Interfacial Tuning of Anisotropic Gilbert Damping.

Tuning of the anisotropic Gilbert damping Δα has been realized in ultrathin single-crystalline Fe films grown on GaAs (001). A nonmonotonic dependence of Δα on film thickness t is observed upon varying t about 10 ML (∼1.4 nm). Δα increases for 16 ML>t>8.5 ML, and then decreases for 8.5 ML>t>6.5 ML accompanied by a sign reversal of Δα for t=6.5 ML. The sign reversal of Δα is captured by first-principle calculations, which show that the anisotropic density of states changes sign upon decreasing t. Moreover, t^{-1} dependence of the anisotropic damping indicates the emergence of an anisotropic effective spin mixing conductance according to the theory of spin pumping. The results establish new opportunities for controlling the Gilbert damping and for fundamental studies of magnetization dynamics in reduced dimension.

Manipulation of Magnetic Skyrmion Density in Continuous Ir/Co/Pt Multilayers.

We show that magnetic skyrmions can be stabilised at room temperature in continuous [Ir/Co/Pt]5 multilayers on SiO2/Si substrates without the prior application of electric current or magnetic field. While decreasing the Co thickness, a transition of the magnetic domain patterns from worm-like state to separated stripes is observed. The skyrmions are clearly imaged in both states using magnetic force microscopy. The density of skyrmions can be significantly enhanced after applying the "in-plane field procedure". Our results provide means to manipulate magnetic skyrmion density, further allowing for the optimised engineering of skyrmion-based devices.

Chiral surface spin textures in Cu2OSeO3 unveiled by soft X-ray scattering in specular reflection geometry.

Resonant elastic soft X-ray magnetic scattering (XRMS) is a powerful tool to explore long-periodic spin textures in single crystals. However, due to the limited momentum transfer range imposed by long wavelengths of photons in the soft x-ray region, Bragg diffraction is restricted to crystals with the large lattice parameters. Alternatively, small-angle X-ray scattering has been involved in the soft energy X-ray range which, however, brings in difficulties with the sample preparation that involves focused ion beam milling to thin down the crystal to below a few hundred nm thickness. We show how to circumvent these restrictions using XRMS in specular reflection from a sub-nanometer smooth crystal surface. The method allows observing diffraction peaks from the helical and conical spin modulations at the surface of a Cu   2 OSeO   3 single crystal and probing their corresponding chirality as contributions to the dichroic scattered intensity. The results suggest a promising way to carry out XRMS studies on a plethora of noncentrosymmetric systems hitherto unexplored with soft X-rays due to the absence of the commensurate Bragg peaks in the available momentum transfer range.

Corrigendum to "Spin structure relation to phase contrast imaging of isolated magnetic Bloch and Néel skyrmions" [Ultramicroscopy 212 (2020) 112973].

Several errors are present in the text and Fig. 3 of the article Ultramicroscopy 212 (2020) 112973. This includes minor confusions concerning the skyrmion helicities and a wrong orientation of a color wheel that represents the electron phase gradient direction. Further, the presented correction factors for finite probe sizes were based on an erratic simulation which is now corrected. This leads to different error values for the measured skyrmion size. These flaws do not affect the main message of the paper which is the relation of the skyrmion structure with the electron phase at all. They only affect the small section of the proof of principle skyrmion size measurement where aberrations were included.

Spin structure relation to phase contrast imaging of isolated magnetic Bloch and Néel skyrmions.

Magnetic skyrmions are promising candidates for future storage devices with a large data density. A great variety of materials have been found that host skyrmions up to the room-temperature regime. Lorentz microscopy, usually performed in a transmission electron microscope (TEM), is one of the most important tools for characterizing skyrmion samples in real space. Using numerical calculations, this work relates the phase contrast in a TEM to the actual magnetization profile of an isolated Néel or Bloch skyrmion, the two most common skyrmion types. Within the framework of the used skyrmion model, the results are independent of skyrmion size and wall width and scale with sample thickness for purely magnetic specimens. Simple rules are provided to extract the actual skyrmion configuration of pure Bloch or Néel skyrmions without the need of simulations. Furthermore, first differential phase contrast (DPC) measurements on Néel skyrmions that meet experimental expectations are presented and showcase the described principles. The work is relevant for material sciences where it enables the engineering of skyrmion profiles via convenient characterization.

