Phase Coexistence of Mn Trimer Clusters and Antiferromagnetic Mn Islands on Ir(111).

Clusters supported by solid substrates are prime candidates for heterogeneous catalysis and can be prepared in various ways. While mass-selected soft-landing methods are often used for the generation of monodisperse particles, self-assembly typically leads to a range of different cluster sizes. Here we show by scanning tunneling microscopy measurements that in the initial stages of growth, Mn forms trimers on a close-packed hexagonal Ir surface, providing a route for self-organized monodisperse cluster formation on an isotropic metallic surface. For an increasing amount of Mn, first a phase with reconstructed monolayer islands is formed, until at full coverage a pseudomorphic Mn phase evolves, which is the most densely packed one of the three different observed Mn phases on Ir(111). The magnetic state of both the reconstructed islands and the pseudomorphic film is found to be the prototypical antiferromagnetic Néel state with a 120° spin rotation between all nearest neighbors in the hexagonal layer.

Nano-scale collinear multi-Q states driven by higher-order interactions.

Complex magnetic order arises due to the competition of different interactions between the magnetic moments. Recently, there has been an increased interest in such states not only to unravel the fundamental physics involved, but also with regards to applications exploiting their unique interplay with moving electrons. Whereas it is the Dzyaloshinskii-Moriya interaction (DMI) that has attracted much attention because of its nature to induce non-collinear magnetic order including magnetic-field stabilized skyrmions, it is the frustration of exchange interactions that can drive magnetic order down to the nano-scale. On top of that, interactions between multiple spins can stabilize two-dimensional magnetic textures as zero-field ground states, known as multi-Q states. Here, we introduce a two-dimensional itinerant magnet with various competing atomic-scale magnetic phases. Using spin-polarized scanning tunneling microscopy we observe several zero-field uniaxial or hexagonal nano-scale magnetic states. First-principles calculations together with an atomistic spin model reveal that these states are stabilized by the interplay of frustrated exchange and higher-order interactions while the DMI is weak. Unexpectedly, it is found that not only non-collinear magnetic states arise, but that higher-order interactions can also lead to collinear nano-scale multi-Q states.

Discovery and characterization of a new type of domain wall in a row-wise antiferromagnet.

Antiferromagnets have recently moved into the focus of application-related research, with the perspective to use them in future spintronics devices. At the same time the experimental determination of the detailed spin texture remains challenging. Here we use spin-polarized scanning tunneling microscopy to investigate the spin structure of antiferromagnetic domain walls. Comparison with spin dynamics simulations allows the identification of a new type of domain wall, which is a superposition state of the adjacent domains. We determine the relevant magnetic interactions and derive analytical formulas. Our experiments show a pathway to control the number of domain walls by boundary effects, and demonstrate the possibility to change the position of domain walls by interaction with movable adsorbed atoms. The knowledge about the exact spin structure of the domain walls is crucial for an understanding and theoretical modelling of their properties regarding, for instance, dynamics, response in transport experiments, and manipulation.

Discovery of Magnetic Single- and Triple-q States in Mn/Re(0001).

We experimentally verify the existence of two model-type magnetic ground states that were previously predicted but so far unobserved. We find them in Mn monolayers on the Re(0001) surface using spin-polarized scanning tunneling microscopy. For fcc stacking of Mn the collinear row-wise antiferromagnetic state occurs, whereas for hcp Mn a three-dimensional spin structure appears, which is a superposition of three row-wise antiferromagnetic states known as the triple-q state. Density-functional theory calculations elucidate the subtle interplay of different magnetic interactions to form these spin structures and provide insight into the role played by relativistic effects.

Plumbene on a Magnetic Substrate: A Combined Scanning Tunneling Microscopy and Density Functional Theory Study.

As a heavy analog of graphene, plumbene is a two-dimensional material with strong spin-orbit coupling effects. Using scanning tunneling microscopy, we observe that Pb forms a flat honeycomb lattice on an Fe monolayer on Ir(111). In contrast, without the Fe layer, a c(2×4) structure of Pb on Ir(111) is found. We use density-functional theory calculations to rationalize these findings and analyze the impact of the hybridization on the plumbene band structure. In the unoccupied states the splitting of the Dirac cone by spin-orbit interaction is clearly observed, while the occupied Pb states are strongly hybridized with the substrate. In a freestanding plumbene we find a band inversion below the Fermi level that leads to the formation of a topologically nontrivial gap. Exchange splitting as mediated by the strong hybridization with the Fe layer drives a quantum spin Hall to quantum anomalous Hall state transition.

Electrical Detection of Domain Walls and Skyrmions in Co Films Using Noncollinear Magnetoresistance.

