Resonant Elastic X-Ray Scattering of Antiferromagnetic Superstructures in EuPtSi_{3}.

We report resonant elastic x-ray scattering of long-range magnetic order in EuPtSi_{3}, combining different scattering geometries with full linear polarization analysis to unambiguously identify magnetic scattering contributions. At low temperatures, EuPtSi_{3} stabilizes type A antiferromagnetism featuring various long-wavelength modulations. For magnetic fields applied in the hard magnetic basal plane, well-defined regimes of cycloidal, conical, and fanlike superstructures may be distinguished that encompass a pocket of commensurate type A order without superstructure. For magnetic field applied along the easy axis, the phase diagram comprises the cycloidal and conical superstructures only. Highlighting the power of polarized resonant elastic x-ray scattering, our results reveal a combination of magnetic phases that suggest a highly unusual competition between antiferromagnetic exchange interactions with Dzyaloshinsky-Moriya spin-orbit coupling of similar strength.

Experimental demonstration of a skyrmion-enhanced strain-mediated physical reservoir computing system.

Physical reservoirs holding intrinsic nonlinearity, high dimensionality, and memory effects have attracted considerable interest regarding solving complex tasks efficiently. Particularly, spintronic and strain-mediated electronic physical reservoirs are appealing due to their high speed, multi-parameter fusion and low power consumption. Here, we experimentally realize a skyrmion-enhanced strain-mediated physical reservoir in a multiferroic heterostructure of Pt/Co/Gd multilayers on (001)-oriented 0.7PbMg1/3Nb2/3O3-0.3PbTiO3 (PMN-PT). The enhancement is coming from the fusion of magnetic skyrmions and electro resistivity tuned by strain simultaneously. The functionality of the strain-mediated RC system is successfully achieved via a sequential waveform classification task with the recognition rate of 99.3% for the last waveform, and a Mackey-Glass time series prediction task with normalized root mean square error (NRMSE) of 0.2 for a 20-step prediction. Our work lays the foundations for low-power neuromorphic computing systems with magneto-electro-ferroelastic tunability, representing a further step towards developing future strain-mediated spintronic applications.

Tunable gigahertz dynamics of low-temperature skyrmion lattice in a chiral magnet.

Recently, it has been shown that the chiral magnetic insulator Cu2OSeO3hosts skyrmions in two separated pockets in temperature and magnetic field phase space. It has also been shown that the predominant stabilization mechanism for the low-temperature skyrmion (LTS) phase is via the crystalline anisotropy, opposed to temperature fluctuations that stabilize the well-established high-temperature skyrmion (HTS) phase. Here, we report on a detailed study of LTS generation by field cycling, probed by GHz spin dynamics in Cu2OSeO3. LTSs are populated via a field cycling protocol with the static magnetic field applied parallel to the ⟨100⟩ crystalline direction of plate and cuboid-shaped bulk crystals. By analyzing temperature-dependent broadband spectroscopy data, clear evidence of LTS excitations with clockwise (CW), counterclockwise (CCW), and breathing mode (BR) character at temperatures belowT= 40 K are shown. We find that the mode intensities can be tuned with the number of field-cycles below the saturation field. By tracking the resonance frequencies, we are able to map out the field-cycle-generated LTS phase diagram, from which we conclude that the LTS phase is distinctly separated from the high-temperature counterpart. We also study the mode hybridization between the dark CW and the BR modes as a function of temperature. By using two Cu2OSeO3crystals with different shapes and therefore different demagnetization factors, together with numerical calculations, we unambiguously show that the magnetocrystalline anisotropy plays a central role for the mode hybridization.

Microwave Spectroscopy of the Low-Temperature Skyrmion State in Cu_{2}OSeO_{3}.

In the cubic chiral magnet Cu_{2}OSeO_{3} a low-temperature skyrmion state (LTS) and a concomitant tilted conical state are observed for magnetic fields parallel to ⟨100⟩. Here, we report on the dynamic resonances of these novel magnetic states. After promoting the nucleation of the LTS by means of field cycling, we apply broadband microwave spectroscopy in two experimental geometries that provide either predominantly in-plane or out-of-plane excitation. By comparing the results to linear spin-wave theory, we clearly identify resonant modes associated with the tilted conical state, the gyrational and breathing modes associated with the LTS, as well as the hybridization of the breathing mode with a dark octupole gyration mode mediated by the magnetocrystalline anisotropies. Most intriguingly, our findings suggest that under decreasing fields the hexagonal skyrmion lattice becomes unstable with respect to an oblique deformation, reflected in the formation of elongated skyrmions.

