, we investigate two stacking geometries of bilayer 1T-TaSe$_2$, A-C and A-C$'$, formed by coupled Star-of-David charge density wave phases. We show that both stackings realize quasi-one-dimensional interacting chains, but are governed by distinct interaction mechanisms. In the A-C stacking, strong interlayer hybridization leads to dimerization and the formation of a band insulating state. In contrast, the A-C$'$ stacking is dominated by interlayer Coulomb interactions, producing a spontaneous charge imbalance between layers that gives rise to an out-of-plane ferroelectric polarization. Furthermore, we demonstrate that ferroelectric and antiferroelectric interchain configurations can be stabilized and electrically switched by an external field. Our results prove that bilayer 1T-TaSe$_2$ is a platform for interaction-driven electronic ferroelectricity, establishing an overlooked family of charge-ordered correlated states in 1T-TaSe$_2$ multilayers.

The recent discovery of type-II multiferroicity in monolayer NiI 2 indicated a new pathway for intrinsic magnetoelectric coupling in the two-dimensional limit. However, whether this phenomenon is a unique feature of NiI 2 or a chemically tunable property of the broader material class has remained unresolved. Here, we demonstrate that type-II multiferroicity in the nickel dihalides is tunable through halide ligand substitution by visualizing the ferroelectric order in monolayer NiBr 2 . Using scanning tunneling microscopy (STM), we resolve atomic-scale ferroelectric domains and confirm their magnetoelectric origin through reciprocal manipulation experiments: reorienting magnetic order via electric fields and suppressing the electric polarization with external magnetic fields. Furthermore, we find that the multiferroic state in NiBr 2 is energetically less robust than in its iodide counterpart, consistent with modified superexchange interactions and the reduced spin-orbit coupling (SOC). Our results establish the nickel dihalides as a versatile platform where the stability of magnetoelectric phases can be engineered through chemical substitution.

Multiferroicity arising from non-collinear spin textures and strong spin-orbit interactions offers a route to magnetoelectric functionality in the monolayer limit. Although theory predicts that the properties of monolayer multiferroics can be tuned by strain, gating, or proximity effects, experimental demonstrations of such control remain scarce. Here we show that the magnetic ground state of monolayer NiI_2, a prototypical two-dimensional multiferroic, is altered by proximity to a superconducting NbSe_2 substrate. Using low-temperature scanning tunnelling microscopy (STM) and spectroscopy (STS), we show that the metallic substrate renormalizes the exchange interactions within NiI_2 and drives it into a ferromagnetic ground state. This can be visualized by probing the Yu-Shiba-Rusinov (YSR) states within the superconducting gap of the NbSe_2 substrate. Our results establish YSR states as an in situ probe of two-dimensional magnetism and demonstrate substrate engineering as a means of controlling magnetic order in atomically thin materials.

Molecular quantum magnets adsorbed on surfaces exhibit rich spin and orbital excitations that can be probed by scanning tunneling microscopy with inelastic electron tunneling spectroscopy (STM-IETS). However, the quantitative extraction of the underlying multiorbital Hamiltonian from experimental spectra remains a fundamental challenge. Here, we introduce molecular Hamiltonian learning, a machine learning strategy that infers the microscopic Hamiltonian parameters of a single adsorbed molecule directly from the setpoint-dependence of STM-IETS data. The method leverages the systematic evolution of spectral features as the STM tip tunes the local electrostatic environment for different tip-sample distances. We demonstrate this approach on iron phthalocyanine on ferroelectric SnTe, training our algorithm on theory spectra from a realistic multiorbital model, including spin-orbit coupling, electrostatic interactions, local crystal field, and substrate effects. The algorithm, trained solely on theoretical many-body simulations, allows reconstructing Hamiltonian parameters directly from experimental spectra. Our manuscript establishes a flexible and automated strategy for Hamiltonian reconstruction from STM-IETS, transforming setpoint-dependent spectroscopy into quantitative characterization of quantum materials at the atomic scale.

