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).

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.

We determined the parameters of a classical spin Hamiltonian describing an Fe monolayer on Pd(111) surface with a Pt1−xIrx alloy overlayer from ab initio calculations. While the ground state of the system is ferromagnetic for x = 0.00, it becomes a spin spiral state as Ir is intermixed into the overlayer. Although the Dzyaloshinsky-Moriya interaction is present in the system, we will demonstrate that the frustrated isotropic exchange interactions play a prominent role in creating the spin spiral state, and these frustrated couplings lead to an attractive interaction between skyrmions at short distances. Using spin dynamics simulations, we show that under these conditions the individual skyrmions form clusters, and that these clusters remain stable at finite temperature.The magnetic skyrmion corresponds to a configuration where the directions of the spin magnetic moments at different lattice sites span the whole sphere[1, 2], in contrast to collinear ferromagnetic or antiferromagnetic systems and spin spiral states. Several years after the theoretical prediction [3, 4] In agreement with the original theoretical description [4, 13], the appearance of skyrmions in the above systems was attributed to the DzyaloshinskyMoriya interaction [14, 15] present in noncentrosymmetric magnets. This chiral interaction competes with the ferromagnetic exchange and easy-axis anisotropy, and may lead to a planar spin spiral ground state in the system [16, 17], which can in turn transform into a skyrmion lattice at finite external magnetic field.Since frustrated isotropic exchange interactions may also stabilize a spin spiral phase, skyrmions could also be present in such systems at finite external magnetic field, even if the Dzyaloshinsky-Moriya interaction is absent due to symmetry reasons. It was shown in Ref. [18] for a model Hamiltonian with competing ferromagnetic and antiferromagnetic interactions on a triangular lattice that at least at finite temperature, this is indeed the case. It was demonstrated later [19][20][21] that the presence of an easy-axis on-site anisotropy extends the stability range of the skyrmion lattice to zero temperature. If only isotropic exchange interactions are present, Blochtype and Néel-type skyrmions with different helicities, as well as skyrmions and antiskyrmions with opposite topological charges [19], are energetically degenerate. Furthermore, the magnetization profile of skyrmions with frustrated exchange interactions is different from that of skyrmions stabilized by the Dzyaloshinsky-Moriya interaction. This leads to an interaction potential between skyrmions with several local energy minima, while the interaction between Dzyaloshinsky-Moriya skyrmions is repulsive at all distances at low temperature [22].Magnetic skyrmions have also been explored in ultrathin film systems such as PdFe bilayer [23] or Fe triplelayer[24] on Ir(111) surface, and Pt|Co|Ir multilayers [25]. Since bulk inversion symmetry is broken at the surface, the Dzyaloshinsky-Moriya interaction is present in such systems;...

We observe metastable localized spin configurations with topological charges ranging from Q = −3 to Q = 2 in a (Pt 0.95 Ir 0.05 )/Fe bilayer on a Pd(111) surface by performing spin dynamics simulations, using a classical Hamiltonian parametrized by ab initio calculations. We demonstrate that the frustration of the isotropic exchange interactions is responsible for the creation of these various types of skyrmionic structures. The DzyaloshinskyMoriya interaction present due to the breaking of inversion symmetry at the surface energetically favors skyrmions with Q = −1, distorts the shape of the other objects, and defines a preferred orientation for them with respect to the underlying lattice.