Machine-learning techniques are revolutionizing the way to perform efficient materials modeling. We here propose a combinatorial machine-learning approach to obtain physical formulas based on simple and easily accessible ingredients, such as atomic properties. The latter are used to build materials features that are finally employed, through linear regression, to predict the energetic stability of semiconducting binary compounds with respect to zinc blende and rocksalt crystal structures. The adopted models are trained using a dataset built from first-principles calculations. Our results show that already one-dimensional (1D) formulas well describe the energetics; a simple grid-search optimization of the automatically obtained 1D-formulas enhances the prediction performance at a very small computational cost. In addition, our approach allows one to highlight the role of the different atomic properties involved in the formulas. The computed formulas clearly indicate that “spatial” atomic properties (i.e., radii indicating maximum probability densities for 𝑠,𝑝,𝑑 electronic shells) drive the stabilization of one crystal structure with respect to the other, suggesting the major relevance of the radius associated with the 𝑝-shell of the cation species.

Curved magnets attract considerable interest for their unusually rich phase diagram, often encompassing exotic (e.g., topological or chiral) spin states. Micromagnetic simulations are playing a central role in the theoretical understanding of such phenomena; their predictive power, however, rests on the availability of reliable model parameters to describe a given material or nanostructure. Here we demonstrate how noncollinear-spin polarized density-functional theory can be used to determine the flexomagnetic coupling coefficients in real systems. By focusing on monolayer CrI3, we find a crossover as a function of curvature between a magnetization normal to the surface to a cycloidal state, which we rationalize in terms of effective anisotropy and Dzyaloshinskii-Moriya contributions to the magnetic energy. Our results reveal an unexpectedly large impact of spin-orbit interactions on the curvature-induced anisotropy, which we discuss in the context of existing phenomenological models

Multiferroic materials have attracted wide interest because of their exceptional static1,2,3 and dynamical4,5,6 magnetoelectric properties. In particular, type-II multiferroics exhibit an inversion-symmetry-breaking magnetic order that directly induces ferroelectric polarization through various mechanisms, such as the spin-current or the inverse Dzyaloshinskii–Moriya effect3,7. This intrinsic coupling between the magnetic and dipolar order parameters results in high-strength magnetoelectric effects3,8. Two-dimensional materials possessing such intrinsic multiferroic properties have been long sought for to enable the harnessing of magnetoelectric coupling in nanoelectronic devices1,9,10. Here we report the discovery of type-II multiferroic order in a single atomic layer of the transition-metal-based van der Waals material NiI2. The multiferroic state of NiI2 is characterized by a proper-screw spin helix with given handedness, which couples to the charge degrees of freedom to produce a chirality-controlled electrical polarization. We use circular dichroic Raman measurements to directly probe the magneto-chiral ground state and its electromagnon modes originating from dynamic magnetoelectric coupling. Combining birefringence and second-harmonic-generation measurements with theoretical modelling and simulations, we detect a highly anisotropic electronic state that simultaneously breaks three-fold rotational and inversion symmetry, and supports polar order. The evolution of the optical signatures as a function of temperature and layer number surprisingly reveals an ordered magnetic polar state that persists down to the ultrathin limit of monolayer NiI2. These observations establish NiI2 and transition metal dihalides as a new platform for studying emergent multiferroic phenomena, chiral magnetic textures and ferroelectricity in the two-dimensional limit.

Two-dimensional (2D) van der Waals (vdW) magnets provide an ideal platform for exploring, on the fundamental side, new microscopic mechanisms and for developing, on the technological side, ultracompact spintronic applications. So far, bilinear spin Hamiltonians have been commonly adopted to investigate the magnetic properties of 2D magnets, neglecting higher order magnetic interactions. However, we here provide quantitative evidence of giant biquadratic exchange interactions in monolayer NiX2 (X=Cl, Br and I), by combining first-principles calculations and the newly developed machine learning method for constructing Hamiltonian. Interestingly, we show that the ferromagnetic ground state within NiCl2 single layers cannot be explained by means of the bilinear Heisenberg Hamiltonian; rather, the nearest-neighbor biquadratic interaction is found to be crucial. Furthermore, using a three-orbitals Hubbard model, we propose that the giant biquadratic exchange interaction originates from large hopping between unoccupied and occupied orbitals on neighboring magnetic ions. On a general framework, our work suggests biquadratic exchange interactions to be important in 2D magnets with edge-shared octahedra.