Quantum spin liquids are quantum phases of matter featuring collectively entangled states and emergent fractional many-body excitations. While methods exist to probe three-dimensional quantum spin liquids experimentally, these techniques lack the sensitivity to probe two-dimensional quantum spin liquids. This seriously hampers the study of potential monolayer quantum spin liquid candidates such as α-RuCl_3 and 1T-TaSe_2. Scanning tunneling microscopy (STM) and spectroscopy (STS) have recently been suggested as promising probes of the quantum spin liquid state, as they can access the spinon spectrum through inelastic tunneling spectroscopy (IETS). In this work, we employ this approach on the quantum spin liquid candidate material 1T-TaSe_2 and directly measure its low-energy inelastic excitations. We observe the emergence of a √(3)×√(3) reconstruction driven by the substrate, equivalent spectroscopy across all spin sites and coexistence of zero and finite energy excitations. We show that these observations are consistent with a modulated √(3)×√(3) spin liquid ground state. Our results demonstrate that IETS provides a powerful route to obtain atomic-scale insight into the magnetic excitations of two-dimensional materials, allowing to explore the effects of moiré modulations on potential quantum liquid phases.

Van der Waals multiferroics have emerged as a promising platform to explore novel magnetoelectric phenomena. Recently, it has been shown that monolayer NiI_2 hosts robust type-II multiferroicity down to the two-dimensional limit, a giant dynamical magnetoelectric coupling at terahertz frequencies, and an electrically switchable spin polarization. These developments present the possibility of engineering ultrafast, low-energy-consumption, and electrically-tunable spintronic devices based on the collective excitations of the multiferroic order, electromagnons. However, the direct visualization of these bosonic modes in real space and within the monolayer limit remains elusive. Here, we report the atomic-scale observation of electromagnons in monolayer NiI_2 using low-temperature scanning tunneling microscopy. By tracking the thermal evolution of the multiferroic phase, we establish the energy scale and resolve coherent in-gap excitations of the symmetry-broken multiferroic state. Comparison with first-principles and spin-model calculations reveals that the low-energy modes originate from electromagnon excitations. Spatially resolved inelastic tunneling spectroscopy maps show a stripe-like modulation of the local spectral function at electromagnon energies, matching theoretical predictions. These results provide direct evidence of the internal structure of electromagnons and establish a methodology to probe these modes at the atomic scale, opening avenues for electrically tunable spintronics.

Extracting the Hamiltonian parameters of nanoscale quantum magnets from experimental measurements is a significant challenge in quantum matter. Here we establish a machine learning strategy to extract the parameters of a spin Hamiltonian from inelastic spectroscopy with scanning tunneling microscopy, and we demonstrate this methodology experimentally with an artificial nanoscale molecular magnet based on cobalt phthalocyanine (CoPC) molecules on NbSe_2. We show that this technique allows us to extract the Hamiltonian parameters of a quantum magnet from the differential conductance, including the substrate-induced spatial variation of the exchange couplings. Our methodology leverages a machine learning algorithm trained on exact quantum many-body simulations with tensor networks of finite quantum magnets, leading to a methodology that predicts the Hamiltonian parameters of CoPC quantum magnets of arbitrary size. Our results demonstrate how quantum many-body methods and machine learning enable us to learn a microscopic description of nanoscale quantum many-body systems with scanning tunneling spectroscopy.

Multiband superconductivity plays an important role in many emergent novel superconductors and has attracted great interest over the years. Various related experimental aspects have been intensely researched, but a quantitative understanding on the Cooper-pair transport remains still elusive, despite its fundamental and technological importance. We study a Josephson junction with a scanning tunneling microscope (STM), where both tip and sample are Pb, a prototypical type I two-band superconductor. We map the properties of the junction across a wide range of normal state conductances revealing in-gap features originating from multiple Andreev reflections (MARs) and the Josephson effect. We present the theoretical framework to extract the transmission through the transport channels and describe the Cooper-pair tunneling with quantitative precision through two superconducting bands. This paves the way for the understanding of increasingly complicated superconductors.

