Session V41: Skyrmion Transport and Topological Hall Effect

Reservoir Computing with Random Skyrmion Fabrics

The topologically protected magnetic spin configurations known as skyrmions offer promising applications due to their stability, mobility and localization. Thanks to their many nanoscale properties, skyrmions have been shown to be promising in many applications ranging from non-volatile memory and spintronic logic devices, to enabling the implementation of unconventional computational standards such as Stochastic computing. In this talk we will discuss how a random skyrmion ``fabric'' composed of skyrmion clusters embedded in a magnetic substrate can be effectively employed to implement a functional Reservoir Computing device for recognizing and predicting spatio-temporal events. This is achieved by leveraging the nonlinear resistive response of the individual skyrmions arising from their current dependent anisotropic magneto-resistance effect (AMR). Complex time-varying current signals injected via contacts into the magnetic substrate are shown to be modulated nonlinearly by the fabric's AMR due to the current distribution following paths of least resistance as it traverses the geometry. By tracking resistances across multiple input and output contacts, we show how the instantaneous current distribution effectively carries temporally correlated information about the injected signal. This in turn allows us to numerically demonstrate simple pattern recognition. We argue that the fundamental ingredients for such a device to work are threefold: i) Concurrent probing of the magnetic state; ii) stable ground state when forcings are removed; iii) nonlinear response to input forcing. Whereas we demonstrate this by employing skyrmion fabrics, the basic ingredients should be general enough to spur the interest of the greater magnetism and magnetic materials community to explore novel reservoir computing systems.   

Rare Earth-Transition Metal Alloys as Promising Materials for Small Skyrmions and Ultrafast Chiral Spin Texture Dynamics

Spintronics aims to understand and control spins on the nanoscale and should enable next-generation data storage and logic devices. One technological and scientific key challenge is to stabilize small spin textures and to manipulate them efficiently with high speeds [1-3]. Inspired by hard disk materials, research has primarily focused on ferromagnetic materials, but these materials show fundamental limits for speed and size [4-6], calling for radically different ideas [4-7].
Here, we demonstrate that compensated ferrimagnets are not affected by these limits. We realize a current-driven domain wall velocity of over 1 km/s near the angular momentum compensation temperature (T_A) and room-temperature stable skyrmions with minimum observed diameters approaching ~10 nm near magnetic compensation (T_M). We present theory explaining these observations and demonstrate that high-speed, high-density spintronics devices based on current-driven spin textures can be realized using materials where T_A and T_M are close together.

[1] Parkin, S & Yang, S-H Nat Nano 10 (2015)
[2] Fert, A et al. Nat Nano 8 (2013)
[3] Emori, S et al. Nat Mat 12 (2013)
[4] Yang, S-H et al. Nat Nano 10 (2015)
[5] Kim, K-J et al. Nat Mat 16 (2017)
[6] Büttner, F et al. Sci Rep 8 (2018)
[7] Jungwirth, T et al. Nat Nano 11 (2016)   

Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet Gd2PdSi3

Frustrated magnets provide abundant opportunities for discovering complex spin textures, which sometimes yield unconventional electromagnetic responses in correlated electron systems. It is theoretically predicted that magnetic frustration may also promote a topologically nontrivial spin state [1], i.e., magnetic skyrmions. Empirically, however, skyrmions are essentially concomitant with noncentrosymmetric lattice structures or interfacial symmetry-breaking heterostructures [2]. Here, we report the emergence of a Bloch-type skyrmion state in a frustrated centrosymmetric triangular-lattice magnet Gd₂PdSi₃ [3]. We identified the field-induced skyrmion phase via a giant topological Hall response, which is further corroborated by the observation of in-plane spin modulation probed by resonant x-ray scattering. Our results exemplify a new platform of magnetic frustration for producing topological spin textures endowed with emergent electrodynamics in centrosymmetric magnets.
[1] C. D. Batista et al., Rep. Prog. Phys. 79, 084504 (2016).
[2] A. Fert et al., Nat. Nanotech. 8, 152 (2013).
[3] T. Kurumaji et al., arXiv:1805.10719.   

Observation of topological Hall effect in amorphous Fe/Gd heterostructures with asymmetric Bloch-type domain wall chirality population.

The non-trivial topological nature of chiral magnetic spin textures results in novel electromagnetic properties, such as the topological Hall effect (THE) which commonly appears as an anomaly in the Hall resistivity. So far, the THE has been primarily observed in magnetic crystals lacking inversion symmetry (e.g. MnSi [1], MnGe [2], SrRuO₃-SrIO₃[3]). In these systems, the magnetic spin textures possess a single Bloch- or Néel-type chirality that is set by either a bulk or an interfacial antisymmetric exchange interaction, commonly known as Dzyaloshinskii–Moriya interaction.

We report the observation of a THE in amorphous rare-earth transition-metal heterostructures with perpendicular magnetic anisotropy that possess a coexistence of left and right chiral Bloch-type domain walls with unequal population distribution. A combination of real-space observations by Lorentz TEM, magnetometry and transport measurements reveal one can engineer amorphous thin-film materials with a controllable THE, as will be discussed, based on temperature dependent studies on several heterostructures.

