France



The broad family of Hall effects comprises phenomena of ordinary, anomalous, planar, topological, and quantum origin. These effects are ubiquitous in electronic systems and are essential tools for studying the physics of condensed-matter systems and spintronic devices. The anomalous Hall effect [1], for instance, allows for probing the appearance of magnetically-ordered phases, field- and current-induced magnetization reversal, domain wall motion, and spin-orbit torques [2]. The planar Hall effect and the spin Hall magnetoresistance can also be used to track the response of antiferromagnets and magnetic insulators to applied magnetic fields, currents, and heat [3].&lt;br/&gt;Despite the fundamental and technological importance of the Hall effects, their detection has been limited so far to the low frequency regime by their inherent small magnitude. There exist only few examples of time-resolved measurements of the magnetization dynamics using the Hall effect [4]. In contrast, measurements of the GHz dynamics associated with other magnetoresistance effects, such as the tunnel magnetoresistance, have become a common routine [5]. Extending this capability to Hall effects would provide an important tool to investigate a vast range of electronic and magnetic systems.&lt;br/&gt;&lt;br/&gt;Here we present a novel concept to perform all-electrical time-resolved measurements of any kind of Hall magnetoresistance [6]. Our approach removes the large non-magnetic potential that originates from the current leakage into the transverse arms of the Hall cross (see Fig. 1a). Since this background is much larger than the Hall voltage, it saturates the acquisition range of the measuring instrument (an oscilloscope) and impedes high-frequency measurements of transverse signals. The key idea to suppress the spurious contribution consists of delivering to the Hall cross two counter-propagating electric pulses of opposite polarity. Their synchronous arrival at the device center forces a local virtual ground that hinders the transverse current shunting (see Fig. 1b). Since the current does flow along the longitudinal direction, the Hall voltage is not removed, differently from the non-magnetic transverse potential. The vertical resolution of the oscilloscope can be thus fully exploited to acquire the background-free Hall voltage and sense the associated dynamics.&lt;br/&gt;Our approach is simple and, as compared to traditional Hall measurements, requires only an additional component, namely, the balun divider that generates the electric signals of opposite polarity (Fig. 1c). Importantly, the amplitude, duration, and waveform of the electrical excitation can be arbitrarily chosen. Moreover, RF and DC components can be combined in a single setup to perform both low and high frequency measurements. Overall, our technique achieves the signal quality necessary for the single-shot acquisition and, hence, for the detection of stochastic events with a resolution &amp;lt;50 ps. This capability is unique to our technique and is an advantage over standard non-electrical pump-probe schemes that can sense only the reproducible dynamics.&lt;br/&gt;We benchmarked our technique by studying the magnetization switching of ferrimagnetic GdFeCo caused by electric pulses with duration ranging between 0.3 and 20 ns. Our time-resolved measurements of the anomalous Hall effect show that the spin-orbit-torque-induced dynamics comprises a fast reversal (equivalent domain wall speed &amp;gt;1 km/s), as typical of ferrimagnets [7,8], and a long, unexpected incubation delay (Fig. 2). We associate this phase with the time required to nucleate a reversed domain assisted by Joule heating. In addition, the single-shot anomalous-Hall traces reveal the existence of broad distributions of the nucleation and reversal times and disclose the stochastic character of the dynamics triggered by the spin-orbit torques.

**References:**

[1] Nagaosa N. et al., Rev. Mod. Phys. 82, 1539–1592 (2010)&lt;br/&gt;[2] A. Manchon et al., Rev. Mod. Phys. 91, 035004 (2019)&lt;br/&gt;[3] Wadley P. et al., Science (80-. ) 351, 587–590 (2016)&lt;br/&gt;[4] Yoshimura Y. et al., Nat. Phys. 12, 157–161 (2016)&lt;br/&gt;[5] Grimaldi E. et al., Nat. Nano. 15, 111–117 (2020).&lt;br/&gt;[6] Sala G. et al., Nat. Comm (in press)&lt;br/&gt;[7] Caretta L. et al., Nat. Nano. 13, 1154-1160 (2018)&lt;br/&gt;[8] Cai K. et al., Nat. Electr. 3, 37-42 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a46aed8e02ec335f79b3f1a3e431bc2c.jpg)
Figure 1. Experimental setup for time-resolved Hall effect measurements. a, The current &lt;i&gt;J&lt;/i&gt; produced by a pulse &lt;i&gt;V&lt;sub&gt;P&lt;/sub&gt;&lt;/i&gt; leaks through the transverse arms of the Hall cross and builds up spurious potential &lt;i&gt;V+&lt;/i&gt; and &lt;i&gt;V-&lt;/i&gt;. b, When the two pulses with opposite polarity meet at the center of the Hall cross, they impose a virtual ground and force the current to propagate along the longitudinal direction. The background-free Hall potential &lt;i&gt;V&lt;sub&gt;H&lt;/sub&gt;&lt;/i&gt; can thus be acquired with improved sensitivity. c, Schematics of the RF setup. The initial pulse is fed to a balun divider, which splits the signal into two half pulses with opposite polarity that reach the device at the same instant. The current-induced transverse Hall potentials &lt;i&gt;V&lt;sub&gt;H&lt;/sub&gt;&lt;/i&gt; are amplified and detected by the oscilloscope, triggered by an attenuated portion of the initial pulse. The lock-in amplifier and the bias-Ts form the DC sub-network (dashed lines).