Building Blocks for Magnon Optics: Emission and Conversion of Short Spin Waves.

Magnons have proven to be a promising candidate for low-power wave-based computing. The ability to encode information not only in amplitude but also in phase allows for increased data transmission rates. However, efficiently exciting nanoscale spin waves for a functional device requires sophisticated lithography techniques and therefore, remains a challenge. Here, we report on a method to measure the full spin wave isofrequency contour for a given frequency and field. A single antidot within a continuous thin film excites wave vectors along all directions within a single excitation geometry. Varying structural parameters or introducing Dzyaloshinskii-Moriya interaction allows the manipulation and control of the isofrequency contour, which is desirable for the fabrication of future magnonic devices. Additionally, the same antidot structure is utilized as a multipurpose spin wave device. Depending on its position with respect to the microstrip antenna, it can either be an emitter for short spin waves or a directional converter for incoming plane waves. Using simulations we show that such a converter structure is capable of generating a coherent spin wave beam. By introducing a short wavelength spin wave beam into existing magnonic gate logic, it is conceivable to reduce the size of devices to the micrometer scale. This method gives access to short wavelength spin waves to a broad range of magnonic devices without the need for refined sample preparation techniques. The presented toolbox for spin wave manipulation, emission, and conversion is a crucial step for spin wave optics and gate logic.

Spin pumping during the antiferromagnetic-ferromagnetic phase transition of iron-rhodium.

FeRh attracts intensive interest in antiferromagnetic (AFM) spintronics due to its first-order phase transition between the AFM and ferromagnetic (FM) phase, which is unique for exploring spin dynamics in coexisting phases. Here, we report lateral spin pumping by which angular momentum is transferred from FM domains into the AFM matrix during the phase transition of ultrathin FeRh films. In addition, FeRh is verified to be both an efficient spin generator and an efficient spin sink, by electrically probing vertical spin pumping from FM-FeRh into Pt and from Py into FeRh, respectively. A dramatic enhancement of damping related to AFM-FeRh is observed during the phase transition, which we prove to be dominated by lateral spin pumping across the FM/AFM interface. The discovery of lateral spin pumping provides insight into the spin dynamics of magnetic thin films with mixed-phases, and the significantly modulated damping advances its potential applications, such as ultrafast spintronics.

X-ray magnetic linear dichroism as a probe for non-collinear magnetic state in ferrimagnetic single layer exchange bias systems.

Ferrimagnetic alloys are extensively studied for their unique magnetic properties leading to possible applications in perpendicular magnetic recording, due to their deterministic ultrafast switching and heat assisted magnetic recording capabilities. On a prototype ferrimagnetic alloy we demonstrate fascinating properties that occur close to a critical temperature where the magnetization is vanishing, just as in an antiferromagnet. From the X-ray magnetic circular dichroism measurements, an anomalous 'wing shape' hysteresis loop is observed slightly above the compensation temperature. This bears the characteristics of an intrinsic exchange bias effect, referred to as atomic exchange bias. We further exploit the X-ray magnetic linear dichroism (XMLD) contrast for probing non-collinear states which allows us to discriminate between two main reversal mechanisms, namely perpendicular domain wall formation versus spin-flop transition. Ultimately, we analyze the elemental magnetic moments for the surface and the bulk parts, separately, which allows to identify in the phase diagram the temperature window where this effect takes place. Moreover, we suggests that this effect is a general phenomenon in ferrimagnetic thin films which may also contribute to the understanding of the mechanism behind the all optical switching effect.

Entropy-limited topological protection of skyrmions.

Magnetic skyrmions are topologically protected whirls that decay through singular magnetic configurations known as Bloch points. We used Lorentz transmission electron microscopy to infer the energetics associated with the topological decay of magnetic skyrmions far from equilibrium in the chiral magnet Fe1-x Co x Si. We observed that the lifetime τ of the skyrmions depends exponentially on temperature, [Formula: see text]. The prefactor τ0 of this Arrhenius law changes by more than 30 orders of magnitude for small changes of the magnetic field, reflecting a substantial reduction of the lifetime of skyrmions by entropic effects and, thus, an extreme case of enthalpy-entropy compensation. Such compensation effects, being well known across many different scientific disciplines, affect topological transitions and, thus, topological protection on an unprecedented level.

