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First-principles calculations are employed to study the ferroelectric properties and the bulk photovoltaic effect (BPVE) of antimony sulfur iodide (SbSI). The BPVE enables direct sunlight-to-electricity conversion in homogeneous materials and, in ferroelectric compounds, can be tuned via an electric field controlling the polarization. However, most ferroelectrics are oxides with large band gaps exceeding visible light energy, limiting their photovoltaic performance. Featuring a visible-range band gap, SbSI instead combines remarkable photovoltaic capabilities with a spin-textured band structure, coupling charge and spin degrees of freedom. The calculations predict ferroelectric and antiferroelectric phases with comparable band gaps but distinct Rashba-Dresselhaus and Weyl-like spin textures relevant for spintronics. The BPVE is driven by the linear and circular photogalvanic effects, exhibiting large photoconductivities under visible light. Furthermore, it can serve to identify the phase of the material, with the circular photogalvanic effect which also reflects spin-texture changes. With its multifunctional properties, SbSI emerges as a promising material candidate for efficient solar energy conversion and advanced electronics, with potential applications extending to spintronics., Comment: 16 + 10 pages, 7 + 5 figures, 1 + 4 Tables

The rich and fascinating physics of topological spin textures in van der Waals two-dimensional magnets has motivated recent growing interests, though a comprehensive understanding remains elusive. Here, in atomistic simulations on monolayer CrSBr, we find two magnetic phases emerging under non-equilibrium conditions at distinct temperatures, a standard ferromagnetic transition Tc and a lower temperature T*. Moreover, the real-space analysis of the spin texture reveals the emergence of metastable topological bimeron defects below T*, showing an algebraic-like decaying spin-spin correlation function. The Dzyaloshinskii-Moriya interaction, induced by the local site asymmetry in the centrosymmetric CrSBr monolayer, is proved to be the origin of the bimerons formation. Furthermore, the increasing bimerons density upon increasing the cooling rate follows a Kibble-Zurek behavior, suggesting a handle to drive and control topological bimerons below T*. Our results put forward CrSBr as an important candidate for the investigation of the dynamical behavior of bimerons in vdW magnets.

Gaining growing attention in spintronics is a class of magnets displaying zero net magnetization and spin-split electronic bands called altermagnets. Here, by combining density functional theory and symmetry analysis, we show that RuF$_4$ monolayer is a two-dimensional $d$-wave altermagnet. Spin-orbit coupling leads to pronounced spin splitting of the electronic bands at the $\Gamma$ point by $\sim 100$ meV and turns the RuF$_4$ into a weak ferromagnet due to non trivial spin-momentum locking that cants the Ru magnetic moments. The net magnetic moment scales linearly with the spin-orbit coupling strength. Using group theory we derive an effective spin Hamiltonian capturing the spin-splitting and spin-momentum locking of the electronic bands. Disentanglement of the altermagnetic and spin-orbit coupling induced spin splitting uncovers to which extent the altermagnetic properties are affected by the spin-orbit coupling. Our results move the spotlight to the non trivial spin-momentum locking and weak ferromagnetism in the two-dimensional altermagnets relevant for novel venues in this emerging field of material science research., Comment: 22 pages, 4 figures

The recent discovery of the persistence of long-range magnetic order when van der Waals layered magnets are thinned towards the monolayer limit has provided a tunable platform for the engineering of novel magnetic structures and devices. Here, we study the evolution of the electronic structure of CrGeTe$_3$ as a function of electron doping in the surface layer. From angle-resolved photoemission spectroscopy, we observe spectroscopic fingerprints that this electron doping drives a marked increase in $T_\mathrm{C}$, reaching values more than double that of the undoped material, in agreement with recent studies using electrostatic gating. Together with density functional theory calculations and Monte Carlo simulations, we show that, surprisingly, the increased $T_\mathrm{C}$ is mediated by the population of spin-minority Cr $t_{2g}$ states, forming a half-metallic 2D electron gas at the surface. We show how this promotes a novel variant of double exchange, and unlocks a significant influence of the Ge -- which was previously thought to be electronically inert in this system -- in mediating Cr-Cr exchange., Comment: 10 pages including supplementary information

Bilayer CrI$_3$ attracted much attention owing to peculiar switching between the layered ferromagnetic and antiferromagnetic order upon stacking alternation. This finding pointed out the importance of the apparently small interlayer exchange, yet, existing literature addresses only its isotropic part. To fill this gap, we combine the density functional theory with Hamiltonian modeling to examine the anisotropic interlayer exchange in bilayer CrI$_3$ - Dzyaloshinskii-Moriya (DMI) and the Kitaev interaction (KI). We develop and apply a novel computational procedure that yields the off-diagonal exchange matrix elements with $\mu$eV accuracy. Inspecting two types of bilayer stacking, we found a weak interlayer KI and much stronger DMI between the sublattices of monoclinic bilayer and their complete absence in rhombohedral bilayer. We show how these anisotropic interactions depend on the interlayer distance, stacking sequence, and the spin-orbit coupling strength and suggest the dominant superexchange processes at play. In addition, we demonstrate that the single-ion anisotropy largely depends on stacking, increasing by 50% from monoclinic to rhombohedral structure. Remarkably, our findings prove that iodines, owing to their spatially extended 5p orbitals featuring strong spin-orbit coupling, are extremely efficient in mediating DMI across the van der Waals gap in two-dimensional magnetic heterostructures. Given that similar findings were previously demonstrated only in metallic multilayers where the DMI shows a much longer range, our study gives promise that the chiral control of spin textures can be achieved in two-dimensional semiconducting magnetic bilayers whose ligands feature strong spin-orbit coupling., Comment: 17 one-column pages, 3 figures, submitted for publication