Scanning Probe Microscopy (SPM) techniques have shown great potential in fabricating nanoscale structures endowed with exotic quantum properties achieved through various manipulations of atoms and molecules. However, precise control requires extensive domain knowledge, which is not necessarily transferable to new systems and cannot be readily extended to large-scale operations. Therefore, efficient and autonomous SPM techniques are needed to learn optimal strategies for new systems, in particular for the challenge of controlling chemical reactions and hence offering a route to precise atomic and molecular construction. In this paper, we developed a software infrastructure named AutoOSS (Autonomous On-Surface Synthesis) to automate bromine removal from hundreds of Zn(II)-5,15-bis(4-bromo-2,6-dimethylphenyl)porphyrin (ZnBr2Me4DPP) on Au(111), using neural network models to interpret STM outputs and deep reinforcement learning models to optimize manipulation parameters. This is further supported by Bayesian Optimization Structure Search (BOSS) and Density Functional Theory (DFT) computations to explore 3D structures and reaction mechanisms based on STM images.

The Kondo effect describes the scattering of conduction electrons by magnetic impurities, manifesting as an electronic resonance at the Fermi energy with a distinctive temperature evolution. In this Letter, we present a critical evaluation of the current methodology employed to demonstrate Kondo behavior in transport measurements, underscoring the limitations of established theoretical frameworks and the influence of extrinsic broadening. We introduce an approach for analyzing spectroscopic indicators of the Kondo effect, employing the Hurwitz-Fano lineshape as a model for the Kondo resonance in the presence of extrinsic broadening. Through precise scanning tunneling spectroscopy measurements on an exemplary spin-1/2 Kondo system, phenalenyl on Au(111), we demonstrate the efficacy of our proposed protocol in extracting accurate intrinsic Kondo linewidths from finite-temperature measurements. The extracted linewidths exhibit a robust fit with a recently derived expression for the temperature-dependent intrinsic Kondo linewidth, providing compelling evidence for the validity of the underlying theory. Published by the American Physical Society 2024

At low temperatures, the interaction of a nanoscale magnet with a Fermi gas can give rise to the Kondo effect. This is signaled by a zero-bias resonance with a characteristic temperature evolution of its linewidth. In order to prove the Kondo nature of the zero-bias peak and to determine the Kondo temperature in scanning tunneling spectroscopy (STS), the extrinsic contributions to the measured linewidth have to be properly taken into account. In this paper, by combination of precise STS measurements of an ideal spin-1/2 Kondo system, phenalenyl on Au(111), and by theoretical considerations, we show how to efficiently extract accurate intrinsic Kondo linewidths from finite-temperature STS measurements. The extracted linewidths fit very well with a recently derived expression for the intrinsic Kondo linewidth as a function of temperature, thus proving the validity of the theory. Finally, we show that the developed methodology allows to reliably extract the intrinsic Kondo width from a single spectrum measured at finite temperature, thus considerably reducing the experimental effort.

Electric control of spins has been a longstanding goal in the field of solid state physics due to the potential for increased efficiency in information processing. This efficiency can be optimized by transferring spintronics to the atomic scale. We present electric control of spin resonance transitions in single TiH molecules by employing electron spin resonance scanning tunneling microscopy (ESR-STM). We find strong bias voltage dependent shifts in the ESR signal of about ten times its line width. We attribute this to the electric field in the tunnel junction, which induces a displacement of the spin system changing the g-factor and the effective magnetic field of the tip. We demonstrate direct electric control of the spin transitions in coupled TiH dimers. Our findings open up new avenues for fast coherent control of coupled spin systems and expands on the understanding of spin electric coupling.

