Motivated by the recent wealth of exotic magnetic phases emerging in two-dimensional frustrated lattices, we investigate the origin of possible magnetism in the monolayer family of triangular lattice materials MX2 (M=V, Mn, Ni and X=Cl, Br, I). We first show that consideration of general properties such as filling and hybridization enables to formulate the trends for the most relevant magnetic interaction parameters. In particular, we observe that the effects of spin-orbit coupling (SOC) can be effectively tuned through the ligand elements as the considered 3d transition metal ions do not strongly contribute to the anisotropic component of the intersite exchange interaction. Consequently, we find that the corresponding SOC matrix elements differ significantly from the atomic limit. In the next step and by using two ab initio based complementary approaches, we extract realistic effective spin models and find that in the case of heavy ligand elements, SOC effects manifest in anisotropic exchange and single-ion anisotropy only for specific fillings.

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 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.

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.

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.

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 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.

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.