![](https://assets.underline.io/uploads/markdown_image/1/image/e414760706b85f028c4bee175fccf4ab.jpg)
Figure 2. Spin-orbit torque magnetization switching of GdFeCo measured by time-resolved Hall effect. Normalized anomalous Hall voltage V&lt;sub&gt;H&lt;/sub&gt; measured during the application of 20-ns-long electric pulses. The duration of the initial quiescent phase and reversal are determined by the pulse amplitude.

INTERMAG 2021

 Real-time detection of Hall effects: measuring current-induced magnetization switching in the time domain

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The broad family of Hall effects comprises phenomena of ordinary, anomalous, planar, topological, and quantum origin. These effects are ubiquitous in electronic systems and are essential tools for studying the physics of condensed-matter systems and spintronic devices. The anomalous Hall effect [1], for instance, allows for probing the appearance of magnetically-ordered phases, field- and current-induced magnetization reversal, domain wall motion, and spin-orbit torques [2]. The planar Hall effect and the spin Hall magnetoresistance can also be used to track the response of antiferromagnets and magnetic insulators to applied magnetic fields, currents, and heat [3]. Despite the fundamental and technological importance of the Hall effects, their detection has been limited so far to the low frequency regime by their inherent small magnitude. There exist only few examples of time-resolved measurements of the magnetization dynamics using the Hall effect [4]. In contrast, measurements of the GHz dynamics associated with other magnetoresistance effects, such as the tunnel magnetoresistance, have become a common routine [5]. Extending this capability to Hall effects would provide an important tool to investigate a vast range of electronic and magnetic systems. Here we present a novel concept to perform all-electrical time-resolved measurements of any kind of Hall magnetoresistance [6]. Our approach removes the large non-magnetic potential that originates from the current leakage into the transverse arms of the Hall cross (see Fig. 1a). Since this background is much larger than the Hall voltage, it saturates the acquisition range of the measuring instrument (an oscilloscope) and impedes high-frequency measurements of transverse signals. The key idea to suppress the spurious contribution consists of delivering to the Hall cross two counter-propagating electric pulses of opposite polarity. Their synchronous arrival at the device center forces a local virtual ground that hinders the transverse current shunting (see Fig. 1b). Since the current does flow along the longitudinal direction, the Hall voltage is not removed, differently from the non-magnetic transverse potential. The vertical resolution of the oscilloscope can be thus fully exploited to acquire the background-free Hall voltage and sense the associated dynamics. Our approach is simple and, as compared to traditional Hall measurements, requires only an additional component, namely, the balun divider that generates the electric signals of opposite polarity (Fig. 1c). Importantly, the amplitude, duration, and waveform of the electrical excitation can be arbitrarily chosen. Moreover, RF and DC components can be combined in a single setup to perform both low and high frequency measurements. Overall, our technique achieves the signal quality necessary for the single-shot acquisition and, hence, for the detection of stochastic events with a resolution &lt;50 ps. This capability is unique to our technique and is an advantage over standard non-electrical pump-probe schemes that can sense only the reproducible dynamics. We benchmarked our technique by studying the magnetization switching of ferrimagnetic GdFeCo caused by electric pulses with duration ranging between 0.3 and 20 ns. Our time-resolved measurements of the anomalous Hall effect show that the spin-orbit-torque-induced dynamics comprises a fast reversal (equivalent domain wall speed &gt;1 km/s), as typical of ferrimagnets [7,8], and a long, unexpected incubation delay (Fig. 2). We associate this phase with the time required to nucleate a reversed domain assisted by Joule heating. In addition, the single-shot anomalous-Hall traces reveal the existence of broad distributions of the nucleation and reversal times and disclose the stochastic character of the dynamics triggered by the spin-orbit torques.