Quantitative separation of the anisotropic magnetothermopower and planar Nernst effect by the rotation of an in-plane thermal gradient.

A thermal gradient as the driving force for spin currents plays a key role in spin caloritronics. In this field the spin Seebeck effect (SSE) is of major interest and was investigated in terms of in-plane thermal gradients inducing perpendicular spin currents (transverse SSE) and out-of-plane thermal gradients generating parallel spin currents (longitudinal SSE). Up to now all spincaloric experiments employ a spatially fixed thermal gradient. Thus, anisotropic measurements with respect to well defined crystallographic directions were not possible. Here we introduce a new experiment that allows not only the in-plane rotation of the external magnetic field, but also the rotation of an in-plane thermal gradient controlled by optical temperature detection. As a consequence, the anisotropic magnetothermopower and the planar Nernst effect in a permalloy thin film can be measured simultaneously. Thus, the angular dependence of the magnetothermopower with respect to the magnetization direction reveals a phase shift, that allows the quantitative separation of the thermopower, the anisotropic magnetothermopower and the planar Nernst effect.

Three-dimensional Character of the Magnetization Dynamics in Magnetic Vortex Structures: Hybridization of Flexure Gyromodes with Spin Waves.

Three-dimensional linear spin-wave eigenmodes of a vortex-state Permalloy disk are studied by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. The simulations confirm that the increase of the disk thickness leads to the appearance of additional exchange-dominated so-called gyrotropic flexure modes having nodes along the disk thickness, and eigenfrequencies that decrease when the thickness is increased. We observe the formation of a gap in the mode spectrum caused by the hybridization of the first flexure mode with one of the azimuthal spin-wave modes of the disk. A qualitative change of the transverse profile of this azimuthal mode is found, demonstrating that in a thick vortex-state disk the influence of the "transverse" and the "azimuthal" coordinates cannot be separated. The three-dimensional character of the eigenmodes is essential to explain the recently observed asymmetries in an experimentally obtained phase diagram of vortex-core reversal in relatively thick Permalloy disks.

Epitaxial Growth of Room-Temperature Ferromagnetic MnAs Segments on GaAs Nanowires via Sequential Crystallization.

We investigate the incorporation of manganese into self-catalyzed GaAs nanowires grown in molecular beam epitaxy. Our study reveals that Mn accumulates in the liquid Ga droplet and that no significant incorporation into the nanowire is observed. Using a sequential crystallization of the droplet, we then demonstrate a deterministic and epitaxial growth of MnAs segments at the nanowire tip. This technique may allow the seamless integration of multiple room-temperature ferromagnetic segments into GaAs nanowires with high-crystalline quality.

Longitudinal spin Seebeck effect contribution in transverse spin Seebeck effect experiments in Pt/YIG and Pt/NFO.

The spin Seebeck effect, the generation of a spin current by a temperature gradient, has attracted great attention, but the interplay over a millimetre range along a thin ferromagnetic film as well as unintended side effects which hinder an unambiguous detection have evoked controversial discussions. Here, we investigate the inverse spin Hall voltage of a 10 nm thin Pt strip deposited on the magnetic insulators Y3Fe5O12 and NiFe2O4 with a temperature gradient in the film plane. We show characteristics typical of the spin Seebeck effect, although we do not observe the most striking features of the transverse spin Seebeck effect. Instead, we attribute the observed voltages to the longitudinal spin Seebeck effect generated by a contact tip induced parasitic out-of-plane temperature gradient, which depends on material, diameter and temperature of the tip.

Nonlinear spin-wave excitations at low magnetic bias fields.

Nonlinear magnetization dynamics is essential for the operation of numerous spintronic devices ranging from magnetic memory to spin torque microwave generators. Examples are microwave-assisted switching of magnetic structures and the generation of spin currents at low bias fields by high-amplitude ferromagnetic resonance. Here we use X-ray magnetic circular dichroism to determine the number density of excited magnons in magnetically soft Ni80Fe20 thin films. Our data show that the common model of nonlinear ferromagnetic resonance is not adequate for the description of the nonlinear behaviour in the low magnetic field limit. Here we derive a model of parametric spin-wave excitation, which correctly predicts nonlinear threshold amplitudes and decay rates at high and at low magnetic bias fields. In fact, a series of critical spin-wave modes with fast oscillations of the amplitude and phase is found, generalizing the theory of parametric spin-wave excitation to large modulation amplitudes.