A large noncollinear magnetoresistance (NCMR) is observed for Rh/Co atomic bilayers on Ir(111) using scanning tunneling microscopy and spectroscopy. The effect is 20% at the Fermi energy and large in a broad energy range. The NCMR can be used to electrically detect nanometer-scale domain walls and skyrmions directly in the tunnel current without the need for a differential measurement. The NCMR results from changes in the density of states of noncollinear spin textures with respect to the ferromagnetic state. Density functional theory calculations reveal that they originate from spin mixing between majority d_{xz} and minority p_{z} states.

Isolated zero field sub-10 nm skyrmions in ultrathin Co films.

Due to their exceptional topological and dynamical properties magnetic skyrmions-localized stable spin structures-show great promise for spintronic applications. To become technologically competitive, isolated skyrmions with diameters below 10 nm stable at zero magnetic field and at room temperature are desired. Despite finding skyrmions in a wide spectrum of materials, the quest for a material with these envisioned properties is ongoing. Here we report zero field isolated skyrmions at T = 4 K with diameters below 5 nm observed in the virgin ferromagnetic state coexisting with 1 nm thin domain walls in Rh/Co atomic bilayers on Ir(111). These spin structures are investigated by spin-polarized scanning tunneling microscopy and can also be detected using non-spin-polarized tips via the noncollinear magnetoresistance. We demonstrate that sub-10 nm skyrmions are stabilized in these ferromagnetic Co films at zero field due to strong frustration of exchange interaction, together with Dzyaloshinskii-Moriya interaction and large magnetocrystalline anisotropy.

Erratum: Guiding Spin Spirals by Local Uniaxial Strain Relief [Phys. Rev. Lett. 116, 017201 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.017201.

Competition of Dzyaloshinskii-Moriya and Higher-Order Exchange Interactions in Rh/Fe Atomic Bilayers on Ir(111).

Using spin-polarized scanning tunneling microscopy and density functional theory we demonstrate the occurrence of a novel type of noncollinear spin structure in Rh/Fe atomic bilayers on Ir(111). We find that higher-order exchange interactions depend sensitively on the stacking sequence. For fcc-Rh/Fe/Ir(111), frustrated exchange interactions are dominant and lead to the formation of a spin spiral ground state with a period of about 1.5 nm. For hcp-Rh/Fe/Ir(111), higher-order exchange interactions favor an up-up-down-down (↑↑↓↓) state. However, the Dzyaloshinskii-Moriya interaction at the Fe/Ir interface leads to a small angle of about 4° between adjacent magnetic moments resulting in a canted ↑↑↓↓ ground state.

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.

Temperature-Induced Increase of Spin Spiral Periods.

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.

Electric-field-driven switching of individual magnetic skyrmions.

Controlling magnetism with electric fields is a key challenge to develop future energy-efficient devices. The present magnetic information technology is mainly based on writing processes requiring either local magnetic fields or spin torques, but it has also been demonstrated that magnetic properties can be altered on the application of electric fields. This has been ascribed to changes in magnetocrystalline anisotropy caused by spin-dependent screening and modifications of the band structure, changes in atom positions or differences in hybridization with an adjacent oxide layer. However, the switching between states related by time reversal, for example magnetization up and down as used in the present technology, is not straightforward because the electric field does not break time-reversal symmetry. Several workarounds have been applied to toggle between bistable magnetic states with electric fields, including changes of material composition as a result of electric fields. Here we demonstrate that local electric fields can be used to switch reversibly between a magnetic skyrmion and the ferromagnetic state. These two states are topologically inequivalent, and we find that the direction of the electric field directly determines the final state. This observation establishes the possibility to combine electric-field writing with the recently envisaged skyrmion racetrack-type memories.

Skyrmions at the Edge: Confinement Effects in Fe/Ir(111).

We have employed spin-polarized scanning tunneling microscopy and Monte Carlo simulations to investigate the effect of lateral confinement onto the nano-Skyrmion lattice in Fe/Ir(111). We find a strong coupling of one diagonal of the square magnetic unit cell to the close-packed edges of Fe nanostructures. In triangular islands this coupling in combination with the mismatching symmetries of the islands and of the square nano-Skyrmion lattice leads to frustration and triple-domain states. In direct vicinity to ferromagnetic NiFe islands, the surrounding Skyrmion lattice forms additional domains. In this case a side of the square magnetic unit cell prefers a parallel orientation to the ferromagnetic edge. These experimental findings can be reproduced and explained by Monte Carlo simulations. Here, the single-domain state of a triangular island is lower in energy, but nevertheless multidomain states occur due to the combined effect of entropy and an intrinsic domain wall pinning arising from the skyrmionic character of the spin texture.

Coupling of Coexisting Noncollinear Spin States in the Fe Monolayer on Re(0001).