[1] A. Neubauer, et al.Phys. Rev. Lett.102, 186602 (2009).
[2] N. Kanazawa, et al. Phys. Rev. Lett. 106, 156603 (2011).
[3] J. Matsuno, et al. Sci. Adv. 2, e1600304 (2016).   

Single magnetic skyrmion creation, detection, and dynamics within a magnetic tunnel junction

We experimentally demonstrate the deterministic creation of a stable topological spin texture in the free layer of a magnetic tunnel junction at cryogenic temperatures. Through simultaneous measurements of tunnel magnetoresistance and spin-polarized current-induced magnetic resonance, we find that the spin texture is characterized by a field-dependent intermediate junction resistance and a unique magnetic resonance signature. Comparing our findings to micromagnetic simulations, we confirm that the spin texture transition is best described by the nucleation of a single Bloch-type skyrmion in the free layer, aided by a spatially nonuniform stray field from surrounding magnetic layers. We subsequently identify the skyrmion breathing mode in the resonance spectrum and obtain an estimate for the skyrmion diameter at zero field of 75 nm. This result is the first confirmation that magnetic tunnel junctions are viable candidates for skyrmion-based memory and logic architectures could lead to non-invasive, on-chip skyrmion measurement and detection.   

Sluggish steady flow of skyrmion lattice in a confined geometry

An aggregate of magnetic skyrmions^1,2, topologically protected particlelike objects, is an emerging exotic fluid that flows under electric current^3,4. From a hydrodynamics point of view, the skyrmion fluid is peculiar in that its steady flow does not necessarily require a closed-loop skyrmion circuit. However, it remains largely unclear how this peculiarity is involved in the skyrmion steady-flow dynamics. Here, we show that the skyrmion steady flow dramatically slowdowns when the influence of system edges is not negligible. In the micrometre-sized MnSi, the steady-flow velocity is anomalously slow, as evidenced by the observation of resistance narrow-band noise with 10–10⁴ Hz, and its temperature evolution suggests that the steady flow entails thermally activated processes, which are due most likely to the skyrmion creation and annihilation at the edges. Moreover, numerical simulations reveal that the edges limit the skyrmion motion. Thus, our findings capture a vital role of the edges on the skyrmion steady flow, especially in a microstructure.

1. S. Mühlbauer, et al. Science 323, 915-919 (2009).
2. X. Z. Yu, et al. Nature 465, 901-904 (2010).
3. F. Jonietz, et al. Science 330, 1648-1651 (2010).
4. T. Schulz, et al. Nat. Phys. 8, 301-304 (2012).   

Visualizing the dynamics of sub-100 nm Néel Skyrmions in Multilayer Nanowires

The emergence of room temperature skyrmions in technologically-relevant multilayers has intensified efforts towards realizing these topologically stable, nanoscale spin structures for next generation technologies, in particular, neuromorphic computing, Internet of Things. Of great interest is the lateral manipulation of skyrmions on a Racetrack, which builds on their deterministic response to current-induced spin torques in nanowires. Thus far,a clear understanding of the factors governing the dynamics of small (sub-100 nm) skyrmions in granular films remains to be established. Here we utilize magnetic force microscopy to investigate the collective dynamics of a dense skyrmion array with individual speeds up to 24ms^-1, in 2um-wide Pt/Co/MgO nanowires. By examining>2x10⁴ instances of skyrmion motion, we observe several emergent behaviours including the interplay of edge confinement and skyrmion Hall effect, which is crucial to understanding edge-induced skyrmion pinning in Racetrack architectures. In this work, we also detail the effects of skyrmion size, skyrmion-skyrmion interactions and pinning on skyrmion dynamics.The rich dynamics of skyrmions uncovered in our study will potentially fast-track the realization of skyrmion-based Racetrack devices.   

Skyrmion Clustering and Dynamics in Strong Pinning or with Strong Magnus Force Dispersion

We show that skyrmions can exhibit density phase separation when driven over strong pinning. This occurs due to the Magnus force interaction, which creates regions of differing effective skyrmion Hall angle, combined with a density dependence of the skyrmion velocity, which is similar to the density dependent velocity observed at clustering transitions in active matter systems. We also investigate the effect of introducing a dispersion in the Magnus force experienced by individual skyrmions, which could arise if different skyrmion species or sizes coexist in a single sample. In this case, we find that the motion of the different species is locked at low drives, but as the drive increases, a disordering transition occurs when the species begin to slide past each other. At higher drives there is a transition to a species phase separated state in which skyrmions with the same Magnus force cluster together. These transitions are associated with signatures in the skyrmion structure, transport response, and velocity fluctuation spectra.   

