ARTICLES https://doi.org/10.1038/s41928-019-0359-2 The role of temperature and drive current in skyrmion dynamics Kai Litzius1,2,3, Jonathan Leliaert 4, Pedram Bassirian1, Davi Rodrigues1, Sascha Kromin1, Ivan Lemesh 5, Jakub Zazvorka1,6, Kyu-Joon Lee1, Jeroen Mulkers4,7, Nico Kerber1,2, Daniel Heinze1, Niklas Keil1, Robert M. Reeve1,2, Markus Weigand3, Bartel Van Waeyenberge4, Gisela Schütz3, Karin Everschor-Sitte1,2, Geoffrey S. D. Beach 5* and Mathias Kläui 1,2* Magnetic skyrmions are topologically stabilized nanoscale spin structures that could be of use in the development of future spintronic devices. When a skyrmion is driven by an electric current it propagates at an angle relative to the flow of current— known as the skyrmion Hall angle (SkHA)—that is a function of the drive current. This drive dependence, as well as thermal effects due to Joule heating, could be used to tailor skyrmion trajectories, but are not well understood. Here we report a study of skyrmion dynamics as a function of temperature and drive amplitude. We find that the skyrmion velocity depends strongly on temperature, while the SkHA does not and instead evolves differently in the low- and high-drive regimes. In particular, the maximum skyrmion velocity in ferromagnetic devices is limited by a mechanism based on skyrmion surface tension and deformation (where the skyrmion transitions into a stripe). Our mechanism provides a complete description of the SkHA in ferromagnetic multilayers across the full range of drive strengths, illustrating that skyrmion trajectories can be engineered for device applications. he manipulation of magnetic states using electric currents and micrometre-sized skyrmion spin structures28. Recently, fast is of increasing interest in the development of spintronic and reproducible skyrmion motion in thin multilayer devices devices1,2, and a wide range of current-driven effects has was demonstrated21. Thermally induced skyrmion diffusion has T 29–31 been studied, from low-power switching to induced oscillations. also been theoretically predicted and observed in ultralow-pin- One promising device proposal is the racetrack memory3, in which ning materials32. propagating domain walls in a track architecture are used for non- The non-zero topological charge of skyrmions is responsible for volatile and fast data storage4. In such a design, however, domain the skyrmion Hall effect6,33. In particular, current-driven skyrmions walls need to be driven deterministically without becoming pinned, acquire a transverse velocity component through a topology- for example at the track edges, which may be challenging. An alter- induced gyroforce, analogous to charged particles in the conven- 5,6 native approach is a skyrmion racetrack architecture , which could tional Hall effect. The skyrmion Hall angle (SkHA, θSkH), related to potentially circumvent some of the drawbacks of the domain-wall- the resulting motion, was originally assumed to depend only on the based system. Magnetic skyrmions7–12 benefit from topological skyrmion size and the material parameters, which are fixed for a stabilization12–17, and due to their non-trivial topology they exhibit given system. However, the SkHA has been experimentally shown complex dynamics and are more robust against inhomogeneities to be drive dependent21,22,34, in contrast to explanations based on (such as edge roughness) compared with domain walls. simple rigid skyrmion models with perfect sample properties. In Skyrmions in multilayer heavy-metal/ferromagnet stacks are addition, the transverse motion caused by the SkHA may expel the commonly stabilized by the interfacial Dzyaloshinskii–Moriya skyrmions from the edges of a track, making the development of interaction (DMI)18,19, which also dictates their chirality. The DMI practical implementations difficult. can arise from broken inversion symmetry in bulk crystals and at Because both the gyroforce and thus the SkHA originate from symmetry-breaking interfaces. Since the DMI favours a perpen- the topological spin structure of the skyrmion, they cannot be com- dicular orientation of adjacent spins, it stabilizes helical magneti- pletely avoided in ferromagnets6,7. One approach to address this zation configurations such as skyrmions and spin spirals, together is to employ (synthetic) antiferro- or ferrimagnetic materials with with the exchange interaction. An efficient and promising approach sublattices of opposite spin orientations27,34–37. However, antiferro- to drive skyrmions along a magnetic track is to use spin–orbit magnets are difficult to tailor and investigate experimentally10,38, torques (SOTs), since they are conveniently generated through the whereas ferrimagnets exhibit a finite SkHA if not operated exactly same heavy-metal/ferromagnet interfaces that also yield a strong at the compensation temperature27,34,39, and Joule heating can make DMI9,20. Much work has been dedicated to investigating these mul- this problematic. To predict and eventually tailor the SkHA for spe- tilayer systems21–26 and trying to engineer the properties and sizes cific applications, it is important to investigate how the magnitude of the resulting spin states, including atomistic8, nanoscale24,27 of the SkHA varies with the electric drive current, as well as the 1Institute of Physics, Johannes Gutenberg-University Mainz, Mainz, Germany. 