Mn$_3$Si$_2$Te$_6$ is a rare example of a layered ferrimagnet. It has recently been shown to host a colossal angular magnetoresistance as the spin orientation is rotated from the in- to out-of-plane direction, proposed to be underpinned by a topological nodal-line degeneracy in its electronic structure. Nonetheless, the origins of its ferrimagnetic structure remain controversial, while its experimental electronic structure, and the role of correlations in shaping this, are little explored to date. Here, we combine x-ray and photoemission-based spectroscopies with first-principles calculations, to probe the elemental-selective electronic structure and magnetic order in Mn$_3$Si$_2$Te$_6$. Through these, we identify a marked Mn-Te hybridisation, which weakens the electronic correlations and enhances the magnetic anisotropy. We demonstrate how this strengthens the magnetic frustration in Mn$_3$Si$_2$Te$_6$, which is key to stabilising its ferrimagnetic order, and find a crucial role of both exchange interactions extending beyond nearest-neighbours and anti-symmetric exchange in dictating its ordering temperature. Together, our results demonstrate a powerful methodology of using experimental electronic structure probes to constrain the parameter space for first-principles calculations of magnetic materials, and through this approach, reveal a pivotal role played by covalency in stabilising the ferrimagnetic order in Mn$_3$Si$_2$Te$_6$.

In this work we analyze the finite-size effects on the structural properties and on the polarization of the rhombohedral phase of HfO$_2$ subjected to a biaxial compressive strain. We show how the presence of surface charges affects the polarization, leading to a strong reduction with respect to its bulk value. This reduction can be ascribed to two mechanisms: the coupling between compressive strain and the phase-transition order parameter; the changes in the ferroelectric distortion. We give two alternative explanations of this phenomenon: from an atomistic point of view, analyzing the evolution of the bond lengths, and from a symmetry-analysis point of view, considering the changes in the amplitude of the symmetry-allowed distortions, when a slab configuration is considered. These results are independent on the slab-thickness in the considered range, suggesting the absence of a critical thickness for ferroelectricity in HfO$_2$, in agreement with the proposed improper nature of hafnia ferroelectricity.

Machine Learning (ML) techniques are revolutionizing the way to perform efficient materials modeling. Nevertheless, not all the ML approaches allow for the understanding of microscopic mechanisms at play in different phenomena. To address the latter aspect, we 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 zincblende and rocksalt crystal structures. The adopted models are trained using 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 performances at a very small computational cost. In addition, our approach allows 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 to the $p$-shell of the cation species., Comment: 11 pages and 5 figures with extra supplementary material

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 non-collinear-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.

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, ultra-compact 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 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., Comment: 3 figures

The effects of competing magnetic interactions in stabilizing different spin configurations are drawing a renewed attention in order to both 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 on a two-dimensional centrosymmetric triangular lattice, focusing on the interplay between the two-ion anisotropy (TIA) and the single-ion anisotropy (SIA). The effects of an external magnetic field applied perpendicularly to the magnetic layer are also investigated. By means of Monte Carlo simulations, we find a profusion 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, whereas the strength and sign of SIA, 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 anisotropic symmetric exchange in systems with dominant short-range interactions, at the same time predicting a rich variety of complex magnetic textures that may arise from a fine tuning of competing anisotropic mechanisms.

Ferroelectricity in hafnia is often regarded as a breakthrough discovery in ferroelectrics, potentially able to revolutionize the whole field. Despite increasing interests, a comprehensive understanding of the many factors driving the ferroelectric stabilization is still lacking. We here address the phase transition in terms of a Landau-theory-based approach, by analyzing symmetry-allowed distortions connecting the high-symmetry paraelectric tetragonal phase to the low-symmetry polar orthorhombic phase. By means of first-principles simulations, we find that the $\Gamma_{3-}$ polar mode is only weakly unstable, whereas the other two symmetry-allowed distortions, non-polar Y$_{2+}$ and anti-polar Y$_{4-}$ are hard modes. None of the modes, taken alone or combined with one other mode, is able to drive the transition: the key factor in stabilizing the polar phase is identified as the strong trilinear coupling among the three modes. Furthermore, the experimentally acknowledged importance of substrate-induced effects in the growth of HfO$_2$ ferroelectric thin films, along with the lack of a clear order parameter in the transition, suggested the extension of our analysis to strain effects. Our findings suggest a complex behaviour of the Y$_{2+}$ mode, which become unstable under certain strain conditions and an overall unstable behaviour for the $\Gamma_{3-}$ polar mode for all the strain states. A robust result emerges from our analysis: independently of the different applied strain (compressive or tensile, applied along orthorhombic axes), the need of a simultaneous excitation of the three coupled modes remain unaltered. Finally, when applied to mimic experimental growth conditions under strain, our analysis show a further stabilization of the ferroelectric phase with respect to the unstrained case, in agreeement with experimental findings.