**References:**

[1] Nagaosa N. et al., Rev. Mod. Phys. 82, 1539–1592 (2010) [2] A. Manchon et al., Rev. Mod. Phys. 91, 035004 (2019) [3] Wadley P. et al., Science (80-. ) 351, 587–590 (2016) [4] Yoshimura Y. et al., Nat. Phys. 12, 157–161 (2016) [5] Grimaldi E. et al., Nat. Nano. 15, 111–117 (2020). [6] Sala G. et al., Nat. Comm (in press) [7] Caretta L. et al., Nat. Nano. 13, 1154-1160 (2018) [8] Cai K. et al., Nat. Electr. 3, 37-42 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a46aed8e02ec335f79b3f1a3e431bc2c.jpg)
Figure 1. Experimental setup for time-resolved Hall effect measurements. a, The current J produced by a pulse VP leaks through the transverse arms of the Hall cross and builds up spurious potential V+ and V-. b, When the two pulses with opposite polarity meet at the center of the Hall cross, they impose a virtual ground and force the current to propagate along the longitudinal direction. The background-free Hall potential VH can thus be acquired with improved sensitivity. c, Schematics of the RF setup. The initial pulse is fed to a balun divider, which splits the signal into two half pulses with opposite polarity that reach the device at the same instant. The current-induced transverse Hall potentials VH are amplified and detected by the oscilloscope, triggered by an attenuated portion of the initial pulse. The lock-in amplifier and the bias-Ts form the DC sub-network (dashed lines).

![](https://assets.underline.io/uploads/markdown_image/1/image/e414760706b85f028c4bee175fccf4ab.jpg)
Figure 2. Spin-orbit torque magnetization switching of GdFeCo measured by time-resolved Hall effect. Normalized anomalous Hall voltage VH measured during the application of 20-ns-long electric pulses. The duration of the initial quiescent phase and reversal are determined by the pulse amplitude.

technical paper

Magnetic skyrmions are long-lived topological excitations in a small subset of magnetic materials, including some heavy-metal / ferromagnet multilayers with strong interfacial spin-orbit interactions. Skyrmions are a rare example of a compact, unbound, and switchable topological state of matter. Here, “compact” means that each skyrmion is confined to a very small area of the sample. Thanks to this property, even micrometer-sized samples can host a very large number of such topological objects and thereby acquire a very large topological charge. “Unbound” means that skyrmions, unlike vortices or hedgehogs, can exist without their topological counterpart, the antiskyrmion. In fact, skyrmions are often found in pure form, such as ordered (crystalline) or disordered (amorphous) arrays. These dense skyrmion states can be considered a topological phase, with the order parameter being the topological charge. Finally, “switchable” means that, due to the discrete nature of the lattice, skyrmions can be nucleated and annihilated, leading to a change of the global topological charge. Switching from a topological trivial state to a skyrmion state is a topological phase transition. Such a phase transition requires the overcoming of strong energy barriers—the same energy barriers that also allow skyrmions to exist at room temperature [1]. Topological phase transitions are therefore expected to be of first order, with a transition dynamic characterized by slow and heterogeneous nucleation, as known, e.g., from the freezing of water. In fact, heterogeneous nucleation is the underlying principle of electrical skyrmion nucleation, which crucially relies on material defects to break the translational symmetry [2]. Surprisingly, however, we find picosecond homogeneous nucleation of an extended topological phase, comprising a dense array of nanometer-scale magnetic skyrmions, after a single femtosecond laser pulse in metallic ferromagnetic multilayers. Lorentz transmission electron microscopy and skyrmion Hall effect measurements confirm that only skyrmions, and not antiskyrmions, are nucleated by the light pulse, even in an achiral Pt/Co/Pt material. This presentation will focus on the nucleation dynamics of this all-optical topological phase transition, which we were able to follow in real time during the early user operation of beamline SCS at the European XFEL [3]. Using time-resolved small angle x-ray scattering, we discovered that rapid, homogeneous nucleation of the skyrmion phase is mediated by a previously undisclosed transient fluctuation state. This state, which is characterized by high spatial frequency magnetic fluctuations, persists for approximately 100 ps after exciting our magnetic multilayer with a femtosecond, infrared laser pulse. The topological phase emerges from these fluctuations by nucleation and coalescence, a mechanism that goes beyond existing theories of topological phase transitions such as the Kibble–Zurek mechanism and the Berezinskii–Kosterlitz–Thouless transition. The process is completed on a time scale of 300 ps. Using atomistic spin dynamics simulations, we confirm that the fluctuation state is key to the ultrafast increase of the global topological charge, enabled by an almost complete elimination of the topological energy barrier in this transient state of matter.

