Session L50: Spin-Orbit Mediated Chiral Spin Textures II

Skyrmion Hall Effect

Theory indicates a large transverse component for the motion of magnetic skyrmions, the skyrmion Hall effect, due to the topological charge resulting in a net gyrotropic force. Here we demonstrate for electric current driven magnetic skyrmions the direct observation of this transverse motion using magneto-optic Kerr effect imaging.\footnote{W, Jiang {\em at al.}, Nature Phys., doi:10.1038/nphys3883 (2016).} We observe that the skyrmion Hall angle varies continuously from zero just above the depinning current threshold until $\approx 30^\circ$ for current densities up to $10^8$~A/cm$^2$. This variation of the skyrmion Hall angle indicates the changing competition between pinning and gyrotropic forces as the skyrmion motion transitions from the creep to the flow regime. The maximum observed Hall angle is in good agreement with theory for rigid skyrmion motion.   

Nonlinear Magnus-induced dynamics and Shapiro spikes for ac and dc driven skyrmions on periodic quasi-one-dimensional substrates

We numerically examine skyrmions interacting with a periodic quasi-one-dimensional substrate. When we drive the skyrmions perpendicular to the substrate periodicity direction, a rich variety of nonlinear Magnus-induced effects arise, in contrast to an overdamped system that shows only a linear velocity-force curve for this geometry. The skyrmion velocity-force curve is strongly nonlinear and we observe a Magnus-induced speed-up effect when the pinning causes the Magnus velocity response to align with the dissipative response. At higher applied drives these components decouple, resulting in strong negative differential conductivity. For skyrmions under combined ac and dc driving, we find a new class of phase locking phenomena in which the velocity-force curves contain a series of what we call Shapiro spikes, distinct from the Shapiro steps observed in overdamped systems. There are also regimes in which the skyrmion moves in the direction opposite to the applied dc drive to give negative mobility.   

Oxygen induced Dzyaloshinskii-Moriya interaction in Pt/CoFe and Cu/CoFe bilayers

The Dzyaloshinskii-Moriya interaction (DMI) can exist in systems with broken inversion symmetry and gives rise to chiral domain-walls and skyrmions. So far research on bilayers has concentrated on systems, where a ferromagnet is in contact with metallic high spin-orbit materials. The early work on DMI has focused on bulk magnetic oxides. The weak ferromagnetism in these oxides, for example Fe$_{\mathrm{2}}$O$_{\mathrm{3}}$, originates from the DMI, which has been explained in terms of anisotropic superexchange. In order to answer the question if ferromagnet/oxide bilayers also exhibit DMI, we have prepared Pt/CoFe and a Cu/CoFe sample series by sputter deposition. The CoFe layer was exposed in-situ for a time T of up to 1000 s to an Oxygen-Argon gas mixture to create an oxide coverage. The samples were subsequently capped by Cu/Ta to prevent further oxidation. We used the magnetic moment of our samples measured by SQUID magnetometry to quantify the thickness reduction during oxidation. We determined the DMI induced frequency-shift in these samples by Brillouin-Light-Scattering spectroscopy. The measured frequency-shift was corrected for surface anisotropy contributions before determining the DMI. We normalized the DMI to a 1nm ferromagnetic film thickness to account for the interfacial nature of the DMI. We found that in both sample series the DMI increases with the degree of oxidation, unambiguously demonstrating that the ferromagnet/oxide interface induces DMI in thin bilayers systems.   

Compositional dependence of interfacial spin-orbit phenomena in Co$_{\mathrm{x}}$Fe$_{\mathrm{1-x}}$/Pt bilayers

We experimentally investigate the dependence of the interfacial Dzyaloshinskii--Moriya interaction (DMI) on the alloy composition in Co$_{\mathrm{x}}$Fe$_{\mathrm{1-x}}$/Pt bilayers. Following the methods in Ref. [1] we use Brillouin light scattering to determine the magnitude of the spin-wave dispersion shift induced by the antisymmetric exchange, allowing us to determine the strength of the DMI constant as a function of Co concentration x. Interestingly, the DMI constant varies significantly as a function of x and peaks at approximately x$=$0.5. These results are compared to measurements of the Heisenberg exchange obtained from fitting Bloch's law to temperature dependent magnetometry data. [1] H. T. Nembach et al., Nature Physics 11, 825--829 (2015)   

Asymmetric domain wall expansion in ultra-thin films with Dzyaloshinskii-Moriya Interaction