Skyrmion Dynamics under the Influence of Defects from DFT to ASD

Any potential skyrmionic application must be able to handle the impact of defects on the skyrmion motion. Until now, most approaches focus on large skyrmions using phenomenological schemes in the micromagnetic regime. Using a combination of first-principles calculations and atomistic spin dynamics, the complex motion of technologically more relevant small skyrmions in Pd/Fe/Ir(111) with 3d and 4d single-atomic defects is studied. Recently, it was shown that such defects can either repel or pin skyrmions [1]. It can be observed that the current threshold needed to overcome the energy barriers, resulting from the impurities, depends on their chemical nature. The obtained dynamical behaviour is richer and goes beyond the expected from the Thiele equation. The complexity of the different motion regimes is revealed and compared with what is known for larger skyrmions. The present study also shines light on how one can engineer defects-based pathways for controlled skyrmion motion.
[1] Lima Fernandes I. et al., Nat. Commun. 9, 4395 (2018).   

Anisotropic magnetoresistance in epitaxial FeGe thin films

The advent of skyrmion imaging and electrical detection is an exciting avenue of research as skyrmions hold promise for next-generation magnetic storage. Presently, in B20 materials, electrical measurements have focused on the detection of non-trivial topological spin textures via topological Hall effect. To further our understanding of transport properties in non-centrosymmetric materials that host skyrmions, we have performed angular-dependent magnetoresistance (ADMR) in the saturated magnetic phase. We have grown epitaxial B20 FeGe/Si(111) films by molecular beam epitaxy. Several features appear in the vicinity of the Curie temperature of 280 K that also persist well above this temperature. Additionally, these features are highly magnetic field dependent. At low temperatures, the signal is dominated by the anisotropic magnetoresistance (AMR) contribution. However, as we approach the magnetic ordering temperature, a strong six-fold symmetric contribution appears. This term, reflecting the crystal symmetry, possibly originates from the magneto-crystalline anisotropy. Curiously, this feature continues to grow in magnitude up to 14 T. We discuss possible origins of these effects above and below the Curie temperature.   

Controlling Skyrmion Hall Angle by engineering mixed skyrmions with stray fields

Skyrmions, topologically protected quasi particles in magnetic materials, are widely explored as candidate excitations to store and transmit information. The dynamics of an isolated skyrmion on a racetrack is limited by the Magnus force for a Neel skyrmion and damping force for a Bloch skyrmion. For identical parameters, Neel and Bloch skyrmions tend to move perpendicular to each other. This orthogonality can be understood by the fact that Neel and Bloch skyrmions can be continuously deformed into each other by a 90 degree rotation in parameter space, which can also be seen as a 90 degree rotation of a frame of reference fixed on a point on the boundary of the skyrmion. Accordingly for a mixed skyrmion it is possible to achieve a movement parallel to the drive current with zero spin Hall angle, which is ideal for controlled skyrmion motion in racetrack applications. The mixed skyrmion can be engineered by a combination of the interfacial DMI, which favors the Neel skyrmion, and the stray field which favors the Bloch skyrmion, without the use of synthetic antiferromagnetic multilayer structures.   

Temperature dependent skyrmion Hall angle in ferrimagnets

Analogous to the Hall effect where electronic charges moving in the presence of a magnetic field acquire a transverse velocity, magnetic solitons with non-zero topological charges (i.e. skyrmions and chiral domains walls) exhibit the skyrmion Hall effect, which opens up new possibilities for manipulating the trajectories of these quasiparticles. The skyrmion Hall effect has been theoretically predicted to vanish for antiferromagnetic skyrmions because of the cancelation of opposite topological charges. We present a study of current driven domain wall dynamics in artificially ferrimagnetic multilayers: Ta(4 nm)/Pt (5 nm)/[Co (0.5 nm)/Gd (1 nm)/Pt(1 nm)]₁₀/Al (2 nm). The magnetic texture in different layers of the multilayer films are coherent and antiferromagnetically aligned. Here we experimentally investigate the current driven magnetization dynamics from room temperature down to temperatures below the compensation point at around 100 K.   

Chiral fluctuation driven topological Hall effect in two-dimensional ferromagnets

Topological Hall effect (THE) is a real space Berry phase phenomenon originated from the non-coplanar spin texture[1]. Recently THE has been associated with the formation of skyrmions in chiral magnets[2][3]. Although chiral fluctuation driven topological charges have been predicted in chiral magnets, the resultant THE has not been observed yet[4]. Herein, we report a surprising observation of THE around ferromagnetic transition temperature T_C in the ferromagnetic SrRuO₃ thin films. The temperature, magnetic field, and thickness dependence of THE are in good agreement with our Monte-Carlo simulations, which provides compelling evidence of the emergence of net topological charges due to chiral fluctuation.

References:
[1] Y. Taguchi, Y. Oohara, H. Yoshizawa, N. Nagaosa, Y. Tokura, Science 291, 2573 (2001).
[2] A. Neubauer, et al., Phys. Rev. Lett. 102, 186602 (2009).
[3] N. Kanazawa, et al., Phys. Rev. Lett. 106, 156603 (2011).
[4] W.-T. Hou, J.-X. Yu, M. Daly, J. Zang, Phys. Rev. B 96, 140403(R) (2017).