Skyrmions with Attractive Interactions in an Ultrathin Magnetic Film.

We determined the parameters of a classical spin Hamiltonian describing an Fe monolayer on Pd(111) surface with a Pt_{1-x}Ir_{x} 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.

Electronic and Magnetic Properties of Building Blocks of Mn and Fe Atomic Chains on Nb(110).

We present results for the electronic and magnetic structure of Mn and Fe clusters on Nb(110) surface, focusing on building blocks of atomic chains as possible realizations of topological superconductivity. The magnetic ground states of the atomic dimers and most of the monatomic chains are determined by the nearest-neighbor isotropic interaction. To gain physical insight, the dependence on the crystallographic direction as well as on the atomic coordination number is analyzed via an orbital decomposition of this isotropic interaction based on the spin-cluster expansion and the difference in the local density of states between ferromagnetic and antiferromagnetic configurations. A spin-spiral ground state is obtained for Fe chains along the [11¯0] direction as a consequence of the frustration of the isotropic interactions. Here, a flat spin-spiral dispersion relation is identified, which can stabilize spin spirals with various wave vectors together with the magnetic anisotropy. This may lead to the observation of spin spirals of different wave vectors and chiralities in longer chains instead of a unique ground state.

Spin-orbit coupling induced splitting of Yu-Shiba-Rusinov states in antiferromagnetic dimers.

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.

A multiscale model of the effect of Ir thickness on the static and dynamic properties of Fe/Ir/Fe films.

The complex magnetic properties of Fe/Ir/Fe sandwiches are studied using a hierarchical multi-scale model. The approach uses first principles calculations and thermodynamic models to reveal the equilibrium spinwave, magnetization and dynamic demagnetisation properties. Finite temperature calculations show a complex spinwave dispersion and an initially counter-intuitive, increasing exchange stiffness with temperature (a key quantity for device applications) due to the effects of frustration at the interface, which then decreases due to magnon softening. Finally, the demagnetisation process in these structures is shown to be much slower at the interface as compared with the bulk, a key insight to interpret ultrafast laser-induced demagnetization processes in layered or interface materials.

Toward tailoring Majorana bound states in artificially constructed magnetic atom chains on elemental superconductors.

Realizing Majorana bound states (MBS) in condensed matter systems is a key challenge on the way toward topological quantum computing. As a promising platform, one-dimensional magnetic chains on conventional superconductors were theoretically predicted to host MBS at the chain ends. We demonstrate a novel approach to design of model-type atomic-scale systems for studying MBS using single-atom manipulation techniques. Our artificially constructed atomic Fe chains on a Re surface exhibit spin spiral states and a remarkable enhancement of the local density of states at zero energy being strongly localized at the chain ends. Moreover, the zero-energy modes at the chain ends are shown to emerge and become stabilized with increasing chain length. Tight-binding model calculations based on parameters obtained from ab initio calculations corroborate that the system resides in the topological phase. Our work opens new pathways to design MBS in atomic-scale hybrid structures as a basis for fault-tolerant topological quantum computing.

Inducing skyrmions in ultrathin Fe films by hydrogen exposure.

Magnetic skyrmions are localized nanometer-sized spin configurations with particle-like properties, which are envisioned to be used as bits in next-generation information technology. An essential step toward future skyrmion-based applications is to engineer key magnetic parameters for developing and stabilizing individual magnetic skyrmions. Here we demonstrate the tuning of the non-collinear magnetic state of an Fe double layer on an Ir(111) substrate by loading the sample with atomic hydrogen. By using spin-polarized scanning tunneling microscopy, we discover that the hydrogenated system supports the formation of skyrmions in external magnetic fields, while the pristine Fe double layer does not. Based on ab initio calculations, we attribute this effect to the tuning of the Heisenberg exchange and the Dzyaloshinsky-Moriya interactions due to hydrogenation. In addition to interface engineering, hydrogenation of thin magnetic films offers a unique pathway to design and optimize the skyrmionic states in low-dimensional magnetic materials.

Tensile strain-induced softening of iron at high temperature.

In weakly ferromagnetic materials, already small changes in the atomic configuration triggered by temperature or chemistry can alter the magnetic interactions responsible for the non-random atomic-spin orientation. Different magnetic states, in turn, can give rise to substantially different macroscopic properties. A classical example is iron, which exhibits a great variety of properties as one gradually removes the magnetic long-range order by raising the temperature towards its Curie point of TC°= 1043 K. Using first-principles theory, here we demonstrate that uniaxial tensile strain can also destabilise the magnetic order in iron and eventually lead to a ferromagnetic to paramagnetic transition at temperatures far below TC°. In consequence, the intrinsic strength of the ideal single-crystal body-centred cubic iron dramatically weakens above a critical temperature of ~500 K. The discovered strain-induced magneto-mechanical softening provides a plausible atomic-level mechanism behind the observed drop of the measured strength of Fe whiskers around 300-500 K. Alloying additions which have the capability to partially restore the magnetic order in the strained Fe lattice, push the critical temperature for the strength-softening scenario towards the magnetic transition temperature of the undeformed lattice. This can result in a surprisingly large alloying-driven strengthening effect at high temperature as illustrated here in the case of Fe-Co alloy.

Imaging spin-reorientation transitions in consecutive atomic Co layers on Ru(0001).

By means of spin-polarized low-energy electron microscopy, we show that the magnetic easy axis of one to three atomic-layer thick cobalt films on Ru(0001) changes its orientation twice during deposition: One-monolayer and three-monolayer thick films are magnetized in plane, while two-monolayer films are magnetized out of plane. The Curie temperatures of films thicker than one monolayer are well above room temperature. Fully relativistic calculations based on the screened Korringa-Kohn-Rostoker method demonstrate that only for two-monolayer cobalt films does the interplay between strain, surface, and interface effects lead to perpendicular magnetization.