Magnetic impurities on superconductors lead to bound states within the superconducting gap, so called Yu-Shiba-Rusinov (YSR) states. They are parity protected, which enhances their lifetime, but makes it more difficult to excite them. Here, we realize the excitation of YSR states by microwaves facilitated by the tunnel coupling to another superconducting electrode in a scanning tunneling microscope (STM). We identify the excitation process through a family of anomalous microwave-assisted tunneling peaks originating from a second-order resonant Andreev process, in which the microwave excites the YSR state triggering a tunneling event transferring a total of two charges. We vary the amplitude and the frequency of the microwave to identify the energy threshold and the evolution of this excitation process. Our work sets an experimental basis and proof-of-principle for the manipulation of YSR states using microwaves with an outlook towards YSR qubits.

Quantum magnets provide a powerful platform to explore complex quantum many-body phenomena. One example is triplon excitations, exotic many-body modes emerging from propagating singlet-triplet transitions. We engineer a minimal quantum magnet from organic molecules and demonstrate the emergence of dispersive triplon modes in one- and two-dimensional assemblies probed with scanning tunneling microscopy and spectroscopy. Our results provide the first demonstration of dispersive triplon excitations from a real-space measurement.

Transport through quantum coherent conductors, such as atomic junctions, is described by conduction channels. Information about the number of channels and their transmissions can be extracted from various sources, such as multiple Andreev reflections, dynamical Coulomb blockade, or shot noise. We complement this set of methods by introducing the superconducting excess current as a new tool to continuously extract the transport channel transmissions of an atomic scale junction in a scanning tunneling microscope. In conjunction with ab initio simulations, we employ this technique in atomic aluminum junctions to determine the influence of the structure adjacent to the contact atoms on the transport properties.

The continuous increase in storage densities and the desire for quantum memories and computers push the limits of magnetic characterization techniques. Ultimately, a tool that is capable of coherently manipulating and detecting individual quantum spins is needed. Scanning tunneling microscopy (STM) is the only technique that unites the prerequisites of high spatial and energy resolution, low temperature, and high magnetic fields to achieve this goal. Limitations in the available frequency range for electron spin resonance STM (ESR-STM) mean that many instruments operate in the thermal noise regime. We resolve challenges in signal delivery to extend the operational frequency range of ESR-STM by more than a factor of two and up to 100 GHz, making the Zeeman energy the dominant energy scale at achievable cryogenic temperatures of a few hundred millikelvin. We present a general method for augmenting existing instruments into ESR-STM to investigate spin dynamics in the high-field limit. We demonstrate the performance of the instrument by analyzing inelastic tunneling in a junction driven by a microwave signal and provide proof of principle measurements for ESR-STM.

Magnetic impurities on superconductors induce discrete bound levels inside the superconducting gap, known as Yu-Shiba-Rusinov (YSR) states. YSR levels are fully spin-polarized such that the tunneling between YSR states depends on their relative spin orientation. Here, we use scanning tunneling spectroscopy to resolve the spin dynamics in the tunneling process between two YSR states by experimentally extracting the angle between the spins. To this end, we exploit the ratio of thermally activated and direct spectral features in the measurement to directly extract the relative spin orientation between the two YSR states. We find freely rotating spins down to 7mK, indicating a purely paramagnetic nature of the impurities. Such a non-collinear spin alignment is essential not only for producing Majorana bound states but also as an outlook manipulating and moving the Majorana state onto the tip.

As scanning tunneling microscopy is pushed towards fast local dynamics, a quantitative understanding of tunnel junctions under the influence of a fast ac driving signal is required, especially at the ultralow temperatures relevant to spin dynamics and correlated electron states. We subject a superconductor-insulator-superconductor junction to a microwave signal from an antenna mounted in situ and examine the dc response of the contact to this driving signal. Quasiparticle tunneling and the Josephson effect can be interpreted in the framework of Tien-Gordon theory. The situation is more complex when it comes to higher-order effects such as multiple Andreev reflections. Microwave-assisted tunneling unravels these complex processes, providing deeper insights into tunneling than are available in a pure dc measurement.