We study twisted bilayer WSe_2 within a continuum moiré model and introduce a method for treating finite geometries directly in the continuum framework, overcoming limitations associated with momentum-space formulations and Wannier obstructions. By projecting a confinement potential onto bulk moiré eigenstates, we obtain a real-space description of edge physics without lattice models. Applying this approach to nanoribbons, we demonstrate chiral edge modes consistent with bulk Chern numbers and reveal their moiré-scale character. In the magic-angle regime, these states are strongly localized, exhibit layer-polarized counter-propagating modes, and are electrically tunable via a displacement field, enabling control of localization, hybridization, and topological transitions. Our results establish a general framework for boundary physics in topological moiré materials.

Recently, there has been renewed interest in coupling of spin waves (magnons) and collective charge oscillations (plasmons), especially in two-dimensional systems. Several mechanisms of the magnon-plasmon hybridization in ferromagnetic and antiferromagnetic systems have been proposed. Here, we consider another mechanism of magnon-plasmon hybridization, which is based on the linear magnetoelectric interaction. As a specific system, we consider a monolayer of vanadium-based diselenide with perpendicular easy-axis magnetic anisotropy and Dzialoshinskii-Moriya interaction. The derived parameter of magnon-plasmon coupling is proportional to the magnetoelectric constant. Assuming for this constant an adequate experimental value, we calculate dispersion relations of the hybridized magnon-plasmon modes. Moreover, we also show that an external electric field normal to the layer (due to a gate voltage) can be used as a tool to tune the magnon modes and this way also hybridized magnon-plasmon coupling. A specific case of magnon-plasmon coupling based on tuning Dzialoshinskii-Moriya interaction is also considered.

We consider longitudinal electronic transport in a graphene monolayer with an external in-plane magnetic field and with extrinsic spin-orbit Rashba interaction. Our main interest is in the in-plane magnetoresistance, observed experimentally. We show, that scattering on Rashba spin-orbit fluctuations leads to a negative magnetoresistance, in agreement with experimental observations. To calculate transport properties we assume an effective model valid for low energy states around the Dirac points, and use the Green function method to derive the electron scattering rate and longitudinal conductivity.

We have considered theoretically nonlinear transport phenomena known as bilinear magnetoresistance (BMR) and nonlinear planar Hall effect (NPHE) within the effective model describing surface states of a 3D topological insulator. Both phenomena can occur in nonmagnetic materials with strong spin-orbit interaction and reveal a term that depends linearly on the charge current density (external electric field) and in-plane magnetic field. In earlier studies, the physical mechanism of BMR and NPHE was related to scattering on spin-momentum locking inhomogeneities or to the hexagonal warping of Dirac cones. Here, we focus on another mechanism related to scattering on impurities that inherently contain spin-orbit coupling. Using the Green's function formalism and diagramatic method, we have derived analytical results for diagonal and transverse conductivities and determined nonlinear signals. The analytical and numerical results on BMR and NPHE indicate the possibility of determining the material constants, such as the Fermi wave vector and spin-orbit coupling parameter, by simple magnetotransport measurements.

We consider the anomalous, spin, valley, and valley spin Hall effects in a pristine ex-so-tic graphene-based van-der-Waals (vdW) heterostructure consisting of a bilayer graphene (BLG) between semiconducting van-der-Waals material with strong SOC (e.g., WS_2) and ferromagnetic and insulating vdW material (e.g. Cr_2Ge_2Te_6). Reducing the effective Hamiltonian derived by Zollner et al [Phys. Rev. Lett. 125(19), 196402 (2020)] to low-energy states, and using the Green function formalism, we derived analytical results for the Hall conductivities as a function of the Fermi level and gate voltage. Depending on these parameters, we found quantized valley conductivity.

We investigate topological Hall effects in a metallic antiferromagnetic (AFM) thin film and/or at the interface of an AFM insulator-normal metal bilayer with a single skyrmion in the diffusive regime. To determine the spin and charge Hall currents, we employed a Boltzmann kinetic equation with both spin-dependent and spin-flip scatterings. The interaction between conduction electrons and static skyrmions is included in the Boltzmann equation via the corresponding emergent magnetic field arising from the skyrmion texture. We compute intrinsic and extrinsic contributions to the topological spin Hall effect and spin accumulation, induced by an AFM skyrmion. We show that although the spin Hall current vanishes rapidly outside the skyrmion, the spin accumulation can be finite at the edges far from the skyrmion, provided the spin diffusion length is longer than the skyrmion radius. In addition, We show that in the presence of a spin-dependent relaxation time, the topological charge Hall effect is finite and we determine the corresponding Hall voltage. Our results may help to explore antiferromagnetic skyrmions by electrical means in real materials.

Bilinear magnetoresistance has been studied theoretically in 2D systems with isotropic cubic form of Rashba spin–orbit interaction. We have derived the effective spin–orbital field due to current-induced spin polarization and discussed its contribution to the unidirectional system response. The analyzed model can be applied to the semiconductor quantum wells as well as 2DEG at the surfaces and interfaces of perovskite oxides.