The Dzyaloshinskii-Moriya interaction (DMI) at heavy-metal/ferromagnet interfaces can stabilize chiral spin textures. Chiral Spin textures, such as spin-helixes, chiral domain walls, and skyrmions have been investigated for use in next generation memory and spin logic applications. It been recently reported that field-driven creep regime bubble domain expansion thin films that exhibit DMI is asymmetric under the application of an in-plane field, which can be used to quantify the DMI effective field in the domain wall (DW). The asymmetric expansion has been attributed to both chiral energy and chiral damping effects. Here, we have imaged domain expansion in Pt(3nm)/Co(0.9nm)/Pt(x)/GdOx(3nm) films using wide-field Kerr microscopy. A Pt spacer later allows us to investigate the sensitivity of the interface between the ferromanget and oxide to the DMI. Small amounts of Pt at this top interface serve to counter the effect of DMI at the bottom interface, as well as change the oxygen coordination at this interface. By separating the symmetric and asymmetric components of the DW velocity, we propose a new, quantitative model to address both an asymmetric response from the DMI and a symmetric response contribution from pinning that is weighted by drive field. Understanding of these contributions can lead to better understanding of the domain wall dynamics in these materials and better quantization of magnetic parameters.   

A study of chiral magnetic stripe domains within an in-plane virtual magnetic field using SPLEEM

Stripe domains form in magnetic thin films at the spin reorientation transition. Different from the typical Bloch type domain walls (DW), it was found recently that Dzyaloshinskii--Moriya interaction (DMI) could lead to chiral N\'{e}el type DMs in the stripe domain phase. While the application of an out-of-plane magnetic field is known to break the stripes into skyrmions, it is unclear how the chiral stripe phase would respond to an in-plane magnetic field? Here we report an experimental study on Fe/Ni/Cu/Co/Cu(001) system using spin-polarized low-energy electron microscopy (SPLEEM). In this system, the Fe/Ni layer exhibits stripe domains with chiral N\'{e}el type DMs and its interlayer coupling to Co across the Cu spacer layer serves as an in-plane virtual magnetic field whose strength can be tuned by changing the Cu spacer layer thickness. We find the in-plane field aligns the stripes parallel to the field direction. Increasing the in-plane field strength gradually changes the N\'{e}el type DWs into Bloch type DWs. However, it is surprising the adjacent N\'{e}el DWs behave asymmetrically in-response to the in-plane magnetic field, suggesting a topological effect in switching the chiral N\'{e}el DWs to the non-chiral Bloch DWs.   

Topological Spin Textures in Confined Geometries

The magnetic skyrmion is a nanostructured spin texture stabilized by the spin-orbital coupling. Its nontrivial topology enables unique dynamical property and thermal stability, which give out promise on future magnetic memory devise. However, to enable its applications, it is essential to understand the skyrmion properties in confined geometries and tackle key challenges including the creation and detection of skyrmions, preferably without magnetic fields. In this talk, I will present our recent theory-experiment collaboration results, covering studies of skyrmions in nanoribbon, nanodisk, and nanowires. Zero field skyrmions and their polarization switch will be discussed. New skyrmion materials and new topological textures in helimagnet heterostructures will be presented.   

Topological spin-transfer drag driven by skyrmion dynamics

The topological stability of skyrmion magnetic textures can be used to transmit spin signals over long distances. We illustrate this idea in a two-terminal geometry in which a thin film of an insulating chiral magnet is intercalated between two metallic reservoirs. We show how spin-transfer forces induced by spin-polarized currents in the metal pump skyrmion charge into the magnet, sustaining an algebraically-decaying skyrmion flux between terminals. The reciprocal electromotive forces induced by the skyrmion dynamics pumps itinerant spins in the metals. The effect is manifested as a current drag in an open geometry, or equivalently, as a positive magnetoresistance when the circuit is closed in parallel. Spin-transport signatures in lateral heterostructures may be employed to monitor the skyrmion dynamics and characterize the different phases of insulating chiral magnets like Cu$_2$OSeO$_3$.   

Relaxation dynamics of interacting skyrmions in thin films

Magnetic skyrmions are topologically protected spin textures which were recently observed in certain chiral magnets and thin films. Skyrmions can be moved by very low current densities which makes them very promising in spintronic applications such as data storage devices and logic gates. A thorough understanding of the relaxation processes for systems of interacting skyrmions far from equilibrium could prove invaluable in real world applications but is currently lacking in the literature. The dynamics are described by the Landau-Lifshitz-Gilbert (LLG) equation, however, simulating many interacting skyrmions by solving the LLG equation is computationally infeasible. We employ a suitable two-dimensional particle based model derived from Thiele's approach to study the two-time density correlation function and other quantities. The particle model differs most notably from similar models which describe vortices in type-II superconductors by the addition of the Magnus force which points perpendicular to the skyrmion velocity in the plane. Numerical studies reveal non-universal scaling of the correlation function where the scaling exponent is a function of the ratio of the Magnus force strength to damping coefficient as well as of the Gaussian noise.   