**References:**

[1] F. Büttner, I. Lemesh, and G. S. D. Beach, Theory of isolated magnetic skyrmions: From fundamentals to room temperature applications. Scientific Reports 8, 4464 (2018). [2] F. Büttner, I. Lemesh, M. Schneider, B. Pfau, C. M. Günther, P. Hessing, J. Geilhufe, L. Caretta, D. Engel, B. Krüger, J. Viefhaus, S. Eisebitt, and G. S. D. Beach, Field-free deterministic ultrafast creation of magnetic skyrmions by spin–orbit torques. Nature Nanotechnology 12, 1040 (2017). [3] F. Büttner, B. Pfau, M. Böttcher, M. Schneider, G. Mercurio, C. M. Günther, P. Hessing, C. Klose, A. Wittmann, K. Gerlinger, L.-M. Kern, C. Strüber., C. von Korff Schmising, J. Fuchs , D. Engel, A. Churikova, S. Huang, D. Suzuki, I. Lemesh, M. Huang, L. Caretta, D. Weder, J. H. Gaida, M. Möller, T. R. Harvey, S. Zayko, K. Bagschik, R. Carley, L. Mercadier, J. Schlappa, A. Yaroslavtsev, L. Le Guyarder, N. Gerasimova , A. Scherz, C. Deiter, R. Gort, D. Hickin, J. Zhu, M. Turcato, D. Lomidze, F. Erdinger, A. Castoldi, S. Maffessanti, M. Porro, A. Samartsev, J. Sinova, C. Ropers, J. H. Mentink, B. Dupé, G. S. D. Beach, and S. Eisebitt, Observation of fluctuation-mediated picosecond nucleation of a topological phase. Nature Materials 20, 30 (2021).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/32457bd794a7357a1245dc6e188b51db.jpg)
Magnetic state of the sample before (left) and after (right) exposure with a single fs laser pulse. The circle (1.5 µm diameter) indicates our field of view. Black (white) indicates magnetization pointing up (down).

![](https://assets.underline.io/uploads/markdown_image/1/image/97b56242ca4e46e74620e4de652ae946.jpg)
Schematic of the process of all-optical topological switching. Starting with a uniform state (1), the sample is heated to a transient fluctuations state (2) by the laser. The fluctuations remove the topological energy barrier and allow skyrmion seeds to nucleate. The final state (3) is a skyrmion state obtained after coalescence and growth of the skyrmion nuclei.

 Colossal Topological Hall Effect at the Transition Between Isolated and Lattice-Phase Interfacial Skyrmions

Systems in which magnetic skyrmions occur at room temperature could enable new computing architectures as well as compact and energetically-efficient storage such as racetrack memories. There are two fundamental problems that prevent the successful implementation of skyrmions in a racetrack device. A first problem is not being able to restrict the skyrmion motion along straight paths and one solution is the use of antiferromagnetically-coupled skyrmions [1]. The second problem is not having stable inter-skyrmion distances, which translates into fluctuating distances among bits. A potential solution was revealed with the first experimental observation of coexisting skyrmions and chiral bobbers [2], opening the possibility that a chain of binary data bits could be encoded by two different solitons. However, this has only been observed in B20-type single crystalline materials and at low temperatures. With our work, we present a ferro-/ferri-/ferromagnetic multilayer system that can host two distinct skyrmion phases at room temperature. The two phases represent a tubular (strong constrast) and a partial (weak contrast) skyrmion (see Figure 1), as revealed from quantitative magnetic force microscopy data complemented by micromagnetic simulations. Furthermore, the tubular skyrmion can be converted into a partial skyrmion. Given its high tunability, this hybrid system serves as a promising platform for future skyrmionic devices.