2Graduate School of Excellence Materials Science in Mainz, Mainz, Germany. 3Max Planck Institute for Intelligent Systems, Stuttgart, Germany. 4Department of Solid State Sciences, Ghent University, Ghent, Belgium. 5Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA. 6Institute of Physics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic. 7Department of Physics, University of Antwerp, Antwerp, Belgium. *e-mail: [email protected]; [email protected] 30 NATURE ELECTRONICS | VOL 3 | JANuarY 2020 | 30–36 | www.nature.com/natureelectronics NATURE ELECTRONICS ARTICLES temperature dependence of the skyrmion Hall effect. In particular, ab it would be useful to identify how the SkHA is affected by the sky- 250 nm rmion’s topological spin structure and dynamics, including effects such as deviations from a rigid spin structure and interactions with defects. Recent work has revealed that in ferromagnets defects of the magnetic material22,40,41 and the deformation of skyrmions21 are possible origins for the drive dependence, though there has been no consistent study of the effects for the full drive region, from the creep to the high-flow regime. Only the insights of the internal dynamics of the skyrmion spin structure that govern the motion Fig. 1 | Measurement principle and typical observed skyrmion contrast. would then allow one to predict and eventually tailor the SkHA for a, X-rays are focused onto a thin-film device sample, placed on top of a specific applications. SiN membrane. The wire is connected by two gold striplines for current In this Article, we explore the effects of temperature and drive injection and moved to scan the magnetization pattern with the focused current on ferromagnetic skyrmion trajectories, defined by the X-ray beam. On the other side, the transmitted photons are counted by SkHA and skyrmion velocity. We compare existing theories based a photodetector. Due to the X-ray magnetic circular dichroism effect, the on defect-induced pinning and deformation, and assess their appli- absorption of circularly polarized photons by the material is dependent cability under various drive and temperature regimes. We find that on the magnetization state. The sample holder provides additional the skyrmion velocity increases with temperature because it follows temperature control. b, Typical image of skyrmions in the studied the increase in the damping-like SOT (DL-SOT). We develop a pic- material system. ture of skyrmion dynamics that covers the full range of creep and flow regimes, which have only been studied separately so far21,22. We also identify a regime where the SkHA drive dependence is no longer linear and follows a more complex scaling, which cannot be faster skyrmion motion, which is a desirable property for applica- explained by existing models. As a result, we develop a model that tions. When renormalizing the data for the temperature-dependent incorporates disorder (such as defects and thermal fluctuations), relative torque values, the curves overlap and form a universal curve internal mode excitations and a new type of skyrmion deformation. above roughly 20 m s−1 (Fig. 2b). This threshold for reproducible motion also corresponds well to previous findings21, where repro- Experimental observations ducible dynamics was only observed above roughly 20 m s−1 in a Our system is a [Pt(2.7 nm)/CoFeB(0.86 nm)/MgO(1.5 nm)]15 nominally identical stack. multilayer stack, similar to the stacks we used in previous mea- The fit of the velocities in this linear regime does not go through surements21. Imaging was performed using scanning transmission the origin due to pinning effects at defects in the material. This X-ray microscopy42, with the X-ray magnetic circular dichroism behaviour is historically attributed to the ‘depinning’ regime, effect43 in static mode (that is, taking before–after pulse images of leading to the conclusion that the flow regime would only start at the magnetic states), and a small offset out-of-plane magnetic field around 75 m s−1. This is, however, inconsistent with our previous was applied to maintain a constant skyrmion