We investigated the element-specific electronic structure and charge-carrier dynamics of a single-crystal ferromagnet CoS2 with complementary x-ray spectroscopy techniques. Hard x-ray photoemission (HAXPES) is used to provide crucial information on the bulk electronic structure and chemical bonding in CoS2 that is compared against the isoelectronic paramagnet CoSe2. The Co 1⁢𝑠 core-level line shows several satellite features for CoS2, showing explicit charge-transfer processes and local screening of the core hole by S ligands, whereas no such features are observed in CoSe2. The satellite structures indicate the electronic configuration of divalent Co2+ as a combination of 𝑑8⁢Ḻ and 𝑑9⁢Ḻ2 in addition to the nominal ionic 𝑑7 state, where Ḻ represents an S 3⁢𝑝 hole. We employ resonant Auger spectroscopy across the S 𝐾-edge for CoS2 to obtain electron delocalization times to adjacent Co atomic sites. The fast carrier dynamics are attributed to strongly screened Coulomb interactions and hence a facile carrier delocalization. The strong hybridization formed between the Co 3⁢𝑑 and S 3⁢𝑝 states with pronounced charge-transfer character reflects a self-doped system with a finite density 𝑛 of holes at the sulfur site (Ḻ𝑛), in line with recent models that indicate a negative charge-transfer energy for CoS2. In addition to HAXPES data, we also report on experimental and theoretical 𝐿-edge x-ray absorption and x-ray magnetic circular dichroism data for CoS2 that demonstrate multiconfiguration effects in the excitation process. To enable a direct comparison of the experimental spectra, we used density functional theory calculations to obtain the projected density of states to describe the ground-state electronic structure. The existence of fast carrier dynamics and strong charge-transfer properties, demonstrated in this study, highlights the unique nature of CoS2 with a wide potential in topological spintronics applications and integration in energy-related device platforms.

Despite extensive research on magnetic skyrmions and antiskyrmions, a significant challenge remains in crafting nontrivial high-order skyrmionic textures with varying, or even tailor-made, topologies. We address this challenge, by focusing on a construction pathway of skyrmionic metamaterials within a monolayer thin film and suggest several skyrmionic metamaterials that are surprisingly stable, i.e., long-lived, due to a self-stabilization mechanism. This makes these new textures promising for applications. Central to our approach is the concept of ’simulated controlled assembly’, in short, a protocol inspired by ’click chemistry’ that allows for positioning topological magnetic structures where one likes, and then allowing for energy minimization to elucidate the stability. Utilizing high-throughput atomistic-spin-dynamic simulations alongside state-of-the-art AI-driven tools, we have isolated skyrmions (topological charge Q = 1), antiskyrmions (Q = − 1), and skyrmionium (Q = 0). These entities serve as foundational ’skyrmionic building blocks’ to form the here-reported intricate textures. In this work, two key contributions are introduced to the field of skyrmionic systems. First, we present a novel combination of atomistic spin dynamics simulations and controlled assembly protocols for the stabilization and investigation of new topological magnets. Second, using the aforementioned methods we report on the discovery of skyrmionic metamaterials.

We develop a multiscale approach to magnetoelectric effects, bridging atomistic and continuum models, with all parameters determined from ab initio electronic structure calculations. We show that the parameters of the model are equivalent to the electric field-induced Dzyaloshinski-Moriya interactions. After careful validation, we apply the models to study electric polarization and dipole moments carried by spin spirals and topological solitons, in the form of magnetic domain walls and Skyrmions, in the prototypical 2D magnet CrI<inf>3</inf>. We show that the reduced symmetry of the material leads to additional magnetoelectric coupling terms, dominating over those expected in high symmetry (cubic) materials. An interesting consequence is that Skyrmions carry an out-of-plane electric dipole moment, while that of anti-Skyrmions is an order of magnitude larger and in-plane. Finally, we discuss the possibility to stabilize non-collinear spin states using electric fields.

We have simulated the magnetic Bragg scattering in transmission electron microscopy in two antiferromagnetic compounds, NiO and LaMnAsO. This weak magnetic phenomenon was experimentally observed in NiO by Loudon (2012). We have computationally reproduced Loudon's experimental data, and for comparison we have performed calculations for the LaMnAsO compound as a more challenging case, containing lower concentration of magnetic elements and strongly scattering heavier non-magnetic elements. We have also described thickness and voltage dependence of the intensity of the antiferromagnetic Bragg spot for both compounds. We have considered lattice vibrations within two computational approaches, one assuming a static lattice with Debye-Waller smeared potentials, and another explicitly considering the atomic vibrations within the quantum excitations of phonons model (thermal diffuse scattering). The structural analysis shows that the antiferromagnetic Bragg spot appears in between (111) and (000) reflections for NiO, while for LaMnAsO the antiferromagnetic Bragg spot appears at the position of the (010) reflection in the diffraction pattern, which corresponds to a forbidden reflection of the crystal structure. Calculations predict that the intensity of the magnetic Bragg spot in NiO is significantly stronger than thermal diffuse scattering at room temperature. For LaMnAsO, the magnetic Bragg spot is weaker than the room-temperature thermal diffuse scattering, but its detection can be facilitated at reduced temperatures.

We have modeled the magnetic Bragg scattering in two antiferromagnetic materials, NiO and LaMnAsO, using transmission electron microscopy. Experimentally, Loudon detected these weak magnetic phenomena in NiO. As a more difficult situation with a lower concentration of magnetic elements and higher concentration of heavier non-magnetic elements that significantly scatter, we did computations for the LaMnAsO compound in order to compare our computational replication of Loudon's experimental data. Additionally, we have discussed the antiferromagnetic Bragg spot's thickness and voltage dependency for both compounds. We used two computational methods, one assuming a static lattice with smeared Debye-Waller potentials and the other explicitly taking into account the atomic vibrations within the quantum excitations of phonons model (thermal diffuse scattering). According to the structural study, the antiferromagnetic Bragg spot in NiO is located between the (111) and (000) reflections. However, in LaMnAsO, it is located at the site of the (110) reflection in the diffraction pattern, which is a forbidden reflection of the crystal structure. According to calculations, the magnetic Bragg spot in NiO has an intensity that is much greater than thermal diffuse scattering at room temperature. The magnetic Bragg spot for LaMnAsO is weaker than the thermal diffuse scattering at room temperature, but its identification can be made easier at lower temperatures.

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.

A systematic numerical study of non-pairwise vortex interaction forces in the Ginzburg-Landau model for single-and multicomponent superconductivity is presented. The interactions are obtained by highly accurate numerical free energy minimization. In particular a three-body interaction is defined as the difference between the total interaction and sum of pairwise interactions in a system of three vortices and such interactions are studied for single and two-component type-1, type-2, and type-1.5 superconductors. In the investigated regimes, the three-body inter action is found to be short-range repulsive but long-range attractive in the type-1 case, zero in the critical kappa (Bogomoln'y) case, attractive in the type-2 case and repulsive in the type-1.5 case. Some systems of four vortices are also studied and results indicate that four-body forces are of substantially less significance than the three-body interactions.