Evidence for a single-layer van der Waals multiferroic.

Multiferroic materials have attracted wide interest because of their exceptional static1-3 and dynamical4-6 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.

Spin-Chirality-Driven Multiferroicity in van der Waals Monolayers.

Driven by the expected contribution of two-dimensional multiferroic systems with strong magnetoelectric coupling to the development of multifunctional nanodevices, here we propose, by means of first-principles calculations, vanadium-halide monolayers as a new class of spin-chirality-driven van der Waals multiferroics. The frustrated 120-deg magnetic structure in the triangular lattice induces a ferroelectric polarization perpendicular to the spin-spiral plane, whose sign is switched by a spin-chirality change. It follows that, in the presence of an applied electric field perpendicular to the monolayers, one magnetic chirality can be stabilized over the other, thereby allowing the long-sought electrical control of spin textures. Moreover, we demonstrate the remarkable role of spin-lattice coupling on magnetoelectricity, which adds to the expected contribution of spin-orbit interaction determined by an anion. Indeed, such compounds exhibit sizeable spin-driven structural distortions, thereby promoting the investigation of multifunctional spin-electric-lattice couplings.

Electron doping as a handle to increase the Curie temperature in ferrimagnetic Mn3Si2X6 (X = Se, Te).

By analysing the results of ab initio simulations performed for Mn3Si2X6 (X = Se, Te), we first discuss the analogies and the differences in electronic and magnetic properties arising from the anion substitution, in terms of size, electronegativity, band widths of p electrons and spin-orbit coupling strengths. For example, through mean-field theory and simulations based on density functional theory, we demonstrate that magnetic frustration, known to be present in Mn3Si2Te6, also exists in Mn3Si2Se6 and leading to a ferrimagnetic ground state. Building on these results, we propose a strategy, electronic doping, to reduce the frustration and thus to increase the Curie temperature (TC). To this end, we first study the effect of electronic doping on the electronic structure and magnetic properties and discuss the differences in the two compounds, along with their causes. Secondly, we perform Monte-Carlo simulations, considering from the first to the fifth nearest-neighbor magnetic interactions and single-ion anisotropy, and show that electron doping efficiently raises the TC.

Angle, Spin, and Depth Resolved Photoelectron Spectroscopy on Quantum Materials.

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.

Influence of Orbital Character on the Ground State Electronic Properties in the van Der Waals Transition Metal Iodides VI3 and CrI3.

Two-dimensional van der Waals magnetic semiconductors display emergent chemical and physical properties and hold promise for novel optical, electronic and magnetic "few-layers" functionalities. Transition-metal iodides such as CrI3 and VI3 are relevant for future electronic and spintronic applications; however, detailed experimental information on their ground state electronic properties is lacking often due to their challenging chemical environment. By combining X-ray electron spectroscopies and first-principles calculations, we report a complete determination of CrI3 and VI3 electronic ground states. We show that the transition metal-induced orbital filling drives the stabilization of distinct electronic phases: a wide bandgap in CrI3 and a Mott insulating state in VI3. Comparison of surface-sensitive (angular-resolved photoemission spectroscopy) and bulk-sensitive (X-ray absorption spectroscopy) measurements in VI3 reveals a surface-only V2+ oxidation state, suggesting that ground state electronic properties are strongly influenced by dimensionality effects. Our results have direct implications in band engineering and layer-dependent properties of two-dimensional systems.

Curved Magnetism in CrI_{3}.

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 CrI_{3}, 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.

Ferroelectric Control of the Spin Texture in GeTe.

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.

Intrinsic Origin of Enhancement of Ferroelectricity in SnTe Ultrathin Films.

Previous studies showed that, as ferroelectric films become thinner, their Curie temperature (T_{c}) and polarization below T_{c} both typically decrease. In contrast, a recent experiment [Chang et al., Science 353, 274 (2016)SCIEAS0036-807510.1126/science.aad8609] observed that atomic-thick SnTe films have a higher T_{c} than their bulk counterpart, which was attributed to extrinsic effects. We find, using first-principles calculations, that the 0-K energy barrier for the polarization switching (which is a quantity directly related to T_{c}) is higher in most investigated defect-free SnTe ultrathin films than that in bulk SnTe, and that the 5-unit-cell (UC) SnTe thin film has the largest energy barrier as a result of an interplay between hybridization interactions and Pauli repulsions. Further simulations, employing a presently developed effective Hamiltonian, confirm that freestanding, defect-free SnTe thin films have a higher T_{c} than bulk SnTe, except for the 1-UC case. Our work, therefore, demonstrates the possibility to intrinsically enhance ferroelectricity of ultrathin films by reducing their thickness.

Magnetic Structures of Heterometallic M(II)-M(III) Formate Compounds.