In this paper we analyse quantized spin waves (also referred to as magnons) in bilayers of two-dimensional van der Waals materials, like Vanadium-based dichalcogenides, VX2 2 (X = S, Se, Te) and other materials of similar symmetry. We assume that the materials exhibit Dzyaloshinskii-Moriya interaction and in-plane easy- axis magnetic anisotropy due to symmetry breaking induced externally (e.g. by strain, gate voltage, proximity effects to an appropriate substrate/oberlayer, etc.). The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong in-plane magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Holstein-Primakoff-Bogoliubov transformation. Accordingly, the description takes into account quantum antiferromagnetic fluctuations. However, it is limited to linear spinwave modes. The Dzyaloshinskii-Moriya interaction is shown to modify the spin wave spectrum of the bilayers, making its low energy part qualitatively similar to the electronic spectrum of the Rashba spin-orbit model.

We analyze magnetic properties of monolayers and bilayers of chromium trihalides, CrI_3, in two different stacking configurations: AA and rhombohedral ones. Our main focus is on the corresponding Curie temperatures, hysteresis curves, equilibrium spin structures, and spin wave excitations. To obtain all these magnetic characteristic, we employ the atomistic spin dynamics and Monte Carlo simulation techniques. The model Hamiltonian includes isotropic exchange coupling, magnetic anisotropy, and Dzyaloshinskii-Moriya interaction. Though the latter is relatively weak in CrI_3, we consider a more general case assuming also an enhancement of Dzyaloshinskii-Moriya interaction in the corresponding Janus structures and by external electric fields. An important issue of the analysis is the correlation between hysteresis curves and spin configurations in the system, as well as formation of the skyrmion textures.

We study the effect of spin-momentum locking inhomogeneity on the planar Hall effect in topological insulators (TIs). Using the minimal model describing surface states of 3D TIs and semiclassical Boltzmann formalism, we have derived the planar Hall conductivity within the generalized relaxation time approximation. We have found that the total planar Hall conductivity is a sum of linear and nonlinear to the external electric field components. The linear term is a conventional planar Hall conductivity which scales quadratically with an external magnetic field, whereas the nonlinear term reveals bilinear behaviour, i.e., changes its sign when either charge current density or in-plane magnetic field orientation is reversed. We have shown that the emergent nonlinear planar Hall effect is a consequence of spin-momentum locking inhomogeneity in the TIs with isotropic energy dispersion and dominates under the conventional planar Hall effect.

Atomically thin van der Waals magnetic materials offer exceptional opportunities to mechanically and electrically manipulate magnetic states and spin textures. The possibility of efficient spin transport in these materials makes them promising for the development of novel nanospintronics technology. Using atomistic spin dynamics simulations, we investigate magnetic ground state, magnon dispersion, critical temperature, and magnon spin transport in CrCl 3 bilayers in the absence and presence of compressive and tensile strains. We show that in the presence of mechanical strain, the magnon band gap at the I . ' point and the critical temperature of the bilayer are increased. Furthermore, our simulations show that the magnon diffusion length is reduced in the presence of strain. Moreover, by exciting magnons through the spin Seebeck effect and spin Hall -induced torque, we illustrate distinctions between magnon spin transport in the antiferromagnetic state, under compressive strains, and ferromagnetic states, under tensile strains or in the unstrained case.

The linear and nonlinear Hall effects in 2D systems are considered theoretically within the isotropic k-cubed Rashba model. We show that the presence of an out-of-plane external magnetic field or net magnetization is a necessary condition to induce a nonzero Berry curvature in the system, whereas an in-plane magnetic field tunes the Berry curvature leading to the Berry curvature dipole. Interestingly, in the linear response regime, the conductivity is dominated by the intrinsic component (Berry curvature component), whereas the second-order correction to the Hall current (i.e., the conductivity proportional to the external electric field) is dominated by the component independent of the Berry curvature dipole.

We consider a film of a topological insulator (TI) sandwiched between two ferromagnetic (FM) layers. The system is additionally under an external gate voltage. The surface electron states of TI are magnetized due to the magnetic proximity effect to the ferromagnetic layers. The magnetization of ferromagnetic layers can be changed by applying an external magnetic field or by varying thickness of the topological insulator (owing to the interlayer exchange coupling). The change in the magnetic configuration of the system affects the transport properties of the surface electronic states. Using the Green function formalism, we calculate spin polarization, anomalous Hall effect, and magnetoresistance of the system. We show, among others, that by tuning the gate voltage and magnetizations of the top and bottom FM layers, one can observe the topological transition to the quantum anomalous Hall state.