Hybridization of electronic states and orbital symmetry in transition metal oxides are generally considered key ingredients in the description of both their electronic and magnetic properties. In the prototypical case of La0.65Sr0.35MnO3 (LSMO), a landmark system for spintronics applications, a description based solely on Mn 3d and O 2p electronic states is reductive. We thus analyzed elemental and orbital distributions in the LSMO valence band through a comparison between density functional theory calculations and experimental photoelectron spectra in a photon energy range from soft to hard x rays. We reveal a number of hidden contributions, arising specifically from La 5p, Mn 4s, and O 2s orbitals, considered negligible in previous analyses; our results demonstrate that all these contributions are significant for a correct description of the valence band of LSMO and of transition metal oxides in general.

The effects of competing magnetic interactions in stabilizing different spin configurations are drawing renewed attention in order to unveil emerging topological spin textures and to highlight microscopic mechanisms leading to their stabilization. The possible key role of the two-site exchange anisotropy in selecting specific helicity and vorticity of skyrmionic lattices has only recently been proposed. In this work, we explore the phase diagram of a frustrated localized magnet characterized by a two-dimensional centrosymmetric triangular lattice, focusing on the interplay between the two-ion anisotropy and the single-ion anisotropy. The effects of an external magnetic field applied perpendicularly to the magnetic layer, are also investigated. By means of Monte Carlo simulations, we find an abundance of different spin configurations, going from trivial to high-order Q skyrmionic and meronic lattices. In closer detail, we find that a dominant role is played by the two-ion over the single-ion anisotropy in determining the planar spin texture; the strength and the sign of single ion anisotropy, together with the magnitude of the magnetic field, tune the perpendicular spin components, mostly affecting the polarity (and, in turn, the topology) of the spin texture. Our analysis confirms the crucial role of the anisotropic symmetric exchange in systems with dominant short-range interactions; at the same time, we predict a rich variety of complex magnetic textures, which may arise from a fine tuning of competing anisotropic mechanisms.

The magnetic properties of the two-dimensional VI3 bilayer are the focus of our first-principles analysis, highlighting the role of t2g orbital splitting and carried out in comparison with the CrI3 prototypical case, where the splitting is negligible. In VI3 bilayers, the empty a1g state is found to play a crucial role in both stabilizing the insulating state and in determining the interlayer magnetic interaction. Indeed, an analysis based on maximally localized Wannier functions allows one to evaluate the interlayer exchange interactions in two different VI3 stackings (labeled AB and AB′), to interpret the results in terms of the virtual-hopping mechanism, and to highlight the strongest hopping channels underlying the magnetic interlayer coupling. Upon application of electric fields perpendicular to the slab, we find that the magnetic ground state in the AB′ stacking can be switched from antiferromagnetic to ferromagnetic, suggesting the VI3 bilayer as an appealing candidate for electric-field-driven miniaturized spintronic devices.

The role of X-ray based electron spectroscopies in determining chemical, electronic, and magnetic properties of solids has been well-known for several decades. A powerful approach is angle-resolved photoelectron spectroscopy, whereby the kinetic energy and angle of photoelectrons emitted from a sample surface are measured. This provides a direct measurement of the electronic band structure of crystalline solids. Moreover, it yields powerful insights into the electronic interactions at play within a material and into the control of spin, charge, and orbital degrees of freedom, central pillars of future solid state science. With strong recent focus on research of lower-dimensional materials and modified electronic behavior at surfaces and interfaces, angle-resolved photoelectron spectroscopy has become a core technique in the study of quantum materials. In this review, we provide an introduction to the technique. Through examples from several topical materials systems, including topological insulators, transition metal dichalcogenides, and transition metal oxides, we highlight the types of information which can be obtained. We show how the combination of angle, spin, time, and depth-resolved experiments are able to reveal “hidden” spectral features, connected to semiconducting, metallic and magnetic properties of solids, as well as underlining the importance of dimensional effects in quantum materials.

Topological spin structures, such as magnetic skyrmions, hold great promises for data storage applications, thanks to their inherent stability. In most cases, skyrmions are stabilized by magnetic fields in non-centrosymmetric systems displaying the chiral Dzyaloshinskii-Moriya exchange interaction, while spontaneous skyrmion lattices have been reported in centrosymmetric itinerant magnets with long-range interactions. Here, a spontaneous anti-biskyrmion lattice with unique topology and chirality is predicted in the monolayer of a semiconducting and centrosymmetric metal halide, NiI2. Our first-principles and Monte Carlo simulations reveal that the anisotropies of the short-range symmetric exchange, when combined with magnetic frustration, can lead to an emergent chiral interaction that is responsible for the predicted topological spin structures. The proposed mechanism finds a prototypical manifestation in two-dimensional magnets, thus broadening the class of materials that can host spontaneous skyrmionic states. Skyrmions, topological spin textures, are typically stabilized by the Dzyaloshinskii-Moriya interaction and an applied magnetic field. In this theoretical study, by analysing monolayer NiI2, the authors suggest that two-site anisotropy with magnetic frustration can stabilize a skyrmion lattice.