Noise Fluctuations and Avalanche Statistics of Skyrmions with Quenched Disorder

Magnetic skyrmions are nanoscopic magnetic textures that enjoy topologically-protected stability and exhibit particle-like behavior. Their novel transport properties have generated extensive basic research and show great potential for using skyrmions as information carriers in future high-density magnetic storage and logic devices. At the particle level, both magnetic skyrmions and superconducting vortices - another kind of topological excitations that also behave as particles - admit a common theoretical description. While in real materials, superconducting vortex dynamics is dissipation-dominated, the so-called Magnus force dominates the dynamics of magnetic skyrmions. Using a particle-based model, we simulate two different systems in the presence of quenched disorder: velocity noise fluctuations of current-driven skyrmions and avalanche statistics of flux-driven skyrmions. We obtain the power spectral density, dynamical phase diagram, as well as the avalanche critical exponents as a function of the Magnus force strength. Our results show that both the noise and avalanche properties of skyrmions depart significantly from the known case of superconducting vortices.   

Skyrmion-Antiskyrmion pair creation by in-plane currents

Magnetic Skyrmions are considered to be topologically protected particles. Due to this stability, their small size and the possibility to move them by low electric currents they are proper candidates for spintronic devices. However, without violating this topological protection, it is should be possible to create Skyrmion-Antiskyrmion pairs as long as the total Skyrmion number does not change. In fact, we derive a Skyrmion equation of motion and show that electric currents can create such Skyrmion-Antiskyrmion pairs. By this equation of motion we are able to give general prerequisites for this pair creation process. We confirm these results by numerical simulations. On a lattice, where topological protection gets imperfect, the Antiskyrmions in these pairs can be destroyed and only the Skyrmions remain. This eventually changes the total Skyrmion number and yields new ways of creating and controlling Skyrmions.   

First-principles simulations and low-energy effective modeling of skyrmion in MnGe

MnGe has been reported as a candidate of three-dimensional (3D) skyrmion crystal, showing the variation of the skyrmion size along the z-direction [1,2]. Also, the small size (3nm) and high density of the skyrmion are the desired properties for information storage. We have performed the first-principles simulations and constructed a tight-binding (TB) model with calculated electronic-structure information to investigate the skyrmion phase in MnGe. Our first-principles study within density functional theory (DFT) shows that the small-sized skyrmion could be stabilized in a 2D structure. Such a high density of the skyrmion is in good agreement with the experimental finding of large topological Hall effect [1]. Using the TB simulation package [3] based on the DFT bandstructure, we have studied skyrmion state in a large supercell of MnGe beyond the DFT capability. The role of the correlation effect and the pinning effect of vacancy have been investigated. Finally, the nature of 3D skyrmion in MnGe has also been discussed. [1] Y. Shiomi et al., Phys. Rev. B 88, 064409 (2013); [2] T. Tanigaki et al., Nano Lett. 15, 5438 (2015); [3] Yuan-Yen Tai and Jian-Xin Zhu, arXiv:1603.03107 (2016)   

Surface Effects In Chiral Magnets

We theoretically studied~a general 3D model of a chiral magnet revealing a variety of unusual localized magnetic states appearing near the free edges of the sample. In particular, we present a recently discovered new type of thermodynamically stable magnetic quasi-particle, which appears at interfaces and surfaces of isotropic chiral magnets [Phys. Rev. Lett.~\textbf{115}, 117201~(2015)]. We use the term chiral bobber (CB) to refer to it. The CB constitute a new class of hybrid particles composed of a smooth magnetization field and a magnetic singularity. Comparing the stability and dynamical properties of CB with ordinary magnetic skyrmions, we conclude that CB can be considered as promising object not only for fundamental research but also for various practical applications in spintronic devices. We predict the existence of such surface states in different B20-type alloys. Moreover, we have calculated the phase diagram of magnetic states for film geometry in applied magnetic field [New J. Phys.~\textbf{18}, 045002 (2016)], where we have found a novel magnetic ground state localized at the surface of the sample and stacked on top of the conical bulk phase. It can be considered as a superposition of helical and cycloidal spin spirals.