Ferromagnetic Resonance with Magnetic Phase Selectivity by Means of Resonant Elastic X-Ray Scattering on a Chiral Magnet.

Cubic chiral magnets, such as Cu_{2}OSeO_{3}, exhibit a variety of noncollinear spin textures, including a trigonal lattice of spin whirls, the so-called skyrmions. Using magnetic resonant elastic x-ray scattering (REXS) on a crystalline Bragg peak and its magnetic satellites while exciting the sample with magnetic fields at gigahertz frequencies, we probe the ferromagnetic resonance (FMR) modes of these spin textures by means of the scattered intensity. Most notably, the three eigenmodes of the skyrmion lattice are detected with large sensitivity. As this novel technique, which we label REXS FMR, is carried out at distinct positions in reciprocal space, it allows us to distinguish contributions originating from different magnetic states, providing information on the precise character, weight, and mode mixing as a prerequisite of tailored excitations for applications.

Coherent Excitation of Heterosymmetric Spin Waves with Ultrashort Wavelengths.

In the emerging field of magnonics, spin waves are foreseen as signal carriers for future spintronic information processing and communication devices, owing to both the very low power losses and a high device miniaturization potential predicted for short-wavelength spin waves. Yet, the efficient excitation and controlled propagation of nanoscale spin waves remains a severe challenge. Here, we report the observation of high-amplitude, ultrashort dipole-exchange spin waves (down to 80 nm wavelength at 10 GHz frequency) in a ferromagnetic single layer system, coherently excited by the driven dynamics of a spin vortex core. We used time-resolved x-ray microscopy to directly image such propagating spin waves and their excitation over a wide range of frequencies. By further analysis, we found that these waves exhibit a heterosymmetric mode profile, involving regions with anti-Larmor precession sense and purely linear magnetic oscillation. In particular, this mode profile consists of dynamic vortices with laterally alternating helicity, leading to a partial magnetic flux closure over the film thickness, which is explained by a strong and unexpected mode hybridization. This spin-wave phenomenon observed is a general effect inherent to the dynamics of sufficiently thick ferromagnetic single layer films, independent of the specific excitation method employed.

Observation of a Goos-Hänchen-like Phase Shift for Magnetostatic Spin Waves.

In optics, a light beam experiences a spatial shift in the beam plane upon total internal reflection. This shift is usually referred to as the Goos-Hänchen shift. When dealing with plane waves, it manifests itself as a phase shift between an incoming and reflected wave that depends on the wave vector component along the interface. In the experiments presented here, plane spin waves are excited in a 60-nm-thick Permalloy film and propagate towards the edge of the film. By means of time-resolved scanning Kerr microscopy, we are able to directly detect a phase shift between the incoming and reflected wave. With the help of a numerical model, we show that this phase shift naturally occurs for spin waves in the dipolar regime.

Layer specific observation of slow thermal equilibration in ultrathin metallic nanostructures by femtosecond X-ray diffraction.

Ultrafast heat transport in nanoscale metal multilayers is of great interest in the context of optically induced demagnetization, remagnetization and switching. If the penetration depth of light exceeds the bilayer thickness, layer-specific information is unavailable from optical probes. Femtosecond diffraction experiments provide unique experimental access to heat transport over single digit nanometer distances. Here, we investigate the structural response and the energy flow in the ultrathin double-layer system: gold on ferromagnetic nickel. Even though the excitation pulse is incident from the Au side, we observe a very rapid heating of the Ni lattice, whereas the Au lattice initially remains cold. The subsequent heat transfer from Ni to the Au lattice is found to be two orders of magnitude slower than predicted by the conventional heat equation and much slower than electron-phonon coupling times in Au. We present a simplified model calculation highlighting the relevant thermophysical quantities.

Quantifying the critical thickness of electron hybridization in spintronics materials.