Bulk PtSn4 has recently attracted the interest of the scientific community for the presence of electronic states exhibiting Dirac node arcs, enabling possible applications in nanoelectronics. Here, by means of surface-science experiments and density functional theory, we assess its suitability for catalysis by studying the chemical reactivity of the (0 1 0)-oriented PtSn4 surface toward CO, H2O, O2 molecules at room temperature and, moreover, its stability in air. We demonstrate that the catalytic activity of PtSn4 is determined by the composition of the outermost atomic layer. Specifically, we find that the surface termination for PtSn4 crystals cleaved in vacuum is an atomic Sn layer, which is totally free from any CO poisoning. In oxygen-rich environment, as well as in ambient atmosphere, the surface termination is a SnOx skin including SnO and SnO2 in comparable amount. However, valence-band states, including those forming Dirac node arcs, are only slightly affected by surface modifications. The astonishingly beneficial influence of surface oxidation on catalytic activity has been demonstrated by electrocatalytic tests evidencing a reduction of the Tafel slope, from 442 down to 86 mV dec−1, whose origin has been explained by our theoretical model. The use of surface-science tools to tune the chemical reactivity of PtSn4 opens the way toward its effective use in catalysis, especially for hydrogen evolution reaction and oxygen evolution reaction.

Two-dimensional (2D) metallic states induced by oxygen vacancies (VOs) at oxide surfaces and interfaces provide opportunities for the development of advanced applications, but the ability to control the behavior of these states is still limited. We used angle resolved photoelectron spectroscopy combined with density-functional theory (DFT) to study the reactivity of VO-induced states at the (001) surface of anatase TiO2, where both 2D metallic and deeper lying in-gap states (IGs) are observed. The 2D and IG states exhibit remarkably different evolutions when the surface is exposed to molecular O2: while IGs are almost completely quenched, the metallic states are only weakly affected. DFT calculations indeed show that the IGs originate from surface VOs and remain localized at the surface, where they can promptly react with O2. In contrast, the metallic states originate from subsurface vacancies whose migration to the surface for recombination with O2 is kinetically hindered on anatase TiO2 (001), thus making them much less sensitive to oxygen dosing.

We present the results of a photon energy and polarization dependent angle-resolved photoemission spectroscopy (ARPES) study on high quality, epitaxial SrNbO3 thin films prepared in situ by pulsed laser deposition (PLD). We show that the Fermi surface is composed of three bands mainly due to t(2g) orbitals of Nb 4d, in analogy with the 3d-based perovskite systems. The bulk band dispersion for the conduction and valence states obtained by density functional theory (DFT) is generally consistent with the ARPES data. The small discrepancy in the bandwidth close to the Fermi level seems to result from the interplay of correlation effects and the presence of vacancies. The ARPES results are complemented by soft x-ray photoemission spectroscopy measurements in order to provide indications on the chemical states and the stoichiometry of the material.

The tetragonal phase of chromium (III) oxide, although unstable in the bulk, can be synthesized in epitaxial heterostructures. Theoretical investigation by density-functional theory predicts an antiferromagnetic ground state for this compound. We demonstrate experimentally antiferromagnetism up to 40 K in ultrathin films of t−Cr2O3 by electrical measurements exploiting interface effect within a neighboring ultrathin Pt layer. We show that magnetotransport in Pt is affected by both spin-Hall magnetoresistance and magnetic proximity effect while we exclude any role of magnetism for the low-temperature resistance anomaly observed in Pt.

Polar lacunar spinels, such as GaV4S8 and GaV4Se8, were proposed to host skyrmion phases under magnetic field. In this work, we put forward, as a candidate for Néel-type skyrmion lattice, the isostructural GaMo4S8, which is systematically studied via both first-principles calculations and Monte Carlo simulations of a model Hamiltonian. Electric polarization, driven by the Jahn-Teller distortion, is predicted to arise in GaMo4S8, showing a comparable size but an opposite sign with respect to that evaluated in V-based counterparts and explained in terms of different electron counting arguments and resulting distortions. Interestingly, a larger spin-orbit coupling of 4d orbitals with respect to 3d orbitals in vanadium spinels leads to stronger Dzyaloshinskii-Moriya interactions, which are beneficial to stabilize a cycloidal spin texture, as well as smaller-sized skyrmions (radius<10nm). Furthermore, the possibly large exchange anisotropy of GaMo4S8 may lead to a ferroelectric-ferromagnetic ground state as an alternative to the ferroelectric-skyrmionic one, thus calling for further experimental verification.