Since its birth in the 1990s, semiconductor spintronics has suffered from poor compatibility with ferromagnets as sources of spin. While the broken inversion symmetry of some semiconductors may alternatively allow for spin-charge interconversion, its control by electric fields is volatile. Ferroelectric Rashba semiconductors stand as appealing materials unifying semiconductivity, large spin-orbit coupling, and non-volatility endowed by ferroelectricity. However, their potential for spintronics has been little explored. Here, we demonstrate the non-volatile, ferroelectric control of spin-to-charge conversion at room temperature in epitaxial GeTe films. We show that ferroelectric switching by electrical gating is possible in GeTe despite its high carrier density. We reveal a spin-to-charge conversion as effective as in Pt, but whose sign is controlled by the orientation of the ferroelectric polarization. The comparison between theoretical and experimental data suggests that spin Hall effect plays a major role for switchable conversion. These results open a route towards devices combining spin-based logic and memory integrated into a silicon-compatible material., Comment: 21 pages, 4 figures

The magnetic properties of two-dimensional VI3 bilayer are the focus of our first-principles analysis, highlighting the role of trigonal crystal-field effects and carried out in comparison with the CrI3 prototypical case, where the effects are absent. In VI3 bilayers, the empty a1g state - consistent with the observed trigonal distortion - is found to play a crucial role in both stabilizing the insulating state and in determining the inter-layer magnetic interaction. Indeed, an analysis based on maximally localized Wannier functions allows to evaluate the interlayer exchange interactions in two different VI3 stackings (labelled AB and AB'), to interpret the results in terms of 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 VI3 bilayer as an appealing candidate for electric-field-driven miniaturized spintronic devices., Comment: 8 pages, 5 figures, submitted for publication

Next-generation spintronic devices will benefit from low-dimensionality, ferromagnetism, and half-metallicity, possibly controlled by electric fields. We find these technologically-appealing features to be combined with an exotic microscopic origin of magnetism in doped CdOHCl, a van der Waals material from which 2D layers may be exfoliated. By means of first principles simulations, we predict homogeneous hole-doping to give rise to $p$-band magnetism in both the bulk and monolayer phases and interpret our findings in terms of Stoner instability: as the Fermi level is tuned via hole-doping through singularities in the 2D-like density of states, ferromagnetism develops with large saturation magnetization of 1 $\mu_B$ per hole, leading to a half-metallic behaviour for layer carrier densities of the order of 10$^{14}$ cm$^{-2}$. Furthermore, we put forward electrostatic doping as an additional handle to induce magnetism in monolayers and bilayers of CdOHCl. Upon application of critical electric fields perpendicular to atomically-thin-films (as low as 0.2 V/$A{\deg}$ and 0.5 V/$A{\deg}$ in the bilayer and monolayer case, respectively), we envisage the emergence of a magnetic half-metallic state. The different behaviour of monolayer vs bilayer systems, as well as an observed asymmetric response to positive and negative electric fields in bilayers, are interpreted in terms of intrinsic polarity of CdOHCl atomic stacks, a distinctive feature of the material. In perspective, given the experimentally accessible magnitude of critical fields in bilayer of CdOHCl, one can envisage $p$ band magnetism to be exploited in miniaturized spintronic devices.

Magnetoelectric effect is a fundamental physics phenomenon that synergizes electric and magnetic degrees of freedom to generate distinct material responses like electrically tuned magnetism, which serves as a key foundation of the emerging field of spintronics. Here, we show by first-principles studies that ferroelectric (FE) polarization of an In2Se3 monolayer can modulate the magnetism of an adjacent transition-metal (TM) decorated graphene layer via an FE induced electronic transition. The TM nonbonding d-orbital shifts downward and hybridizes with carbon p states near the Fermi level, suppressing the magnetic moment, under one FE polarization, but on reversed FE polarization this TM d-orbital moves upward, restoring the original magnetic moment. This finding of robust magnetoelectric effect in TM decorated graphene/In2Se3 heterostructure offers powerful insights and a promising avenue for experimental exploration of FE controlled magnetism in 2D 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, NiI$_2$. 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., Comment: submitted

The tetragonal phase of chromium (III) oxide, although unstable in the bulk, can be synthesized in epitaxial heterostructures. The 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., Comment: 23 pages, 5 figures, Accepted in PRB (2019)