A study of the magnetic structure of the [NH2(CH3)2]n[FeIIIMII(HCOO)6]n niccolite-like compounds, with MII = CoII (2) and MnII (3) ions, has been carried out using neutron diffraction and compared with the previously reported FeII-containing compound (1). The inclusion of two different metallic atoms into the niccolite-like structure framework leads to the formation of isostructural compounds with very different magnetic behaviors due to the compensation or not of the different spins involved in each lattice. Below TN, the magnetic order in these compounds varies from ferrimagnetic behavior for 1 and 2 to an antiferromagnetic behavior with a weak spin canting for 3. Structure refinements of 2 and 3 at low temperature (45 K) have been carried out combining synchrotron X-ray and high-resolution neutron diffraction in a multipattern approach. The magnetic structures have been determined from the difference patterns between the neutron data in the paramagnetic and the magnetically ordered regions. These difference patterns have been analyzed using a simulated annealing protocol and symmetry analysis techniques. The obtained magnetic structures have been further rationalized by means of ab initio DFT calculations. The direction of the magnetic moment of each compound has been determined. The easy axis of the MII for compound 1 (FeII) is along the c axis; for compound 2 (CoII), the moments are mainly within the ab plane; finally, for compound 3 (MnII), the calculations show that the moments have components both in the ab plane and along the c axis.

Polar Nature of (CH3NH3)3Bi2I9 Perovskite-Like Hybrids.

High-quality single crystals of perovskite-like (CH3NH3)3Bi2I9 hybrids have been synthesized, using a layered-solution crystal-growth technique. The large dielectric constant is strongly affected by the polar ordering of its constituents. Progressive dipolar ordering of the methylammonium cation upon cooling below 300 K gradually converts the hexagonal structure (space group P63/mmc) into a monoclinic phase (C2/c) at 160 K. A well-pronounced, ferrielectric phase transition at 143 K is governed by in-plane ordering of the bismuth lone pair that breaks inversion symmetry and results in a polar phase (space group P21). The dielectric constant is markedly higher in the C2/c phase above this transition. Here, the bismuth lone pair is disordered in-plane, allowing the polarizability to be substantially enhanced. Density functional theory calculations estimate a large ferroelectric polarization of 7.94 µC/cm2 along the polar axis in the P21 phase. The calculated polarization has almost equal contributions of the methylammonium and Bi3+ lone pair, which are fairly decoupled.

Intertwined Rashba, Dirac, and Weyl Fermions in Hexagonal Hyperferroelectrics.

By means of density functional theory based calculations, we study the role of spin-orbit coupling in the new family of ABC hyperferroelectrics [Garrity, Rabe, and Vanderbilt Phys. Rev. Lett. 112, 127601 (2014)]. We unveil an extremely rich physics strongly linked to ferroelectric properties, ranging from the electric control of bulk Rashba effect to the existence of a three-dimensional topological insulator phase, with concomitant topological surface states even in the ultrathin film limit. Moreover, we predict that the topological transition, as induced by alloying, is followed by a Weyl semimetal phase of finite concentration extension, which is robust against disorder, putting forward hyperferroelectrics as promising candidates for spin-orbitronic applications.

Above-room-temperature ferroelectricity in a single-component molecular crystal.

Ferroelectrics are electro-active materials that can store and switch their polarity (ferroelectricity), sense temperature changes (pyroelectricity), interchange electric and mechanical functions (piezoelectricity), and manipulate light (through optical nonlinearities and the electro-optic effect): all of these functions have practical applications. Topological switching of pi-conjugation in organic molecules, such as the keto-enol transformation, has long been anticipated as a means of realizing these phenomena in molecular assemblies and crystals. Croconic acid, an ingredient of black dyes, was recently found to have a hydrogen-bonded polar structure in a crystalline state. Here we demonstrate that application of an electric field can coherently align the molecular polarities in crystalline croconic acid, as indicated by an increase of optical second harmonic generation, and produce a well-defined polarization hysteresis at room temperature. To make this simple pentagonal molecule ferroelectric, we switched the pi-bond topology using synchronized proton transfer instead of rigid-body rotation. Of the organic ferroelectrics, this molecular crystal exhibits the highest spontaneous polarization ( approximately 20 muC cm(-2)) in spite of its small molecular size, which is in accord with first-principles electronic-structure calculations. Such high polarization, which persists up to 400 K, may find application in active capacitor and nonlinear optics elements in future organic electronics.

Coupling Ferroelectricity with Spin-Valley Physics in Oxide-Based Heterostructures.

The coupling of spin and valley physics is nowadays regarded as a promising route toward next-generation spintronic and valleytronic devices. In the aim of engineering functional properties for valleytronic applications, we focus on the ferroelectric heterostructure BiAlO3/BiIrO3, where the complex interplay among a trigonal crystal field, layer degrees of freedom, and spin-orbit coupling mediates a strong spin-valley coupling. Furthermore, we show that ferroelectricity provides a nonvolatile handle to manipulate and switch the emerging valley-contrasting spin polarization.

Topological tuning in three-dimensional dirac semimetals.

We study with first-principles methods the interplay between bulk and surface Dirac fermions in three dimensional Dirac semimetals. By combining density functional theory with the coherent potential approximation, we reveal a topological phase transition in Na_{3}Bi_{1-x}Sb_{x} and Cd_{3}[As_{1-x}P_{x}]_{2} alloys, where the material goes from a Dirac semimetal to a trivial insulator upon changing Sb or P concentrations. Tuning the composition allows us to engineer the position of the bulk Dirac points in reciprocal space. Interestingly, the phase transition coincides with the reversal of the band ordering between the conduction and valence bands.