Currently, there is a flurry of research interest on materials with an unconventional electronic structure, and we have already seen significant progress in their understanding and engineering towards real-life applications. The interest erupted with the discovery of graphene and topological insulators in the previous decade. The electrons in graphene simulate massless Dirac Fermions with a linearly dispersing Dirac cone in their band structure, while in topological insulators, the electronic bands wind non-trivially in momentum space giving rise to gapless surface states and bulk bandgap. Weyl semimetals in condensed matter systems are the latest addition to this growing family of topological materials. Weyl Fermions are known in the context of high energy physics since almost the beginning of quantum mechanics. They apparently violate charge conservation rules, displaying the 'chiral anomaly', with such remarkable properties recently theoretically predicted and experimentally verified to exist as low energy quasiparticle states in certain condensed matter systems. Not only are these new materials extremely important for our fundamental understanding of quantum phenomena, but also they exhibit completely different transport phenomena. For example, massless Fermions are susceptible to scattering from non-magnetic impurities. Dirac semimetals exhibit non-saturating extremely large magnetoresistance as a consequence of their robust electronic bands being protected by time reversal symmetry. These open up whole new possibilities for materials engineering and applications including quantum computing. In this review, we recapitulate some of the outstanding properties of WTe2, namely, its non-saturating titanic magnetoresistance due to perfect electron and hole carrier balance up to a very high magnetic field observed for the very first time. It also indicative of hosting Lorentz violating type-II Weyl Fermions in its bandstructure, again first predicted candidate material to host such a remarkable phase. We primarily focus on the findings of our ARPES, spin-ARPES, and time-resolved ARPES studies complemented by first-principles calculations.

By performing density functional theory and Green's functions calculations, complemented by x-ray photoemission spectroscopy, we investigate the electronic structure of Fe/GeTe(111), a prototypical ferromagnetic/Rashba-ferroelectric interface. We reveal that such a system exhibits several intriguing properties resulting from the complex interplay of exchange interaction, electric polarization, and spin-orbit coupling. Despite a rather strong interfacial hybridization between Fe and GeTe bands, resulting in a complete suppression of the surface states of the latter, the bulk Rashba bands are hardly altered by the ferromagnetic overlayer. This could have a deep impact on spin-dependent phenomena observed at this interface, such as spin-to-charge interconversion, which are likely to involve bulk rather than surface Rashba states.

We report on the influence of spin-orbit coupling (SOC) in Fe-based superconductors via application of circularly polarized spin and angle-resolved photoemission spectroscopy. We combine this technique in representative members of both the Fe-pnictides (LiFeAs) and Fe-chalcogenides (FeSe) with tight-binding calculations to establish an ubiquitous modification of the electronic structure in these materials imbued by SOC. At low energy, the influence of SOC is found to be concentrated on the hole pockets, where the largest superconducting gaps are typically found. This effect varies substantively with the
kzdispersion, and in FeSe we find SOC to be comparable to the energy scale of orbital order. These results contest descriptions of superconductivity in these materials in terms of pure spin-singlet eigenstates, raising questions regarding the possible pairing mechanisms and role of SOC therein.

The delicate interplay of electronic charge, spin, and orbital degrees of freedom is in the heart of many novel phenomena across the transition metal oxide family. Here, by combining high-resolution angle-resolved photoemission spectroscopy and first principles calculations (with and without spin-orbit coupling), the electronic structure of the rutile binary iridate,
IrO2, is investigated. The detailed study of electronic bands measured on a high-quality single crystalline sample and use of a wide range of photon energy provide a huge improvement over the previous studies. The excellent agreement between theory and experimental results shows that the single-particle DFT description of IrO2 band structure is adequate, without the need of invoking any treatment of correlation effects. Although many observed features point to a 3D nature of the electronic structure, clear surface effects are revealed. The discussion of the orbital character of the relevant bands crossing the Fermi level sheds light on spin-orbit-coupling-driven phenomena in this material, unveiling a spin-orbit-induced avoided crossing, a property likely to play a key role in its large spin Hall effect.