The Dresselhaus and Rashba effects are well-known phenomena in solid-state physics, in which spin-orbit coupling (SOC) splits spin-up and spin-down energy bands of nonmagnetic non-centrosymmetric crystals. Here, we discover a new phenomenon, dubbed as band splitting with vanishing spin polarizations (BSVSP), in which, as usual, SOC splits the energy bands in nonmagnetic non-centrosymmetric systems; surprisingly, however, both split bands show no net spin polarization along certain high-symmetry lines in the Brillouin zone. In order to rationalize this phenomenon, we propose a new classification of point groups into pseudo-polar and non-pseudo-polar groups. By means of first-principles simulations, we demonstrate that BSVSP can take place in both symmorphic (e.g., bulk GaAs) and non-symmorphic systems (e.g., two dimensional ferroelectric SnTe). Furthermore, we propose a novel linear magnetoelectric coupling in reciprocal space, which could be employed to tune the spin polarization with an external electric field. The BSVSP effect and its manipulation could therefore pave a new way to novel spintronic devices.

Ferroelectric Rashba semiconductors (FERSC) have recently emerged as a promising class of spintronics materials. The peculiar coupling between spin and polar degrees of freedom responsible for several exceptional properties, including ferroelectric switching of Rashba spin texture, suggests that the electron's spin could be controlled by using only electric fields. In this regard, recent experimental studies revealing charge-to-spin interconversion phenomena in two prototypical FERSC, GeTe and SnTe, appear extremely relevant. Here, by employing density functional theory calculations, we investigate spin Hall effect (SHE) in these materials and show that it can be large either in ferroelectric or paraelectric structure. We further explore the compatibility between doping required for the practical realization of SHE in semiconductors and polar distortions which determine Rashba-related phenomena in FERSC, but which could be suppressed by free charge carriers. Based on the analysis of the lone pairs which drive ferroelectricity in these materials, we have found that the polar displacements in GeTe can be sustained up to a critical hole concentration of over $\sim 10^{21}$/cm$^{3}$, while the tiny distortions in SnTe vanish at a minimal level of doping. Finally, we have estimated spin Hall angles for doped structures and demonstrated that the spin Hall effect could be indeed achieved in a polar phase. We believe that the confirmation of spin Hall effect, Rashba spin textures and ferroelectricity coexisting in one material will be helpful for design of novel multifunctional spintronics devices operating without magnetic fields., Comment: 9 pages, 6 figures

Polar lacunar spinels, such as GaV$_4$S$_8$ and GaV$_4$Se$_8$, were proposed to host skyrmion phases under magnetic field. In this work, we put forward, as a candidate for N\'eel-type skyrmion lattice, the isostructural GaMo$_4$S$_8$, here systematically studied via both first-principles calculations and Monte Carlo simulations of model Hamiltonian. Electric polarization, driven by Jahn-Teller distortion, is predicted to arise in GaMo$_4$S$_8$, 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<10 nm). Furthermore, the possibly large exchange anisotropy of GaMo4S8 may lead to a ferroelectric-ferromagnetic ground state, as an alternative to the ferroelectric-skyrmionic one, calling for further experimental verification., Comment: 6 figures

Ferroelectric Rashba semiconductors (FERSC) are a novel class of multifunctional materials showing a giant Rashba spin splitting which can be reversed by switching the electric polarization. Although they are excellent candidates as channels in spin field effect transistors, the experimental research has been limited so far to semiconducting GeTe, in which ferroelectric switching is often prevented by heavy doping and/or large leakage currents. Here, we report that CsBiNb2O7, a layered perovskite of Dion-Jacobson type, is a robust ferroelectric with sufficiently strong spin-orbit coupling and spin texture reversible by electric field. Moreover, we reveal that its topmost valence band's spin texture is quasi-independent from the momentum, as a result of the low symmetry of its ferroelectric phase. The peculiar spin polarization pattern in the momentum space may yield the so-called "persistent spin helix", a specific spin-wave mode which protects the spin from decoherence in diffusive transport regime, potentially ensuring a very long spin lifetime in this material., Comment: 7 pages, 6 figures

We report a combined theoretical and experimental investigation of magnetic proximity and Hall transport in Pt/Cr bilayers. Density functional theory indicates that an interfacial magnetization can be induced in the Pt layer and a strong magnetocrystalline anisotropy with an easy axis out of plane arises in the antiferromagnet. A signal ascribed to the anomalous Hall effect is detected and associated to the interface between Pt and Cr layers. We show that this effect originates from the combination of proximity-induced magnetization and a nontrivial topology of the band structure at the interface.

