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Vortices in topological superconductors are predicted to host Majorana bound states (MBSs) as exotic quasiparticles. In recent experiments, the spatially non-split zero-energy vortex bound state in topological superconductors has been regarded as an essential spectroscopic signature for the observation of MBSs. Here, we report the observation of anisotropic non-split zero-energy vortex bound states in a conventional elemental superconductor with a topologically trivial band structure using scanning tunneling microscopy and spectroscopy. The experimental results, corroborated by quasi-classical theoretical calculations, indicate that the non-split states directly reflect the quasiparticle trajectories governed by the surface electronic structure. Our study implies that non-split zero-energy states are not a conclusive signature of MBSs in vortex cores, in particular for superconducting systems not being in the quantum limit, stimulating a revision of the current understanding of such states. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We determined the magnetic B-T phase diagram of PdFe bilayer on Ir(111) surface by performing Monte Carlo and spin dynamics simulations based on an effective classical spin model. The parameters of the spin model were determined by ab initio methods. At low temperatures we found three types of ordered phases, while at higher temperatures, below the completely disordered paramagnetic phase, a large region of the phase diagram is associated with a fluctuation-disordered phase. Within the applied model, this state is characterized by the presence of skyrmions with finite lifetime. According to the simulations, this lifetime follows the Arrhenius law as a function of temperature. [ABSTRACT FROM AUTHOR]

We present detailed investigations of the magnetic properties of an Fe monolayer on W and Ta(110) surfaces based on the ab initio screened Korringa-Kohn-Rostoker method. By calculating tensorial exchange coupling coefficients, the ground states of the systems are determined using atomistic spin dynamics simulations. Different types of ground states are found in the systems as a function of relaxation of the Fe layer. In the case of the W(110) substrate this is reflected in a reorientation of the easy axis from in-plane to out-of-plane. For Ta(110) a switching appears from the ferromagnetic state to a cycloidal spin spiral state, then to another spin spiral state with a larger wave vector, and for large relaxations, a rotation of the normal vector of the spin spiral is found. Classical Monte Carlo simulations indicate temperature-induced transitions between the different magnetic phases observed in the Fe/Ta(110) system. These phase transitions are analyzed both quantitatively and qualitatively by finite-temperature spin wave theory. [ABSTRACT FROM AUTHOR]

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 [ 1 1 ¯ 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. [ABSTRACT FROM AUTHOR]

Magnetic textures are often treated as quasiparticles following Thiele's equation of motion. We demonstrate via spin model simulations of the current-driven and Brownian motion of ferromagnetic skyrmions that the existing theory based on Thiele's equation is insufficient to describe the dynamics of skyrmions at finite temperatures. We propose an extended equation of motion that goes beyond Thiele's equation by taking into account the coupling of the skyrmion to the magnonic heat bath leading to an additional dissipative term that is linear in temperature. Our results indicate that this so-far-neglected magnon-induced friction dominates for finite temperatures and Gilbert damping values typical for thin films and multilayers. [ABSTRACT FROM AUTHOR]

The temperature scaling of the micromagnetic Dzyaloshinsky-Moriya exchange interaction is calculated from saturated to vanishing magnetization. We use Green's function theory to derive the finite-temperature spin wave spectrum of ferromagnetic systems described by a classical atomistic spin model Hamiltonian with temperature-independent parameters. Within this model, we find universal expressions for the temperature scaling not only of the Dzyaloshinsky-Moriya interaction but also of the Heisenberg exchange stiffness and the single-ion anisotropy. In the spirit of multiscale models, we establish a clear connection between the atomistic interactions and the temperature-dependent coefficients in the spin wave spectrum and in the micromagnetic free-energy functional. We demonstrate that the corrections to mean-field theory or the random phase approximation for the temperature scaling of Dzyaloshinsky-Moriya and Heisenberg exchange interactions have very similar forms. In the presence of thermal fluctuations and Dzyaloshinsky-Moriya interaction an anisotropylike term emerges in the spin wave spectrum which, at low temperature, increases with temperature, in contrast to the decreasing single-ion anisotropy. We evaluate the accuracy of the theoretical method by comparing it to the spin wave spectrum calculated from Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Spin-polarized scanning tunneling microscopy investigations reveal a significant increase of the magnetic period of spin spirals in three-atomic-layer-thick Fe films on Ir(111), from about 4 nm at 8 K to about 65 nm at room temperature. We attribute this considerable influence of temperature on the magnetic length scale of noncollinear spin states to different exchange interaction coefficients in the different Fe layers. We thus propose a classical spin model that reproduces the experimental observations and in which the crucial feature is the presence of magnetically coupled atomic layers with different interaction strengths. This model might also apply for many other systems, especially magnetic multilayers. [ABSTRACT FROM AUTHOR]