Spin-polarized scanning tunneling microscopy is used to investigate the magnetic state of the Fe monolayer on Re(0001). Two coexisting atomic-scale noncollinear spin textures are observed with a sharp transition between them on the order of the atomic lattice spacing. A position correlation between the two spin states is observed both in experiments and in Monte Carlo simulations, demonstrating their coupling behavior.

Guiding Spin Spirals by Local Uniaxial Strain Relief.

We report on the influence of uniaxial strain relief on the spin spiral state in the Fe double layer grown on Ir(111). Scanning tunneling microscopy (STM) measurements reveal areas with reconstruction lines resulting from uniaxial strain relief due to the lattice mismatch of Fe and Ir atoms, as well as pseudomorphic strained areas. Magnetic field-dependent spin-polarized STM measurements of the reconstructed Fe double layer reveal cycloidal spin spirals with a period on the nm scale. Globally, the spin spiral wave fronts are guided along symmetry-equivalent [112̅] crystallographic directions of the fcc(111) substrate. On an atomic scale the spin spiral propagation direction is linked to the [001] direction of the bcc(110)-like Fe, leading to a zigzag shaped wave front. The isotropically strained pseudomorphic areas also exhibit a preferred magnetic periodicity on the nm scale but no long-range order. We find that already for local strain relief with a single set of reconstruction lines a strict guiding of the spin spiral is realized.

Electrical detection of magnetic skyrmions by tunnelling non-collinear magnetoresistance.

Magnetic skyrmions are localized non-collinear spin textures with a high potential for future spintronic applications. Skyrmion phases have been discovered in a number of materials and a focus of current research is to prepare, detect and manipulate individual skyrmions for implementation in devices. The local experimental characterization of skyrmions has been performed by, for example, Lorentz microscopy or atomic-scale tunnel magnetoresistance measurements using spin-polarized scanning tunnelling microscopy. Here we report a drastic change of the differential tunnel conductance for magnetic skyrmions that arises from their non-collinearity: mixing between the spin channels locally alters the electronic structure, which makes a skyrmion electronically distinct from its ferromagnetic environment. We propose this tunnelling non-collinear magnetoresistance as a reliable all-electrical detection scheme for skyrmions with an easy implementation into device architectures.

Field-dependent size and shape of single magnetic Skyrmions.

The atomic-scale spin structure of individual isolated Skyrmions in an ultrathin film is investigated in real space by spin-polarized scanning tunneling microscopy. Their axial symmetry as well as their unique rotational sense is revealed by using both out-of-plane and in-plane sensitive tips. The size and shape of Skyrmions change as a function of the magnetic field. An analytical expression for the description of Skyrmions is proposed and applied to connect the experimental data to the original theoretical model describing chiral Skyrmions. Thereby, the relevant material parameters responsible for Skyrmion formation can be obtained.

Influence of the local atom configuration on a hexagonal skyrmion lattice.

Spin-resolved scanning tunneling microscopy is used to reveal a commensurate hexagonal nanoskyrmion lattice in the hcp stacked Fe monolayer on Ir(111). The exact nature of the spin configuration is due to magnetic interactions between the Fe atoms and the Ir substrate, either originating from polarization effects, or due to a three-site hopping mechanism of the Dzyaloshinsky-Moriya interaction leading to a canting of the Dzyaloshinsky-Moriya vector with respect to the interface.

Interface-induced chiral domain walls, spin spirals and skyrmions revealed by spin-polarized scanning tunneling microscopy.

The spin textures of ultra-thin magnetic layers exhibit surprising variety. The loss of inversion symmetry at the interface of the magnetic layer and substrate gives rise to the so-called Dzyaloshinskii-Moriya interaction which favors non-collinear spin arrangements with unique rotational sense. Here we review the application of spin-polarized scanning tunneling microscopy to such systems, which has led to the discovery of interface-induced chiral domain walls and spin spirals. Recently, different interface-driven skyrmion lattices have been found, and the writing as well as the deleting of individual skyrmions based on local spin-polarized current injection has been demonstrated. These interface-induced non-collinear magnetic states offer new exciting possibilities to study fundamental magnetic interactions and to tailor material properties for spintronic applications.

Parity effects in 120° spin spirals.

The magnetic ground state of biatomic Fe chains on the reconstructed (5×1)-Ir(001) surface is a cycloidal 120° spin spiral. Spin-resolved scanning tunneling microscopy reveals a striking variation of magnetic field dependences among the chains, which we attribute to parity effects resulting from finite lengths. Numerical simulations show that the chains are divided in three symmetry classes with the exact number of atoms in the chain determining the size and direction of their net magnetic moment. In contrast to antiferromagnetic systems, the three-atom periodicity causes the effective anisotropy to alternate between out of plane, in plane, and quenched.