The electric and nonvolatile control of the spin texture in semiconductors would represent a fundamental step toward novel electronic devices combining memory and computing functionalities. Recently, GeTe has been theoretically proposed as the father compound of a new class of materials, namely ferroelectric Rashba semiconductors. They display bulk bands with giant Rashba-like splitting due to the inversion symmetry breaking arising from the ferroelectric polarization, thus allowing for the ferroelectric control of the spin. Here, we provide the experimental demonstration of the correlation between ferroelectricity and spin texture. A surface-engineering strategy is used to set two opposite predefined uniform ferroelectric polarizations, inward and outward, as monitored by piezoresponse force microscopy. Spin and angular resolved photoemission experiments show that these GeTe(111) surfaces display opposite sense of circulation of spin in bulk Rashba bands. Furthermore, we demonstrate the crafting of nonvolatile ferroelectric patterns in GeTe films at the nanoscale by using the conductive tip of an atomic force microscope. Based on the intimate link between ferroelectric polarization and spin in GeTe, ferroelectric patterning paves the way to the investigation of devices with engineered spin configurations.

By combining bulk sensitive soft-x-ray angular-resolved photoemission spectroscopy and first-principles calculations we explored the bulk electron states of WTe2, a candidate type-II Weyl semimetal featuring a large nonsaturating magnetoresistance. Despite the layered geometry suggesting a two-dimensional electronic structure, we directly observe a three-dimensional electronic dispersion. We report a band dispersion in the reciprocal direction perpendicular to the layers, implying that electrons can also travel coherently when crossing from one layer to the other. The measured Fermi surface is characterized by two well-separated electron and hole pockets at either side of the Γ point, differently from previous more surface sensitive angle-resolved photoemission spectroscopy experiments that additionally found a pronounced quasiparticle weight at the zone center. Moreover, we observe a significant sensitivity of the bulk electronic structure of WTe2 around the Fermi level to electronic correlations and renormalizations due to self-energy effects, previously neglected in first-principles descriptions.

The recent discovery of hidden spin polarization emerging in bulk electronic states of specific nonmagnetic crystals is a fascinating phenomenon, though hardly explored yet. Here, we study from a theoretical perspective nonmagnetic
BaNiS2, recently suggested to exhibit a giant Rashba-like spin-orbit splitting of the bulk bands, despite the absence of heavy elements. We employ density functional theory and Green's functions calculations to reveal the exact spin textures of both bulk and surface. We predict unambiguous signatures of spin-polarized electronic states at the surface, which reflect the bulk Rashba splitting and which could be experimentally measured with sufficient resolution: this would constitute a clear report of a bulk-Rashba-induced spin splitting at the surface of centrosymmetric crystals.

PtBi2 with a layered hexagonal crystal structure was recently reported to exhibit an unconventional large linear magnetoresistance, while the mechanism involved is still elusive. Using high-resolution angle-resolved photoemission spectroscopy, we present a systematic study on its bulk and surface electronic structure. Through careful comparison with first principle calculations, our experiment distinguishes the low-lying bulk bands from entangled surface states, allowing the estimation of the real composition of samples. We find significant electron doping in PtBi2, implying a substantial Bi-deficiency-induced disorder therein. Intriguingly, we discover a Dirac-cone-like surface state on the boundary of the Brillouin zone, which is identified as an accidental Dirac band without topological protection. Our findings exclude linear band dispersion in the quantum limit as the cause of the unconventional large linear magnetoresistance but give support to the classical disorder model from the perspective of the electronic structure.

The electronic structure of the chiral helimagnet
Cr1/3NbS2 has been studied with core level and angle-resolved photoemission spectroscopy (ARPES). Intercalated Cr atoms are found to be effective in donating electrons to the NbS2 layers but also cause significant modifications of the electronic structure of the host NbS2 material. In particular, the data provide evidence that a description of the electronic structure of Cr1/3NbS2 on the basis of a simple rigid band picture is untenable. The data also reveal substantial inconsistencies with the predictions of standard density functional theory. The relevance of these results to the attainment of a correct description of the electronic structure of chiral helimagnets, magnetic thin films/multilayers, and transition metal dichalcogenides intercalated with 3d magnetic elements is discussed.

We investigated the influence of surfaces in the formation of different crystal structures of a spin crossover compound, namely [Fe(L)2] (LH: (2-(pyrazol-1-yl)-6-(1H-tetrazol-5-yl)pyridine), which is a neutral compound thermally switchable around room temperature. We observed that the surface induces the formation of two different crystal structures, which exhibit opposite spin transitions, i.e. on heating them up to the transition temperature, one polymorph switches from high spin to low spin and the second polymorph switches irreversibly from low spin to high spin. We attributed this inversion to the presence of water molecules H-bonded to the complex tetrazolyl moieties in the crystals. Thin deposits were investigated by means of polarized optical microscopy, atomic force microscopy, X-ray diffraction, X-ray absorption spectroscopy and micro Raman spectroscopy; moreover the analysis of the Raman spectra and the interpretation of spin inversion were supported by DFT calculations.