Spin Hall voltages from a.c. and d.c. spin currents.

In spin electronics, the spin degree of freedom is used to transmit and store information. To this end the ability to create pure spin currents--that is, without net charge transfer--is essential. When the magnetization vector in a ferromagnet-normal metal junction is excited, the spin pumping effect leads to the injection of pure spin currents into the normal metal. The polarization of this spin current is time-dependent and contains a very small d.c. component. Here we show that the large a.c. component of the spin currents can be detected efficiently using the inverse spin Hall effect. The observed a.c.-inverse spin Hall voltages are one order of magnitude larger than the conventional d.c.-inverse spin Hall voltages measured on the same device. Our results demonstrate that ferromagnet-normal metal junctions are efficient sources of pure spin currents in the gigahertz frequency range.

Vortex core reversal due to spin wave interference.

In this Letter we address spin wave dynamics involved in fast and selective vortex core polarity reversal by rotating magnetic field bursts. In a first example we explain the origin of the delayed switching for excitations with short bursts of only one period duration as an interference effect between spin wave modes. Second, when the vortex core is initially no longer at rest but in gyrotropic motion, the magnetization dynamics become more complicated and the interaction of spin waves with the vortex core leads to a variety of nonlinear effects. Our analysis allows us to explain the experimentally observed switching diagram for simultaneous excitation of spin waves and gyrotropic mode.

Magnetic vortex core reversal by excitation of spin waves.

Micron-sized magnetic platelets in the flux-closed vortex state are characterized by an in-plane curling magnetization and a nanometer-sized perpendicularly magnetized vortex core. Having the simplest non-trivial configuration, these objects are of general interest to micromagnetics and may offer new routes for spintronics applications. Essential progress in the understanding of nonlinear vortex dynamics was achieved when low-field core toggling by excitation of the gyrotropic eigenmode at sub-GHz frequencies was established. At frequencies more than an order of magnitude higher vortex state structures possess spin wave eigenmodes arising from the magneto-static interaction. Here we demonstrate experimentally that the unidirectional vortex core reversal process also occurs when such azimuthal modes are excited. These results are confirmed by micromagnetic simulations, which clearly show the selection rules for this novel reversal mechanism. Our analysis reveals that for spin-wave excitation the concept of a critical velocity as the switching condition has to be modified.

Vortex core switching by coherent excitation with single in-plane magnetic field pulses.

The response of magnetic vortex cores to subnanosecond in-plane magnetic field pulses was studied by time-resolved x-ray microscopy. Vortex core reversal was observed and the switching events were located in space and time. This revealed a mechanism of coherent excitation by the leading and trailing edges of the pulse, lowering the field amplitude required for switching. The mechanism was confirmed by micromagnetic simulations and can be understood in terms of gyration around the vortex equilibrium positions, displaced by the applied field.

Polarization selective magnetic vortex dynamics and core reversal in rotating magnetic fields.

We report on the observation of magnetic vortex dynamics in response to rotating magnetic fields in submicron platelets. Unlike linear fields or spin polarized currents, which excite both vortex core polarization states, an in-plane rotating field can selectively excite one of the polarization states. We demonstrate by direct imaging with time-resolved scanning x-ray microscopy that the rotating field only excites the gyrotropic mode if the rotation sense of the field coincides with the vortex gyration sense and that such a field can selectively reverse the vortex polarization.

Microwave assisted switching of single domain Ni80Fe20 elements.

We study the switching behavior of thin single domain magnetic elements in the presence of microwave excitation. The application of a microwave field strongly reduces the coercivity of the elements. We show that this effect is most profound at the ferromagnetic resonance frequency of the elements. Observations using time-resolved magneto-optic Kerr microscopy in combination with pulsed microwave excitation further support that the microwave assisted switching process is indeed based on the coherent motion of the magnetization.

Spin-wave eigenmodes of permalloy squares with a closure domain structure.

Quantized spin-wave eigenmodes in single, 16 nm thick and 0.75 to 4 mum wide square permalloy islands with a fourfold closure domain structure have been investigated by microfocus Brillouin light scattering spectroscopy and time resolved scanning magneto-optical Kerr microscopy. Up to six eigenmodes were detected and classified. The main direction of the spin-wave quantization in the domains was found to be perpendicular to the local static magnetization. An additional less pronounced quantization along the direction parallel to the static magnetization was also observed.