Ferroelectric Rashba semiconductors (FERSC), in which Rashba spin-splitting can be controlled and reversed by an electric field, have recently emerged as a new class of functional materials useful for spintronic applications. The development of concrete devices based on such materials is, however, still hampered by the lack of robust FERSC compounds. Here, we show that the coexistence of large spontaneous polarisation and sizeable spin-orbit coupling is not sufficient to have strong Rashba effects and clarify why simple ferroelectric oxide perovskites with transition metal at the B-site are typically not suitable FERSC candidates. By rationalizing how this limitation can be by-passed through band engineering of the electronic structure in layered perovskites, we identify the Bi$_2$WO$_6$ Aurivillius crystal as the first robust ferroelectric with large and reversible Rashba spin-splitting, that can even be substantially doped without losing its ferroelectric properties. Importantly, we highlight that a unidirectional spin-orbit field arises in layered Bi$_2$WO$_6$, resulting in a protection against spin-decoherence.We highlight moreover that a unidirectional spin-orbit field arises in Bi$_2$WO$_6$, in which the spin-texture is so protected against spin-decoherence.

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 WTe$_2$, 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. (Continued. Please see the main article)., Comment: 33 pages, 7 figures

Geometric phases in condensed matter play a central role in topological transport phenomena such as the quantum, spin and anomalous Hall effect (AHE). In contrast to the quantum Hall effect - which is characterized by a topological invariant and robust against perturbations - the AHE depends on the Berry curvature of occupied bands at the Fermi level and is therefore highly sensitive to subtle changes in the band structure. A unique platform for its manipulation is provided by transition metal oxide heterostructures, where engineering of emergent electrodynamics becomes possible at atomically sharp interfaces. We demonstrate that the Berry curvature and its corresponding vector potential can be manipulated by interface engineering of the correlated itinerant ferromagnet SrRuO$_3$ (SRO). Measurements of the AHE reveal the presence of two interface-tunable spin-polarized conduction channels. Using theoretical calculations, we show that the tunability of the AHE at SRO interfaces arises from the competition between two topologically non-trivial bands. Our results demonstrate how reconstructions at oxide interfaces can be used to control emergent electrodynamics on a nanometer-scale, opening new routes towards spintronics and topological electronics., Comment: 8 pages, 4 figures, (+ Supplementary Information)

By performing density functional theory (DFT) 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 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., Comment: 8 pages, 4 figures

Previous studies showed that, as ferroelectric films become thinner, their Curie temperature (Tc) and polarization below Tc both typically decrease. In contrast, a recent experiment [Chang et al., Science 353, 274 (2016)] observed that atomic-thick SnTe films have a higher Tc than their bulk counterpart, which was attributed to extrinsic effects. Here, we find, using first-principles calculations, that the 0K energy barrier for the polarization switching (which is a quantity directly related to Tc) 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 free-standing defect-free SnTe thin films have a higher Tc 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.

The electrical manipulation of spins in semiconductors, without magnetic fields or auxiliary ferromagnetic materials, represents the holy grail for spintronics. The use of Rashba effect is very attractive because the k-dependent spin-splitting is originated by an electric field. So far only tiny effects in two-dimensional electron gases (2DEG) have been exploited. Recently, GeTe has been predicted to have bulk bands with giant Rashba-like splitting, originated by the inversion symmetry breaking due to ferroelectric polarization. In this work, we show that GeTe(111) surfaces with inwards or outwards ferroelectric polarizations display opposite sense of circulation of spin in bulk Rashba bands, as seen by spin and angular resolved photoemission experiments. Our results represent the first experimental demonstration of ferroelectric control of the spin texture in a semiconductor, a fundamental milestone towards the exploitation of the non-volatile electrically switchable spin texture of GeTe in spintronic devices., Comment: 18 pages, 4 figures

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, IrO$_2$ 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 IrO$_2$ 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 key role in its large spin Hall effect.

By combining bulk sensitive soft-X-ray angular-resolved photoemission spectroscopy and accurate first-principles calculations we explored the bulk electronic properties of WTe$_2$, a candidate type-II Weyl semimetal featuring a large non-saturating magnetoresistance. Despite the layered geometry suggesting a two-dimensional electronic structure, we find a three-dimensional electronic dispersion. We report an evident 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 $\Gamma$ point, differently from previous more surface sensitive ARPES experiments that additionally found a significant quasiparticle weight at the zone center. Moreover, we observe a significant sensitivity of the bulk electronic structure of WTe$_2$ around the Fermi level to electronic correlations and renormalizations due to self-energy effects, previously neglected in first-principles descriptions.

We investigate the electronic structure and the ferroelectric properties of the recently discovered multiferroic ScFeO$_3$ by means of ab-initio calculations. The $3d$ manifold of Fe in the half-filled configuration naturally favors an antiferromagnetic ordering, with a theoretical estimate of the antiferromagnetic N\'eel temperature in good agreement with the experimental values. We find that the inversion symmetry-breaking is driven by the off-centering of Sc atoms, which results in a large ferroelectric polarization of $\sim$105\,$\mu$C/cm$^{2}$. Surprisingly the ferroelectric polarization is sensitive to the local magnetization of the Fe atoms resulting in a large negative magnetoelectric interaction. This behavior is unexpected in type-I multiferroic materials because the magnetic and ferroelectric orders are of different origins.