Avoided metallicity in a hole-doped Mott insulator on a triangular lattice.

Doping of a Mott insulator gives rise to a wide variety of exotic emergent states, from high-temperature superconductivity to charge, spin, and orbital orders. The physics underpinning their evolution is, however, poorly understood. A major challenge is the chemical complexity associated with traditional routes to doping. Here, we study the Mott insulating CrO2 layer of the delafossite PdCrO2, where an intrinsic polar catastrophe provides a clean route to doping of the surface. From scanning tunnelling microscopy and angle-resolved photoemission, we find that the surface stays insulating accompanied by a short-range ordered state. From density functional theory, we demonstrate how the formation of charge disproportionation results in an insulating ground state of the surface that is disparate from the hidden Mott insulator in the bulk. We demonstrate that voltage pulses induce local modifications to this state which relax over tens of minutes, pointing to a glassy nature of the charge order.

Tuning the ferroelectric polarization in a multiferroic metal-organic framework.

We perform density functional theory calculations on a recently synthesized metal-organic framework (MOF) with a perovskite-like topology ABX3, i.e., [CH3CH2NH3]Mn(HCOO)3, and predict a multiferroic behavior, i.e., a coexistence of ferroelectricity and ferromagnetism. A peculiar canted ordering of the organic A-cation dipole moments gives rise to a ferroelectric polarization of ~2 µC/cm(2). Starting from these findings, we show that by choosing different organic A cations, it is possible to tune the ferroelectric polarization and increase it up to 6 µC/cm(2). The possibility of changing the magnitude and/or the canting of the organic molecular dipole opens new routes toward engineering ferroelectric polarization in the new class of multiferroic metal-organic frameworks.

Synthesis and characterization of MnCrO4, a new mixed-valence antiferromagnet.

A new orthorhombic phase, MnCrO4, isostructural with MCrO4 (M = Mg, Co, Ni, Cu, Cd) was prepared by evaporation of an aqueous solution, (NH4)2Cr2O7 + 2 Mn(NO3)2, followed by calcination at 400 °C. It is characterized by redox titration, Rietveld analysis of the X-ray diffraction pattern, Cr K edge and Mn K edge XANES, ESR, magnetic susceptibility, specific heat and resistivity measurements. In contrast to the high-pressure MnCrO4 phase where both cations are octahedral, the new phase contains Cr in a tetrahedral environment suggesting the charge balance Mn(2+)Cr(6+)O4. However, the positions of both X-ray absorption K edges, the bond lengths and the ESR data suggest the occurrence of some mixed-valence character in which the mean oxidation state of Mn is higher than 2 and that of Cr is lower than 6. Both the magnetic susceptibility and the specific heat data indicate an onset of a three-dimensional antiferromagnetic order at TN ≈ 42 K, which was confirmed also by calculating the spin exchange interactions on the basis of first principles density functional calculations. Dynamic magnetic studies (ESR) corroborate this scenario and indicate appreciable short-range correlations at temperatures far above TN. MnCrO4 is a semiconductor with activation energy of 0.27 eV; it loses oxygen on heating above 400 °C to form first Cr2O3 plus Mn3O4 and then Mn1.5Cr1.5O4 spinel.

Structural, electronic and ferroelectric properties of croconic acid crystal: a DFT study.

The recent discovery of high polarization at room temperature in croconic acid crystals as large as 21 µC cm(-2) [Horiuchi et al., Nature, 2010, 463, 789] has lead to renewed interest in organic ferroelectrics, a promising class of materials for future electronic devices. We present here an extended ab initio study of this molecular crystal, using different approximations for the exchange-correlation functionals, ranging from local and semi-local types to more sophisticated hybrid functionals and van der Waals corrected functionals. Furthermore, by using distortion mode analysis, we focus on the different contributions to the polarization and on their microscopic origins.

From Quantum Materials to Microsystems.

The expression "quantum materials" identifies materials whose properties "cannot be described in terms of semiclassical particles and low-level quantum mechanics", i.e., where lattice, charge, spin and orbital degrees of freedom are strongly intertwined. Despite their intriguing and exotic properties, overall, they appear far away from the world of microsystems, i.e., micro-nano integrated devices, including electronic, optical, mechanical and biological components. With reference to ferroics, i.e., functional materials with ferromagnetic and/or ferroelectric order, possibly coupled to other degrees of freedom (such as lattice deformations and atomic distortions), here we address a fundamental question: "how can we bridge the gap between fundamental academic research focused on quantum materials and microsystems?". Starting from the successful story of semiconductors, the aim of this paper is to design a roadmap towards the development of a novel technology platform for unconventional computing based on ferroic quantum materials. By describing the paradigmatic case of GeTe, the father compound of a new class of materials (ferroelectric Rashba semiconductors), we outline how an efficient integration among academic sectors and with industry, through a research pipeline going from microscopic modeling to device applications, can bring curiosity-driven discoveries to the level of CMOS compatible technology.