The topological charge Hall effect (TCHE) and the topological spin Hall effect (TSHE), arising from ferromagnetic (FM) and antiferromagnetic (AFM) skyrmions, respectively, can be elucidated through the emergence of spin-dependent Berry gauge fields that affect the adiabatic flow of electrons within the skyrmion texture. TCHE is absent in systems with parity-time (PT) symmetry, such as collinear AFM systems. In this paper, we theoretically study TCHE and TSHE in a canted antiferromagnet within the diffusive transport regime. Spin canting or weak ferromagnetism in canted AFMs, which break the PT symmetry, may arise, e.g., from strong homogeneous Dzyaloshinskii-Moriya interactions. Using a semiclassical Boltzmann approach, we obtain diffusion equations for the spin and charge accumulations in the presence of finite spin flip and spin-dependent momentum relaxation times. We show that the weak ferromagnetic moment stemming from spin canting and the subsequent breaking of PT symmetry, results in the emergence of both finite TCHE and TSHE in AFM systems.

In this paper we analyze spin waves in bilayers of two-dimensional van der Waals materials, like Vanadium based dichalcogenides, VX$_2$ (X=S, Se, Te) and other materials of similar symmetry. We assume that the materials exhibit Dzialoshinskii- Moriya interaction and in-plane easy-axis magnetic anisotropy due to symmetry breaking induced externally (eg, by strain, gate voltage, proximity effects to an appropriate substrate/oberlayer, etc). The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong in-plane magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Hollstein-Primakoff-Bogolubov transformation.

Transition metal dichalcogenides (TMDs), like VS2, display unique electronic, magnetic, and optical properties, making them promising for spintronic and optoelectronic applications. Using first-principles calculations based on the Density Functional Theory (DFT), we study the effect of Fe-doping on the electronic and magnetic properties of a VS2 monolayer. The pristine VS2 monolayer has ferromagnetic order and a small energy bandgap. This work aims to comprehensively study the substitution of selected Vanadium atoms in the VS2 monolayer by Iron (Fe) atoms, where the substitution concerns Vanadium atoms at various sites within the 2x2 and 3x3 supercells. This leads to significant modifications of the electronic band structure, magnetic anisotropy energy (MAE), and optical response (e.g., dielectric constant and absorption coefficient). The results provide valuable insights into engineering the VS2 monolayer properties for future applications, ranging from spintronics to cancer therapy in medical science.

It is well known that electronic states in graphene with a uniform Rashba spin -orbit interaction and uniform magnetization, e.g., due to exchange coupling to a magnetic substrate, display an energy gap around the Dirac K and K ' points. When the magnetization of graphene is nonuniform and forms a magnetic domain wall, electronic states localized at the wall emerge in the energy gap. In this paper we show that similar localized electronic states appear in the gap when the graphene is uniformly magnetized, while a domain wall appears in the Rashba spin -orbit interaction (i.e., opposite signs of the Rashba parameter on both sides of the wall). These electronic states propagate along the wall and are localized exponentially at the Rashba domain wall. They form narrow and nearly parabolic (at small wave vectors) bands, with relatively large effective electron mass. However, contrary to the magnetic domain wall, these states do not close the energy gap. We also consider the situation when the magnetic domain wall coexists with the Rashba domain wall, and both walls are localized at the same position. Electronic states due to the interplay of both domain walls are determined analytically and it is shown that the electronic states localized at the walls close the gap when a magnetic domain wall (symmetric or asymmetric) exists, independently of the Rashba parameter behavior.

Van der Waals magnetic materials are currently of great interest as materials for applications in future ultrathin nanoelectronics and nanospintronics. Due to weak coupling between individual monolayers, these materials can be easily obtained in the monolayer and bilayer forms. The latter are of specific interest as they may be considered as natural two-dimensional spin valves. In this paper, we study theoretically spin waves in bilayers of transition metal dichalcogenides. The considerations are carried within the general spin wave theory based on effective spin Hamiltonian and Hollstein-Primakoff-Bogolubov transformation. The spin Hamiltonian includes intra-layer as well as inter-layer nearest-neighbour exchange interactions, easy-plane anisotropy, and additionally a weak in-plane easy-axis anisotropy. The bilayer systems consist of two ferromagnetic (in-plane magnetization) monolayers that are coupled either ferromagnetically or antiferromagnetically. In the latter case, we analyse the spin wave spectra in all magnetic phases, i.e. in the antiferromagnetic, spin-flop, and ferromagnetic ones.

Using the Density Functional Theory (DFT) calculations, we determined the electronic and magnetic properties of a T-phase VS$_2$ bilayer as a function of tensile and compressive strain. First, we determine the ground state structural parameters and then the band structure, magnetic anisotropy, exchange parameters, and Curie temperature. Variation of these parameters with the strain is carefully analyzed and described. The easy-plane anisotropy, which is rather small in the absence of strain, becomes remarkably enhanced by tensile strain and reduced almost to zero by compressive strain. We also show that the exchange parameters and the Curie temperature are remarkably reduced for the compressive strains below roughly -4$\%$.

Dzyaloshinski-Moriya interaction, known also as the antisymmetric exchange coupling, leads to a variety of interesting spin phenomena, like spin canting, skyrmion formation, nonreciprocal spin wave propagation, and others. In this paper we analyze spin waves in monolayers of two-dimensional van-der-Waals materials, such as Vanadium-based dichalcogenides, VX2 (X=S, Se, Te) and other materials of similar symmetry. The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Holstein-Primakoff-Bogoliubov transformation.