**References:**

[1] W. Legrand et al., Nat. Mater. 19, 34–42 (2020) [2] F. Zheng et al., Nat. Nanotechnol. 13, 1–7 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8658ad08d7d440f2f349350bb470ce35.jpg)
Fig. 1 Upper: Schematics of the trilayer sample consisting of two ferromagnetic skyrmion (SK) layers separated by a 3.8-nm thick ferrimagnetic (Fi) layer; SK = [Ir(1nm)/Fe(0.3nm)/Co(0.6nm)/Pt(1nm)]×5 and Fi = [TbGd(0.2m)/Co(0.4nm)]×6/TbGd(0.2nm). The weak skyrmions are depicted by the vertical pale blue rectangles penetrating through the SK layers only. The strong skyrmions are indicated by wider dark blue rectangles penetrating through all layers. Lower: 2 × 2 µm2 magnetic force microscopy image taken in a magnetic field of about 133 mT, highlighting a weak and a strong skyrmion in the lower two panels.

 Coexistence of distinct skyrmion phases observed in hybrid ferromagnetic/ferrimagnetic multilayers

Thanks to its extreme surface sensitivity and element specificity, X-ray photoemission electron microscopy permits imaging magnetic nanostructures with sub-nanometer thickness and even fully compensated synthetic antiferromagnets. In addition, XPEEM is sensitive to both in plane and out of plane magnetization components, so it can unambiguously determine the character and chirality of domain walls. Several skyrmionic systems have been measured at the ALBA Synchrotron Light Source XPEEM, profiting the functional sample environments that allow applying small magnetic fields and/or current pulses in order to study skyrmion nucleation and propagation and the effect, for example, of disorder or of targeted modulations of the magnetic anisotropy. I will give an overview of the strenghts and limits of the technique, the experiments carried out in DMI systems over the past few years, and an outlook for the near future including instrumental upgrades in development.

**References:**

Olivier Boulle et al., Room temperature chiral magnetic skyrmion in ultrathin magnetic nanostructures, Nature Nanotechnology 11, 449 (2016) MIchael Foerster et al., Custom sample environments at the ALBA XPEEM, Ultramicroscopy 171, 63 (2016) Roméo Juge et al., Magnetic skyrmions in confined geometries: Effect of the magnetic field and the disorder, Journal of Magnetism and Magnetic Materials 455, 3 (2018) Lucia Aballe et al., Pulse picking in synchrotron-based XPEEM, Ultramicroscopy 202, 10 (2019) Roméo Juge et al., Current-Driven Skyrmion Dynamics and Drive-Dependent Skyrmion Hall Effect in an Ultrathin Film, Physical Review Applied, 12, 044007 (2019) Anna Mandziak et al., Combining high temperature sample preparation and in-situ magnetic fields in XPEEM, Ultramicroscopy 214, 113010 (2020) Sachin Krishnia et al., Making spin-orbit coupling visible in single layer ferrimagnets: direct observation of spin-orbit torques and chiral spin textures, submitted Teng Xu et al., Ferrimagnetic Néel skyrmions stabilized on top of noncollinear antiferromagnetic Mn3Sn, submitted Kumari Gaurav Rana et al., Room temperature skyrmions in an exchange biased antiferromagnet, submitted

**Images:**

 A close look at skyrmions in ultrathin films and synthetic antiferromagnets.

The magnetic skyrmion is a particle-like topologically stable spin texture that has been observed in chiral bulk magnets and asymmetric magnetic multilayers. Skyrmions can be generated and driven through the spin-polarized electric currents in the presence of an external magnetic field. Our early results show that the skyrmions can be thermally activated and behave like Brownian particles [1], which motivates us to explore the thermal control of skyrmion dynamics. Through using on-chip heaters, we are able to thermally generate, manipulate and thermoelectrically detect skyrmions [2]. Figure 1 shows that the skyrmion nucleation from the edge of the microstructured [Ta/CoFeB/MgO]15 multilayer, upon applying an electric current pulse to the upper heater on the side that generates local joule heating. The local creation of joule heating can facilitate a domain morphological transition and nucleate skyrmions by overcoming the low energy barrier. As the temperature of the heater is increased, more skyrmions are generated, which is accompanied by a unidirectional diffusion motion from the hot to the cold regions. This is due to the interplay among the repulsive forces between skyrmions, thermal spin-orbit torques, magnonic spin torques, and entropic forces. The ability to generate and manipulate skyrmions using heat opens another avenue of exploiting skyrmions in insulating and metallic materials. Moreover, by utilizing the anomalous Nernst effect in the same device, we can obtain the Nernst voltage which develops in the presence of a thermal gradient and magnetization perpendicular to each other. Since the magnetization can be varied by the change in the total number of skyrmions. We observed several discretized steps in the time evolution of Nernst voltages, as shown in Fig. 2. Each step is 90±10 nV which is attributed to the annihilation of a single skyrmion. The thermoelectric detection of skyrmion is important because the electrical detection of skyrmions is still challenging in many materials systems, but it is key to enabling spintronic applications.