In the rapidly growing field of spintronics, simultaneous control of electronic and magnetic properties is essential, and the perspective of building novel phases is directly linked to the control of tuning parameters, for example, thickness and doping. Looking at the relevant effects in interface-driven spintronics, the reduced symmetry at a surface and interface corresponds to a severe modification of the overlap of electron orbitals, that is, to a change of electron hybridization. Here we report a chemically and magnetically sensitive depth-dependent analysis of two paradigmatic systems, namely La1-xSrxMnO3 and (Ga,Mn)As. Supported by cluster calculations, we find a crossover between surface and bulk in the electron hybridization/correlation and we identify a spectroscopic fingerprint of bulk metallic character and ferromagnetism versus depth. The critical thickness and the gradient of hybridization are measured, setting an intrinsic limit of 3 and 10 unit cells from the surface, respectively, for (Ga,Mn)As and La1-xSrxMnO3, for fully restoring bulk properties.

Time Resolved Measurements of the Switching Trajectory of Pt/Co Elements Induced by Spin-Orbit Torques.

We report the experimental observation of spin-orbit torque induced switching of perpendicularly magnetized Pt/Co elements in a time resolved stroboscopic experiment based on high resolution Kerr microscopy. Magnetization dynamics is induced by injecting subnanosecond current pulses into the bilayer while simultaneously applying static in-plane magnetic bias fields. Highly reproducible homogeneous switching on time scales of several tens of nanoseconds is observed. Our findings can be corroborated using micromagnetic modeling only when including a fieldlike torque term as well as the Dzyaloshinskii-Moriya interaction mediated by finite temperature.

Dynamical Defects in Rotating Magnetic Skyrmion Lattices.

The chiral magnet Cu_{2}OSeO_{3} hosts a Skyrmion lattice that may be equivalently described as a superposition of plane waves or a lattice of particlelike topological objects. A thermal gradient may break up the Skyrmion lattice and induce rotating domains, raising the question of which of these scenarios better describes the violent dynamics at the domain boundaries. Here, we show that in an inhomogeneous temperature gradient caused by illumination in a Lorentz transmission electron microscope different parts of the Skyrmion lattice can be set into motion with different angular velocities. Tracking the time dependence, we show that the constant rearrangement of domain walls is governed by dynamic 5-7 defects arranging into lines. An analysis of the associated defect density is described by Frank's equation and agrees well with classical 2D Monte Carlo simulations. Fluctuations of boundaries show a surgelike rearrangement of Skyrmion clusters driven by defect rearrangement consistent with simulations treating Skyrmions as point particles. Our findings underline the particle character of the Skyrmion.

Robust spin-orbit torque and spin-galvanic effect at the Fe/GaAs (001) interface at room temperature.

Interfacial spin-orbit torques (SOTs) enable the manipulation of the magnetization through in-plane charge currents, which has drawn increasing attention for spintronic applications. The search for material systems providing efficient SOTs, has been focused on polycrystalline ferromagnetic metal/non-magnetic metal bilayers. In these systems, currents flowing in the non-magnetic layer generate-due to strong spin-orbit interaction-spin currents via the spin Hall effect and induce a torque at the interface to the ferromagnet. Here we report the observation of robust SOT occuring at a single crystalline Fe/GaAs (001) interface at room temperature. We find that the magnitude of the interfacial SOT, caused by the reduced symmetry at the interface, is comparably strong as in ferromagnetic metal/non-magnetic metal systems. The large spin-orbit fields at the interface also enable spin-to-charge current conversion at the interface, known as spin-galvanic effect. The results suggest that single crystalline Fe/GaAs interfaces may enable efficient electrical magnetization manipulation.

Anisotropic Polar Magneto-Optic Kerr Effect of Ultrathin Fe/GaAs(001) Layers due to Interfacial Spin-Orbit Interaction.

We report the observation of the anisotropic polar magneto-optical Kerr effect in thin layers of epitaxial Fe/GaAs(001) at room temperature. A clear twofold symmetry of the Kerr rotation angle depending on the orientation of the linear polarization of the probing laser beam with respect to the crystallographic directions of the sample is detected for ultrathin magnetic films saturated out of the film plane. The amplitude of the anisotropy decreases with increasing Fe film thickness, suggesting that the interfacial region is the origin of the anisotropy. The twofold symmetry is fully reproduced by model calculations based on an interference of interfacial Bychkov-Rashba and Dresselhaus spin-orbit coupling.

Tuning Spin Hall Angles by Alloying.

