Machine-learning techniques are revolutionizing the way to perform efficient materials modeling. We here propose a combinatorial machine-learning approach to obtain physical formulas based on simple and easily accessible ingredients, such as atomic properties. The latter are used to build materials features that are finally employed, through linear regression, to predict the energetic stability of semiconducting binary compounds with respect to zinc blende and rocksalt crystal structures. The adopted models are trained using a dataset built from first-principles calculations. Our results show that already one-dimensional (1D) formulas well describe the energetics; a simple grid-search optimization of the automatically obtained 1D-formulas enhances the prediction performance at a very small computational cost. In addition, our approach allows one to highlight the role of the different atomic properties involved in the formulas. The computed formulas clearly indicate that “spatial” atomic properties (i.e., radii indicating maximum probability densities for 𝑠,𝑝,𝑑 electronic shells) drive the stabilization of one crystal structure with respect to the other, suggesting the major relevance of the radius associated with the 𝑝-shell of the cation species.
Curved magnets attract considerable interest for their unusually rich phase diagram, often encompassing exotic (e.g., topological or chiral) spin states. Micromagnetic simulations are playing a central role in the theoretical understanding of such phenomena; their predictive power, however, rests on the availability of reliable model parameters to describe a given material or nanostructure. Here we demonstrate how noncollinear-spin polarized density-functional theory can be used to determine the flexomagnetic coupling coefficients in real systems. By focusing on monolayer CrI3, we find a crossover as a function of curvature between a magnetization normal to the surface to a cycloidal state, which we rationalize in terms of effective anisotropy and Dzyaloshinskii-Moriya contributions to the magnetic energy. Our results reveal an unexpectedly large impact of spin-orbit interactions on the curvature-induced anisotropy, which we discuss in the context of existing phenomenological models
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.
The effects of competing magnetic interactions in stabilizing different spin configurations are drawing renewed attention in order to unveil emerging topological spin textures and to highlight microscopic mechanisms leading to their stabilization. The possible key role of the two-site exchange anisotropy in selecting specific helicity and vorticity of skyrmionic lattices has only recently been proposed. In this work, we explore the phase diagram of a frustrated localized magnet characterized by a two-dimensional centrosymmetric triangular lattice, focusing on the interplay between the two-ion anisotropy and the single-ion anisotropy. The effects of an external magnetic field applied perpendicularly to the magnetic layer, are also investigated. By means of Monte Carlo simulations, we find an abundance of different spin configurations, going from trivial to high-order Q skyrmionic and meronic lattices. In closer detail, we find that a dominant role is played by the two-ion over the single-ion anisotropy in determining the planar spin texture; the strength and the sign of single ion anisotropy, together with the magnitude of the magnetic field, tune the perpendicular spin components, mostly affecting the polarity (and, in turn, the topology) of the spin texture. Our analysis confirms the crucial role of the anisotropic symmetric exchange in systems with dominant short-range interactions; at the same time, we predict a rich variety of complex magnetic textures, which may arise from a fine tuning of competing anisotropic mechanisms.
The magnetic properties of the two-dimensional VI3 bilayer are the focus of our first-principles analysis, highlighting the role of t2g orbital splitting and carried out in comparison with the CrI3 prototypical case, where the splitting is negligible. In VI3 bilayers, the empty a1g state is found to play a crucial role in both stabilizing the insulating state and in determining the interlayer magnetic interaction. Indeed, an analysis based on maximally localized Wannier functions allows one to evaluate the interlayer exchange interactions in two different VI3 stackings (labeled AB and AB′), to interpret the results in terms of the virtual-hopping mechanism, and to highlight the strongest hopping channels underlying the magnetic interlayer coupling. Upon application of electric fields perpendicular to the slab, we find that the magnetic ground state in the AB′ stacking can be switched from antiferromagnetic to ferromagnetic, suggesting the VI3 bilayer as an appealing candidate for electric-field-driven miniaturized spintronic devices.
Topological spin structures, such as magnetic skyrmions, hold great promises for data storage applications, thanks to their inherent stability. In most cases, skyrmions are stabilized by magnetic fields in non-centrosymmetric systems displaying the chiral Dzyaloshinskii-Moriya exchange interaction, while spontaneous skyrmion lattices have been reported in centrosymmetric itinerant magnets with long-range interactions. Here, a spontaneous anti-biskyrmion lattice with unique topology and chirality is predicted in the monolayer of a semiconducting and centrosymmetric metal halide, NiI2. Our first-principles and Monte Carlo simulations reveal that the anisotropies of the short-range symmetric exchange, when combined with magnetic frustration, can lead to an emergent chiral interaction that is responsible for the predicted topological spin structures. The proposed mechanism finds a prototypical manifestation in two-dimensional magnets, thus broadening the class of materials that can host spontaneous skyrmionic states. Skyrmions, topological spin textures, are typically stabilized by the Dzyaloshinskii-Moriya interaction and an applied magnetic field. In this theoretical study, by analysing monolayer NiI2, the authors suggest that two-site anisotropy with magnetic frustration can stabilize a skyrmion lattice.