It has been recently suggested that the coexistence of ferroelectricity and Rashba-like spin-splitting effects due to spin-orbit coupling in a single material may allow for a non-volatile electric control of spin degrees of freedom. In the present work, we compared the structural and ferroelectric properties of tetragonal and rhombohedral phases of ferroelectric BiAlO$_3$ by means of density-functional calculations. In both phases, we carefully investigated Rashba and Dresselhaus effects, giving rise to spin-splitting in their bulk electronic structure, particularly near the conduction band minimum, supplementing our first-principles results with an effective $ k\cdot p$ model analysis. The full reversal of the spin texture with ferroelectric polarization switching was also predicted. BiAlO$_3$ can therefore be considered as the first known oxide to exhibit a coexistence of ferroelectricity and Rashba-Dresselhaus effects., Comment: 8 pages, 5 figures

By means of density functional theory based calculations, we study the role of spin-orbit coupling in the new family of ABC hyperferroelectrics [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 semi-metal phase of finite concentration extension, which is robust against disorder, putting forward hyperferroelectrics as promising candidates for spin-orbitronic applications., Comment: 5 pages, 3 figures

The development of high efficiency perovskite solar cells has sparked a multitude of measurements on the optical properties of these materials. For the most studied methylammonium(MA)PbI$_3$ perovskite, a large range (6-55 meV) of exciton binding energies has been reported by various experiments. The existence of excitons at room temperature is unclear. For the MAPb$X_3$ perovskites we report on relativistic $GW$-BSE calculations. This method is capable to directly calculate excitonic properties from first-principles. At low temperatures it predicts exciton binding energies in agreement with the reported 'large' values. For MAPbI$_3$, phonon modes present in this frequency range have a negligible contribution to the ionic screening. By calculating the polarisation in time from finite temperature molecular dynamics, we show that at room temperature this does not change. We therefore exclude ionic screening as an explanation for the experimentally observed reduction of the exciton binding energy at room temperature.

In developing physical theories analogical reasoning has been found to be very powerful, as attested by a number of important historical examples. An analogy between two apparently different phenomena, once established, allows one to transfer information and bring new concepts from one phenomenon to the other. Here we discuss an important analogy between two widely different physical problems, namely, the Jahn-Teller distortion in molecular physics and the Rashba spin splitting in condensed matter physics. By exploring their conceptual and mathematical features and by searching for the counterparts between them, we examine the orbital texture in Jahn-Teller systems, as the counterpart of the spin texture of the Rashba physics, and put forward a possible way of experimentally detecting the orbital texture. Finally, we discuss the analogy by comparing the coexistence of linear Rashba+Dresselhaus effects and Jahn-Teller problems for specific symmetries, which allow for non-trivial spin and orbital textures, respectively., Comment: Text revised

The Jahn-Teller effect is a fascinating and ubiquitous phenomenon in modern quantum physics and chemistry. We propose a class of oxides with melilite structure Ba$_2$TGe$_2$O$_7$ (T=V,Ni) where Jahn-Teller distortions are the main responsibles for the appearance of electric polarization. At the hearth of the proposed mechanism lies the lack of inversion symmetry displayed by tetrahedrally coordinated transition-metal ions, which allows for the condensation of polar Jahn-Teller distortions, at odds with octahedral coordination typical of conventional ferroelectric oxides with perovskite structure. Since the noncentrosymmetric local environment of transition-metal ions also activates the proposed spin-dependent hybridization mechanism for magnetically-induced electric polarization, proper multiferroic phases with intrinsic magnetoelectric interaction could be realized in this class of low-symmetry materials.

The properties of two molecular-based magnetic helices, composed of 3$d$ metal Co and Mn ions bridged by Nitronyl Nitroxide radicals, are investigated by density functional calculations. Their peculiar and distinctive magnetic behavior is here elucidated by a thorough description of their magnetic, electronic, and anisotropy properties. Metal ions are antiferromagnetically coupled with the radicals, leading to a ferrimagnetically ordered ground state. A strong metal-radical exchange coupling is found, about 44 meV and 48 meV for Co- and Mn-helices, respectively. The latter have also relevant next-nearest-neighbor Mn-Mn antiferromagnetic interactions (of $\sim$ 6 meV). Co-sites are characterized by non-collinear uniaxial anisotropies, whereas Mn-sites are rather isotropic. A key result pertains to the Co-helix: the microscopic picture resulting from density-functional calculations allows us to propose a spin Hamiltonian of increased complexity with respect to the commonly employed Ising Hamiltonian, suitable for the study of finite-temperature behavior, and that seems to clarify the puzzling scenario of multiple characteristic energy scales observed in experiments., Comment: 17 pages, 9 figures

Motivated by the potential applications of their intrinsic cross-coupling properties, the interest in multiferroic materials has constantly increased recently, leading to significant experimental and theoretical advancements. From the theoretical point of view, recent progresses have allowed to identify different mechanisms responsible for the appearence of ferroelectric polarization coexisting with -- and coupled to -- magnetic properties. This chapter aims at reviewing the fundamental mechanisms devised so far, mainly in transition-metal oxides, which lie at the origin of multiferroicity.

