We demonstrate the artificial construction of magnetic atom chains on a conventional superconductor as a Majorana platform.

In order to study spin-wave excitations of itinerant ferromagnets a relativistic first-principles method based on the adiabatic approach is presented. The derivatives of the free energy up to second order with respect of the polar and azimuthal angles are derived within the framework of the magnetic force theorem and the fully relativistic Korringa-Kohn-Rostoker method. Exchange and spin-orbit coupling are thus incorporated on equal footing in the Hamiltonian. Furthermore, a detailed comparison to classical spin Hamiltonians is given and it is shown that the magnetocrystalline anisotropy energy contains contributions from both the on-site anisotropy and the off-site exchange coupling terms. The method is applied to an Fe monolayer on Cu͑001͒ and Au͑001͒ surfaces and for a Co monolayer on Cu͑001͒. The calculations provide with the gap at zero wave number due to the spin-orbit coupling and uniaxial anisotropy energies in good agreement with the results of the band energy difference method. It is pointed out that the terms in the spin-wave Hamiltonian related to the mixed partial derivatives of the free energy, absent within a nonrelativistic description, introduce an asymmetry in the magnon spectrum with respect to two in-plane easy axes. Moreover, in the case of an in-plane magnetized system the long-wavelength magnons are elliptically polarized due to the difference of the second-order uniaxial and fourth-order in-plane magnetic anisotropy.

The tip of a low-temperature scanning tunneling microscope is brought into contact with individual cobalt atoms adsorbed on Cu(100). A smooth transition from the tunneling regime to contact occurs at a conductance of G approximately G0. Spectroscopy in the contact regime, i.e., at currents in a muA range, was achieved and indicated a significant change of the Kondo temperature TK. Calculations indicate that the proximity of the tip shifts the cobalt d band and thus affects TK.

In order to explain the anisotropic Rashba-Bychkov effect observed in several metallic surfacestate systems, we use k·p perturbation theory with a simple group-theoretical analysis and construct effective Rashba Hamiltonians for different point groups up to third order in the wavenumber. We perform relativistic ab initio calculations for the (• Bi/Ag(111) surface alloy and from the calculated splitting of the band dispersion we find evidence of the predicted third-order terms. Furthermore, we derive expressions for the corresponding third-order Rashba parameters to provide a simple explanation to the qualitative difference concerning the Rashba-Bychkov splitting of the surface states at Au(111) and Bi/Ag(111).

Magnetic atoms coupled to the Cooper pairs of a superconductor induce Yu-Shiba-Rusinov states (in short Shiba states). In the presence of sufficiently strong spin-orbit coupling, the bands formed by hybridization of the Shiba states in ensembles of such atoms can support low-dimensional topological superconductivity with Majorana bound states localized on the ensembles’ edges. Yet, the role of spin-orbit coupling for the hybridization of Shiba states in dimers of magnetic atoms, the building blocks for such systems, is largely unexplored. Here, we reveal the evolution of hybridized multi-orbital Shiba states from a single Mn adatom to artificially constructed ferromagnetically and antiferromagnetically coupled Mn dimers placed on a Nb(110) surface. Upon dimer formation, the atomic Shiba orbitals split for both types of magnetic alignment. Our theoretical calculations attribute the unexpected splitting in antiferromagnetic dimers to spin-orbit coupling and broken inversion symmetry at the surface. Our observations point out the relevance of previously unconsidered factors on the formation of Shiba bands and their topological classification.

We have developed a method for simulating multiple electron scattering in a vacuum barrier using real-space single-electron wavefunctions for the separate surfaces. The Green functions in the vacuum barriers are calculated to first order in the Dyson series. We find that the zero-order current is equal to the usual Bardeen approach only in the limit of zero bias and derive the modifications in the finite bias regime. We also derive a first-principles formulation for the energy of interaction between the two surfaces, and show that it is proportional to the tunnelling current. With this method the tunnelling current can in principle be computed to any order in the Dyson expansion.

The inherent instability of CHNHPbX remains a major technical barrier for the industrial applications of perovskite materials. Recently, the most stable surface structures of CHNHPbX have been successfully characterized by using density functional theory (DFT) calculations together with the high-resolution scanning tunneling microscopy (STM) results. The two coexisting phases of the perovskite surfaces have been ascribed to the alternate orientation of the methylammonium (MA) cations. Notably, similar surface defect images (a dark depression at the sites of X atoms) have been observed on surfaces produced with various experimental methods. As such, these defects are expected to be intrinsic to the perovskite crystals and may play an important role in the structural decomposition of perovskite materials. Understanding the nature of such defects should provide some useful information toward understanding the instability of perovskite materials. Thus, we investigate the chemical identity of the surface defects systematically with first-principles density functional theory calculations and STM simulations. The calculated STM images of the Br and Br-MA vacancies are both in good agreement with the experimental measurements. In vacuum conditions, the formation energy of Br-MA is 0.43 eV less than the Br vacancy. In the presence of solvation effects, however, the formation energy of a Br vacancy becomes 0.42 eV lower than the Br-MA vacancy. In addition, at the vacancy sites, the adsorption energies of water, oxygen, and acetonitrile molecules are significantly higher than those on the pristine surfaces. This clearly demonstrated that the structural decomposition of perovskites are much easier to start from these vacancy sites than the pristine surfaces. Combining DFT calculations and STM simulations, this work reveals the chemical identities of the intrinsic defects in the CHNHPbX perovskite crystals and their effects on the stability of perovskite materials.

We perform an extensive study of the spin-configurations in a PdFe bilayer on Ir(111) in terms of ab initio and spin-model calculations. We use the spin-cluster expansion technique to obtain spin model parameters, and solve the Landau-Lifshitz-Gilbert equations at zero temperature. In particular, we focus on effects of layer relaxations and the evolution of the magnetic ground state in external magnetic field. In the absence of magnetic field, we find a spin-spiral ground state, while applying external magnetic field skyrmions are generated in the system. Based on energy calculations of frozen spin configurations with varying magnetic field we obtain excellent agreement for the phase boundaries with available experiments. We find that the wave length of spin-spirals and the diameter of skyrmions decrease with increasing inward Fe layer relaxation which is correlated with the increasing ratio of the nearest neighbor Dzyaloshinskii-Moriya interaction and the isotropic exchange coupling, D/J. Our results also indicate that the applied field needed to stabilize the skyrmion lattice increases when the diameter of individual skyrmions decreases. Based on our observations, we suggest that the formation of the skyrmion lattice can be tuned by small structural modification of the thin film.