The correct identification of topological magnetic objects in experiments is an important issue. In the present paper we report on the characterization of metastable skyrmionic spin structures with various topological charges (Q = - 3, - 2, - 1, 0, + 1, + 2) in the (Pt1-x Irx) Fe/Pd (111) ultrathin magnetic film by performing spin-polarized scanning tunneling microscopy (SP-STM) calculations. We find that an out-of-plane magnetized tip already results in distinguished SP-STM contrasts for the different skyrmionic structures corresponding to their symmetries. Our paper also establishes an understanding of the relationship between in-plane SP-STM contrasts and skyrmionic topologies through an investigation of the variation of the in-plane angle between the spins along the perimeter of the structures, which can be characterized by the local vorticity or linear density of the winding number. For spin structures exhibiting a uniform sign of the local vorticity throughout the whole skyrmionic area, we demonstrate that (i) | Q | can be determined from a single SP-STM image taken by any in-plane magnetized tip and (ii) an in-plane tip magnetization rotation provides the sign of Q independently of the sign of the effective spin polarization in the tunnel junction. We also discuss cases where the local vorticity is changing sign. Finally, by increasing the Ir content of the PtIr overlayer, we find an appearing secondary outer ring in-plane SP-STM contrast that is indicative of attractive skyrmions or antiskyrmions. [ABSTRACT FROM AUTHOR]

We observe metastable localized spin configurations with topological charges ranging from Q = -3 to Q = 2 in a (Pt0.95 Ir0.05)/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 Dzyaloshinsky-Moriya 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The article focuses on the study of majorana bound states (MBS) in condensed matter systems which is an important challenge focused on topological quantumcomputing. It focuses on the novel approach to design model-type atomic-scale systems for studying MBS by using single-atom manipulation techniques.

The exchange interaction of a brominated Co-porphyrin molecule with the Cooper pair condensate of Pb(111) is modified by reducing the Co-surface separation. The stepwise dehalogenation and dephenylation change the Co adsorption height by a few picometers. Only the residual Co-porphine core exhibits a Yu-Shiba-Rusinov bound state with low binding energy in the Bardeen-Cooper-Schrieffer energy gap. Accompanying density functional calculations reveal that the Co d z 2 orbital carries the molecular magnetic moment and is responsible for the intragap state. The calculated spatial evolution of the Yu-Shiba-Rusinov wave function is compatible with the experimentally observed oscillatory attenuation of the electron-hole asymmetry with increasing lateral distance from the magnetic porphine center.

Equilibrium properties and localized magnon excitations are investigated in topologically distinct skyrmionic textures. The observed shape of the structures and their orientation on the lattice is explained based on their vorticities and the symmetry of the crystal. The transformation between different textures and their annihilation as a function of magnetic field is understood based on the energy differences between them. The angular momentum spin-wave eigenmodes characteristic of cylindrically symmetric structures are combined in the distorted spin configurations, leading to avoided crossings in the magnon spectrum. The susceptibility of the skyrmionic textures to homogeneous external fields is calculated, revealing that a high number of modes become detectable due to the hybridization between the angular momentum eigenmodes. These findings should contribute to the observation of spin waves in distorted skyrmionic structures via experiments and numerical simulations, widening the range of their possible applications in magnonic devices., (© 2020 IOP Publishing Ltd.)

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.

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.