By means of density functional theory calculations, we predict that several two dimensional AB binary monolayers, where A and B atoms belong to group IV or III-V, are ferroelectric. Dipoles arise from the buckled structure, where the A and B ions are located on the sites of a bipartite corrugated honeycomb lattice with trigonal symmetry. We discuss the emerging valley-dependent properties and the coupling of spin and valley physics, which arise from the loss of inversion symmetry, and explore the interplay between ferroelectricity and Rashba spin-spitting phenomena. We show that valley-related properties originate mainly from the binary nature of AB monolayers, while the Rashba spin-texture developing around valleys is fully controllable and switchable by reversing the ferroelectric polarization.

Electrostatic doping in materials can lead to various exciting electronic properties, such as metal-insulator transition and superconductivity, by altering the Fermi level position or introducing exotic phases. Cd3As2, a three-dimensional (3D) analog of graphene with extraordinary carrier mobility, was predicted to be a 3D Dirac semimetal, a feature confirmed by recent experiments. However, most research so far has been focused on metallic bulk materials that are known to possess ultra-high mobility and giant magnetoresistance but limited carrier transport tunability. Here, we report on the first observation of a gate-induced transition from band conduction to hopping conduction in single-crystalline Cd3As2 thin films via electrostatic doping by solid electrolyte gating. The extreme charge doping enables the unexpected observation of p-type conductivity in a 50 nm-thick Cd3As2 thin film grown by molecular beam epitaxy. More importantly, the gate-tunable Shubnikov-de Haas (SdH) oscillations and the temperature-dependent resistance reveal a unique band structure and bandgap opening when the dimensionality of Cd3As2 is reduced. This is also confirmed by our first-principles calculations. The present results offer new insights towards nanoelectronic and optoelectronic applications of Dirac semimetals in general, and provide new routes in the search for the intriguing quantum spin Hall effect in low-dimension Dirac semimetals, an effect that is theoretically predicted but not yet experimentally realized., Comment: 22 pages, 5 figures, accepted by NPG Asia Materials

GeTe has been proposed as the father compound of a new class of functional materials displaying bulk Rashba effects coupled to ferroelectricity: ferroelectric Rashba semiconductors. In nice agreement with first principle calculations, we show by angular resolved photoemission and piezo-force microscopy that GeTe displays surface and bulk Rashba bands arising from the intrinsic inversion symmetry breaking provided by the remanent ferroelectric polarization. This work points to the possibility to control the spin chirality of bands in GeTe by acting on its ferroelectric polarization., Comment: 10 pages, 4 figures

Recent experimental and theoretical work has shown that the double perovskite NaLaMnWO$_6$ exhibits antiferromagnetic ordering owing to the Mn $d$ states, and computational studies further predict it to exhibit a spontaneous electric polarization due to an improper mechanism for ferroelectricity [King \textit{et al., Phys.\ Rev.\ B}, 2009, \textbf{79}, 224428; Fukushima \textit{et al., Phys.\ Chem.\ Chem.\ Phys.}, 2011, \textbf{13}, 12186], which make it a candidate multiferroic material. Using first-principles density functional calculations, we investigate nine isostructural and isovalent $AA^{\prime}$MnWO$_6$ double perovskites ($A$=Na, K, and Rb; $A^{\prime}$=La, Nd, and Y) with the aim of articulating crystal-chemistry guidelines describing how to enhance the magnitude of the electric polarization through chemical substitution of the $A$-site while retaining long-range magnetic order. We find that the electric polarization can be enhanced by up to 150\% in compounds which maximize the difference in the ionic size of the $A$ and $A^{\prime}$ cations. By examining the tolerance factors, bond valences, and structural distortions (described by symmetry-adapted modes) of the nine compounds, we identify the atomic scale features that are strongly correlated with the ionic and electronic contributions to the electric polarization. We also find that each compound exhibits a purely electronic remnant polarization, even in the absence of a displacive polar mode. The analysis and design strategies presented here can be further extended to additional members of this family ($B$=Fe, Co, etc.), and the improper ferroelectric nature of the mechanism allows for the decoupling of magnetic and ferroelectric properties and the targeted design of novel multiferroics., Comment: 10 pages, 9 figures

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., Comment: Updated text, published version

In order to carefully address the interplay between substitutional disorder and spin-orbit-coupling in IV-VI alloys, we propose a novel theoretical approach that integrates the reliability of plane-wave based density-functional theory beyond the local-density approximation with the Coherent Potential Approximation. By applying the proposed method to ternary chalcogenide alloys, we predict a substantial robustness of spectral features close to the Fermi energy against substitutional disorder. Supplementing our first-principles calculations with the analysis of the $k \cdot p$ model for rock-salt chalcogenides, we show that the disorder self-energy is vanishingly small close to the band gap, thus allowing for bulk Rashba-like spin splitting to be observed in ferroelectric alloys, such as PbS$_x$Te$_{1-x}$, and protecting the band-character inversion related to the topological transition in the recently discovered Topological Crystalline Insulator Pb$_{1-x}$Sn$_x$Te., Comment: 5 pages, 3 figures

