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.

Dirac fermions play a central role in the study of topological phases, for they can generate a variety of exotic states, such as Weyl semimetals and topological insulators. The control and manipulation of Dirac fermions constitute a fundamental step toward the realization of novel concepts of electronic devices and quantum computation. By means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, here, we show that Dirac states can be effectively tuned by doping a transition metal sulfide, BaNiS2, through Co/Ni substitution. The symmetry and chemical characteristics of this material, combined with the modification of the charge-transfer gap of BaCo1−xNixS2 across its phase diagram, lead to the formation of Dirac lines, whose position in k-space can be displaced along the Γ−M symmetry direction and their form reshaped. Not only does the doping x tailor the location and shape of the Dirac bands, but it also controls the metal-insulator transition in the same compound, making BaCo1−xNixS2 a model system to functionalize Dirac materials by varying the strength of electron correlations.

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.

Extremely large magnetoresistance (XMR), observed in transition-metal dichalcogenides,
WTe2, has attracted recently a great deal of research interest as it shows no sign of saturation up to a magnetic field as high as 60 T, in addition to the presence of type-II Weyl fermions. Currently, there is a great deal of discussion on the role of band structure changes in the temperature-dependent XMR in this compound. In this contribution, we study the band structure of WTe2 using angle-resolved photoemission spectroscopy and first-principles calculations to demonstrate that the temperature-dependent band structure has no substantial effect on the temperature-dependent XMR, as our measurements do not show band structure changes upon increasing the sample temperature between 20 and 130 K. We further observe an electronlike surface state, dispersing in such a way that it connects the top of bulk holelike band to the bottom of bulk electronlike band. Interestingly, similarly to bulk states, the surface state is also mostly intact with the sample temperature. Our results provide valuable information in shaping the mechanism of temperature-dependent XMR in WTe2.

Transition-metal dichalcogenides (WTe2 and MoTe2) have recently drawn much attention, because of the
nonsaturating extremely large magnetoresistance (XMR) observed in these compounds in addition to the
predictions of likely type-II Weyl semimetals. Contrary to the topological insulators or Dirac semimetals where XMR is linearly dependent on the field, in WTe2 and MoTe2 the XMR is nonlinearly dependent on the field, suggesting an entirely different mechanism. Electron-hole compensation has been proposed as a mechanism of this nonsaturating XMR in WTe2, while it is yet to be clear in the case of MoTe2 which has an identical crystal structure of WTe2 at low temperatures. In this Rapid Communication, we report low-energy electronic structure and Fermi surface topology of MoTe2 using angle-resolved photoemission spectrometry (ARPES) technique and first-principles calculations, and compare them with that of WTe2 to understand the mechanism of XMR. Our measurements demonstrate that MoTe2 is an uncompensated semimetal, contrary to WTe2 in which compensated electron-hole pockets have been identified, ruling out the applicability of charge compensation theory for the nonsaturating XMR in MoTe2. In this context, we also discuss the applicability of other existing conjectures on the XMR of these compounds.

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.

Topological insulators are a promising class of materials for applications in the field of spintronics. New perspectives in this field can arise from interfacing metal–organic molecules with the topological insulator spin-momentum locked surface states, which can be perturbed enhancing or suppressing spintronics-relevant properties such as spin coherence. Here we show results from an angle-resolved photemission spectroscopy (ARPES) and scanning tunnelling microscopy (STM) study of the prototypical cobalt phthalocyanine (CoPc)/Bi2Se3 interface. We demonstrate that that the hybrid interface can act on the topological protection of the surface and bury the Dirac cone below the first quintuple layer.