Modification of the electronic and crystal structure of zero-layer graphene grown on $6H$-SiC(0001) after Co intercalation is reported. Using a wide range of techniques including angle-resolved photoelectron spectroscopy, x-ray photoelectron spectroscopy, Raman spectroscopy, low-energy electron diffraction, we found that zero-layer graphene on SiC transforms into graphene monolayer as a result of cobalt intercalation. The Dirac cone of $\pi$ band characteristic of quasi-freestanding graphene is observed. In combination with high-resolution transmission electron microscopy and atomic force microscopy data, we conclude that ultrathin silicide $\mathrm{CoSi}\text{/}{\mathrm{CoSi}}_2$ structure is formed between graphene and SiC substrate. Investigation of magnetic properties reveals ferromagnetic behavior with open hysteresis loop. The results of this work are the basis for further implementation of magneto-spin-orbit graphene on a semiconducting substrate and are important for the future application of such graphene in spintronics.

The antiferromagnetic ordering that MnBi${}_2$Te${}_4$ shows makes it invariant with respect to the combination of the time-reversal and primitive-lattice translation symmetries, giving rise to its topologically nontrivial nature and a number of fundamental phenomena. At the same time, the possibility to control the electronic and magnetic properties of this system can provide new effective ways for its application in devices. One of the approaches to manipulate MnBi${}_2$Te${}_4$ properties is the partial substitution of magnetic atoms in the compound with atoms of non-magnetic elements, which inevitably affect the interplay of magnetism and band topology in the system. In this work, we have carried out theoretical modelling of changes in the electronic structure that occur as a result of increasing the concentration of Sn atoms at Mn positions in the (Mn${}_{1-x}$Sn${}_x$)Bi${}_2$Te${}_4$ compound both using Korringa–Kohn–Rostoker (KKR) Green’s function method as well as the widespread approach of using supercells with impurity in DFT methods. The calculated band structures were also compared with those experimentally measured by angle-resolved photoelectron spectroscopy (ARPES) for samples with x values of 0, $0.19$, $0.36$, $0.52$ and $0.86$. We assume that the complex hybridization of Te-p${}_z$ and Bi-p${}_z$ orbitals with Sn and Mn ones leads to a non-linear dependence of band gap on Sn content in Mn positions, which is characterized by a plateau with a zero energy gap at some concentration values, suggesting possible topological phase transitions in the system.

We show that graphene can be magnetized by coupling to a ferromagnetic Co film through a Au monolayer. The presence of dislocation loops under graphene leads to a ferrimagnetic ordering of moments in the two C sublattices. It is shown that the band gap of $\sim 80\mathrm{meV}$ in the $\overline{K}$ point has a magnetic nature and exists for ferrimagnetic ordering. Interplay between Rashba and exchange couplings is evidenced by spin splitting asymmetry in spin-ARPES measurements and fully supported by DFT calculation of a ($9\times 9$) unit cell. Owing to sign-opposite Berry curvatures for $\overline{K}$ and ${\overline{K}}^{\prime }$ valleys, the synthesized system is promising for the realization of a circular dichroism Hall effect.

One of the approaches to manipulate MnBi${}_2$Te${}_4$ properties is the magnetic dilution, which inevitably affects the interplay of magnetism and band topology in the system. In this work, we carried out angle-resolved photoemission spectroscopy (ARPES) measurements and density functional theory (DFT) calculations for analysing changes in the electronic structure of Mn${}_{1-x}$Ge${}_x$Bi${}_2$Te${}_4$ that occur under parameter x variation. We consider two ways of Mn/Ge substitution: (i) bulk doping of the whole system; (ii) surface doping of the first septuple layer. For the case (i), the experimental results reveal a decrease in the value of the bulk band gap, which should be reversed by an increase when the Ge concentration reaches a certain value. Ab-initio calculations show that at Ge concentrations above 50%, there is an absence of the bulk band inversion of the Te $p_z$ and Bi $p_z$ contributions at the $\Gamma$-point with significant spatial redistribution of the states at the band gap edges into the bulk, suggesting topological phase transition in the system. For case (ii) of the vertical heterostructure Mn${}_{1-x}$Ge${}_x$Bi${}_2$Te${}_4$/MnBi${}_2$Te${}_4$, it was shown that an increase of Ge concentration in the first septuple layer leads to effective modulation of the Dirac gap in the absence of significant topological surface states of spatial redistribution. The results obtained indicate that surface doping compares favorably compared to bulk doping as a method for the Dirac gap value modulation.

Band structure and topology of magneto-spin–orbit graphene is investigated using the proposed tight-binding model that incorporates both Rashba and sublattice-resolved collinear exchange couplings in a generic ferrimagnetic (FIM) setting for in-plane and out-of-plane magnetization directions. The resulting band structures were analyzed for possibilities to extract the strengths of exchange and Rashba couplings from experimental spin-resolved ARPES measurements of the valley gaps and $\pi$-state spin-splittings. It was shown that the topologically trivial in-plane FIM situation admits simple expressions for these quantities, whereas the out-of-plane FIM, which admits a nontrivial band topology, is harder to analyze. The obtained topological phase diagrams for the out-of-plane FIM case show that the anomalous Hall conductance is quite stable with respect to the antiferromagnetic (AFM) interaction, which tends to interfere with the QAHE phase; moreover, the topological phase transition has a rather smooth character with respect to the AFM coupling strength.