**References:**

[1] L. Zhao, Z. Wang and W. Jiang, PRL, 125, 027206 (2020). [2] Z. Wang, M. Guo and W. Jiang, Nat. Electron., 3, 672 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d0769f89c8b455dd1173267ed8956388.jpg)
Fig. 1 Optical image of the microstructured magnetic multilayer with two Ta/Pt heaters on top of a 100-nm-thick Si3N4 membrane and the consecutive X-ray images acquired from the multilayer sample after applying pulse voltages to the upper heater.

![](https://assets.underline.io/uploads/markdown_image/1/image/382300011f11c8401b110ae6a6c01013.jpg)
Fig. 2 ‘Discretized’ steps of the Nernst voltage difference ΔVANE = 90±10 nV are detected after switching off the 6 mA current and applying a small current of 3 mA.

 Thermal generation, manipulation and thermoelectric detection of skyrmions

Competing interactions can give rise to a variety of interesting noncollinear magnetization states. An interesting model system in which such states can be explored is the bilayer PdFe/Ir (111), which exhibits frustrated exchange and a sizeable Dzyaloshinskii-Moriya interaction (DMI). In particular, such systems can simultaneously support skyrmions and antiskyrmions – their antiparticle counterpart [1-5]. This provides an interesting testbed to investigate how opposite topological charges respond to drive forces such as spin-orbit torques (SOTs). In this talk, we will describe results from atomistic spin dynamics simulations in which we studied skyrmion and antiskyrmion dynamics under spin-orbit torques in PdFe/Ir (111), where the Hamiltonian parameters have been extracted from first-principles calculations. In the single particle limit, a divergence between the skyrmion and antiskyrmion motion appears above a current threshold, whereby antiskyrmions are found to deviate from rectilinear motion and execute instead trochoidal trajectories in the film plane [6]. This behavior represents the transition to the Walker regime, whereby helicity oscillations drive the trochoidal motion, much like the large-angle magnetization precession above Walker breakdown in domain wall dynamics in which the wall profile oscillates continuously between Bloch and Néel states. Through an extended Thiele model in which a deformation amplitude and helicity are elevated to dynamical variables, we show that simulated antiskyrmion trajectories can be reproduced by accounting for the helicity dependence of the DMI. For a range of strong damping-like SOTs, the single-particle dynamics gives way to pair-production, whereby a single antiskyrmion initial state can result in a gas of skyrmions and antiskyrmions. This occurs in an analogous fashion to magnetic vortex core reversal, whereby strong deformations in the antiskyrmion motion results in the formation of an additional skyrmion-antiskyrmion pair, which then separates because the opposite charges move in different ways. We have identified three main scattering mechanisms by which this occurs, which are either elastic, result in antiskyrmion bound states, or annihilation of a generated antiskyrmion – see Fig. 1 [7]. Together, these processes can drive a proliferation of particles whose growth rate and production asymmetry depends on the strength of the chiral interactions and the damping-like SOT. Interestingly, we can draw close parallels with conditions for baryogenesis in high-energy physics, which describes the prevalences of matter over antimatter in the observable universe. The generation processes also raise the question of energy barriers and minimum-energy paths towards antiskyrmion merging and annihilation. Through geodesic nudged elastic band calculations, we find that both processes involve similar energy barriers and depend on the relative helicities of the scattering particles. Annihilation is found to occur via intermediate meron-antimeron states, as seen in previous work [8]. We will also discuss the Langevin dynamics of such skyrmion and antiskyrmion states. This work was partially supported by the Agence Nationale de la Recherche under Contract No. ANR-17-CE240025 (TOPSKY), the Deutsche Forschungsgemeinschaft via TRR 227, and the University of Strasbourg Institute for Advanced Study (USIAS) via a fellowship, within the French national program “Investment for the Future” (IdEx-Unistra).