Within a combined experimental and theoretical study it is shown that the spin Hall angle of a substitutional alloy system can be continuously varied via its composition. For the alloy system Au_{x}Pt_{1-x} a substantial increase of the maximum spin Hall angle compared to the pure alloy partners could be achieved this way. The experimental findings for the longitudinal charge conductivity σ, the transverse spin Hall conductivity σ_{SH}, and the spin Hall angle α_{SH} could be confirmed by calculations based on Kubo's linear response formalism. Calculations of these response quantities for different temperatures show that the divergent behavior of σ and σ_{SH} is rapidly suppressed with increasing temperature. As a consequence, σ_{SH} is dominated at higher temperatures by its intrinsic contribution that has only a rather weak temperature dependence.

Snell's Law for Spin Waves.

We report the experimental observation of Snell's law for magnetostatic spin waves in thin ferromagnetic Permalloy films by imaging incident, refracted, and reflected waves. We use a thickness step as the interface between two media with different dispersion relations. Since the dispersion relation for magnetostatic waves in thin ferromagnetic films is anisotropic, deviations from the isotropic Snell's law known in optics are observed for incidence angles larger than 25° with respect to the interface normal between the two magnetic media. Furthermore, we can show that the thickness step modifies the wavelength and the amplitude of the incident waves. Our findings open up a new way of spin wave steering for magnonic applications.

Emergence of spin-orbit fields in magnetotransport of quasi-two-dimensional iron on gallium arsenide.

The desire for higher information capacities drives the components of electronic devices to ever smaller dimensions so that device properties are determined increasingly more by interfaces than by the bulk structure of the constituent materials. Spintronic devices, especially, benefit from the presence of interfaces--the reduced structural symmetry creates emergent spin-orbit fields that offer novel possibilities to control device functionalities. But where does the bulk end, and the interface begin? Here we trace the interface-to-bulk transition, and follow the emergence of the interfacial spin-orbit fields, in the conducting states of a few monolayers of iron on top of gallium arsenide. We observe the transition from the interface- to bulk-induced lateral crystalline magnetoanisotropy, each having a characteristic symmetry pattern, as the epitaxially grown iron channel increases from four to eight monolayers. Setting the upper limit on the width of the interface-imprinted conducting channel is an important step towards an active control of interfacial spin-orbit fields.

Real-time observation of domain fluctuations in a two-dimensional magnetic model system.

Domain patterns of perpendicularly magnetized ultra-thin ferromagnetic films are often determined by the competition of the short range but strong exchange interaction favouring ferromagnetic alignment of magnetic moments and the long range but weak antiferromagnetic dipolar interaction. Detailed phase diagrams of the resulting stripe domain patterns have been evaluated in recent years; however, the domain fluctuations in these pattern forming systems have not been studied in great detail so far. Here we show that domain fluctuations can be observed in ultra-thin two-dimensional ferromagnetic Fe/Ni/Cu(001) films with perpendicular magnetization in the stripe domain phase. Non-stroboscopic time-resolved threshold photoemission electron microscopy with high temporal resolution allows analysing the dynamic fingerprint of the topological excitations in the nematic domain phase. Furthermore, proliferation of domain ending defects in the vicinity of the spin reorientation transition is witnessed.

Magnetic damping: domain wall dynamics versus local ferromagnetic resonance.

Magnetic relaxation is one of the dominating features of magnetization dynamics. Depending on the magnetic structure and the experimental approach, different magnitudes of the damping parameter are reported even for a given material. In this study, we experimentally address this issue by accessing the damping parameter in the same magnetic nanotracks using different approaches: local ferromagnetic resonance (α=0.0072) and field-driven domain wall dynamics (α=0.023). The experimental results cannot fully be accounted for by modeling only roughness in micromagnetic simulations. Consequently, we have included nonlocal texture induced damping to the micromagnetic code. We find excellent agreement with the observed increased damping in the vortex structures for the same input Gilbert alpha when texture-induced nonlocal damping is included.

Transverse spin Seebeck effect versus anomalous and planar Nernst effects in Permalloy thin films.

Transverse magnetothermoelectric effects are studied in Permalloy thin films grown on MgO and GaAs substrates and compared to those grown on suspended SiN(x) membranes. The transverse voltage along platinum strips patterned on top of the Permalloy films is measured versus the external magnetic field as a function of the angle and temperature gradients. After the identification of the contribution of the planar and anomalous Nernst effects, we find an upper limit for the transverse spin Seebeck effect, which is several orders of magnitude smaller than previously reported.