There is great interest in hybrid organic-inorganic materials such as metal-organic frameworks (MOFs). The compounds [C(NH$_{2}$)$_{3}$]M(HCOO)$_{3}$, where M=Cu$^{2+}$ or Cr$^{2+}$ are Jahn-Teller (JT) active ions, are MOF with perovskite topology which crystallizes in polar space group Pna2$_{1}$. In inorganic compounds, octahedral tilting and Jahn-Teller structural distortions are usually non-polar distortions. However, in this MOF cooperative interactions between the antiferro-distortive distortions of the framework and the C(NH2)$_{3}$ organic cation via hydrogen bonding breaks the inversion symmetry and induces a ferroelectric polarization.[Angew. Chem. Int. Ed. 50, 5847, 2011] Our ab-initio study supports the picture of an orbital-order-induced ferroelectricity, a rare example of dipolar ordering caused by electronic degrees of freedom. The switching of polarization direction implies the reversal of the weak ferromagnetic component. The microscopic mechanism in this JT-based MOF with ABX$_{3}$ perovskite structure displays a Hybrid Improper Ferroelectric (HIF) state, arising from a trilinear coupling between different structural deformations that comprise tilting, rotations and Jahn-Teller distortions of both the BX$_{3}$ framework and the organic cation at the A sites. Since these distortion modes in perovskite-inorganic compounds usually freeze-in at elevated temperatures, the trilinear coupling in MOF compounds may provide an interesting route towards high-temperature multiferroicity. These results offer an important starting point for tailoring multiferroic properties in this emerging class of materials for various technological applications. In particular, the high tunability of the ferroelectric polarization by means of the modification of the organic A cation has been recently shown[J. Am. Chem. Soc. 135 18126 (2013)], Comment: 8 pages; 3 figures- Supplementary material can be found at Wiley Online Library

The high Curie temperature multiferroic compound, CuO, has a quasidegenerate magnetic ground state that makes it prone to manipulation by the so called ``order-by-disorder'' mechanism. First principle computations supplemented with Monte Carlo simulations and experiments show that isovalent doping allows to stabilize the multiferroic phase in non-ferroelectric regions of the pristine material phase-diagram with experiments reaching a 250% widening of the ferroelectric temperature window with 5% of Zn doping. Our results allow to validate the importance of a quasidegenerate ground state on promoting multiferroicity on CuO at high temperatures and open a path to the material engineering of new multiferroic materials., Comment: 10 pages, 7 figures

Spin-orbit coupling is increasingly seen as a rich source of novel phenomena, as shown by the recent excitement around topological insulators and Rashba effects. We here show that the addition of ferroelectric degrees of freedom to a semiconductor featuring topologically-non-trivial properties, such as SnTe, merges the intriguing field of spin-orbit-driven physics with non-volatile functionalities appealing for spintronics. By using a variety of modelling techniques, we show that a strikingly rich sequence of phases can be induced in SnTe, when going from a room-temperature cubic phase to a low-temperature ferroelectric structure, ranging from a topological crystalline insulator to a time-reversal-invariant $Z_2$ topological insulator to a "ferroelectric Rashba semiconductor", exhibiting a huge electrically-controllable Rashba effect in the bulk band structure., Comment: 5 pages, 2 figures

The discovery of novel properties, effects or microscopic mechanisms in modern materials science is often driven by the quest for combining, into a single compound, several functionalities: not only the juxtaposition of the latter functionalities, but especially their coupling, can open new horizons in basic condensed matter physics as well as in technology. Semiconductor spintronics makes no exception. In this context, we have discovered by means of density-functional simulations that, when a sizeable spin-orbit coupling is combined with ferroelectricity, such as in GeTe, one obtains novel multifunctional materials - called Ferro-Electric Rashba Semi-Conductors (FERSC) - where, thanks to a giant Rashba spin-splitting, the spin texture is controllable and switchable via an electric field. This peculiar spin-electric coupling can find a natural playground in small-gap insulators, such as chalcogenides, and can bring brand new assets into the field of electrically-controlled semiconductor spintronics, Comment: 9 pages, 2 figures, in press on "Frontiers in Condensed Matter Physics"

Recent interests towards novel functionalities arising at domain walls of ferroic materials naturally call for a microscopic understanding. To this end, first-principles calculations have been performed in order to provide solid evidence of ferroelectricity in the twin walls of nonpolar CaTiO3 and magnetic CaMnO3. We show that ferroelectricity arises from rotation/tilting octahedral distortions --- cooperatively acting at the twin wall in both considered systems --- rather than from a proper secondary ferroelectric instability, as often believed. Our results are in excellent agreement with experimental observations of domain walls in CaTiO3. In addition, we show that magnetic properties at the twin wall in CaMnO3 are also modified, thus suggesting an unexplored route to achieve and detect multiferroic ordering in a single-phase material.