**References:**

[1] B. Dupé, C. N. Kruse, T. Dornheim, and S. Heinze, New J. Phys. 18, 055015 (2016). [2] S.-Z. Lin and S. Hayami, Phys. Rev. B 93, 064430 (2016). [3] L. Rózsa et al., Phys. Rev. B 95, 094423 (2017). [4] X. Zhang et al., Nat. Commun. 8, 1717 (2017). [5] A. O. Leonov and M. Mostovoy, Nat. Commun. 8, 14394 (2017). [6] U. Ritzmann, S. von Malottki, J.-V. Kim, S. Heinze, J. Sinova, and B. Dupé, Nat. Electron. 1, 451 (2018). [7] U. Ritzmann, L. Desplat, B. Dupé, R. E. Camley, and J.-V. Kim, Phys. Rev. B 102, 174409 (2020). [8] L. Desplat, J.-V. Kim, and R. L. Stamps, Phys. Rev. B 99, 174409 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d7db361992f4c2a6a2c686784d91d029.jpg)
Main scattering processes involving antiskyrmions: (a) elastic; (b) bound-state; (c) annihilation.

 Nonlinear and stochastic dynamics of skyrmions in frustrated magnets

The development of approaches that can efficiently control the magnetization of magnetic materials is central to the creation of fast and low-power spintronic devices. Spin transfer torque can be used to electrically manipulate magnetic order in devices, but is typically limited to nanosecond timescales. Alternatively, spin–orbit torque can be employed, and switching with current pulses down to about 200 ps has been demonstrated [1,2]. However, the upper limit to magnetization switching speed remains unestablished. In this talk I will present our recent results [3], were we show that photoconductive switches can be used to apply 6-ps-wide electrical pulses and deterministically switch the out-of-plane magnetization of a common thin cobalt film via spin–orbit torque. We probe the ultrafast magnetization dynamics due to spin-orbit torques with sub-picosecond resolution using the time-resolved magneto-optical Kerr effect (MOKE). We also estimate that the magnetization switching consumes less than 50 pJ in micrometre-sized devices.

**References:**

[1] Garello, K. et al. Ultrafast magnetization switching by spin–orbit torques. Appl. Phys. Lett. 105, 212402 (2014) [2] Grimaldi, E. et al. Single-shot dynamics of spin–orbit torque and spin– transfer torque switching in three-terminal magnetic tunnel junctions. Nat. Nanotechnol. 15, 111–117 (2020) [3] Jhuria, K. et al. Spin–orbit torque switching of a ferromagnet with picosecond electrical pulses. Nat. Electronics. 3, 680–686 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7befe162d030419aa1923731179fcace.jpg)
Fig 1. Schematic of time-resolved picosecond spin-orbit torque experiments. A femtosecond-wide optical pump is used to trigger a picosecond-wide electrical pulse via the excitation of anAuston photo-switch. A second optical probe beam is used to detect the induced dynamics on the magnetization with sub-picosecond resolution.

 Spin–orbit torque switching of a ferromagnet with picosecond electrical pulses INVITED

Magnetic Skyrmions are nanometer-sized spin textures with a defined chirality induced by the Dzyalonshinskii-Moriya interaction. Due to their specific configuration and chirality, magnetic skyrmions are said to be topologically protected and they show a well-defined behaviour under the effect of external excitations such as spin-polarized currents. Because of their properties, magnetic Skyrmions are considered promising candidates for their implementation in next-generation spintronic devices[1]. However, the usage of Skyrmions in technological applications is constrained by the ability to nucleate, stabilize and manipulate them. The main drawback related to the nucleation of magnetic skyrmions arises from the fact that they are usually metastable magnetic configurations, so special protocols must be designed in order to access these skyrmionic states. In many different scientific fields and due to their interesting properties, the study of metastable phases and the dynamical paths needed to reach them are of great interest. In this sense, it is usually necessary to supply and/or remove a substantial amount of energy to the system in a short timescale, so the system evolves towards a far-from-equilibrium path in the configuration space. In the recent years, the study of the light-induced magnetization-dynamics has gained relevance due to its ultrafast and localized character. Particularly, recent experiments have shown the feasibility of the laser-induced nucleation of skyrmions by means of ultrafast magnetization dynamics[2,3]. In these experiments the nucleation takes place under external magnetic fields which are known to transform skyrmionic states from metastable to stable ground states of the system. In the present work we explore the nucleation of magnetic skyrmions in realistically parametrised[4,5] Pt/Co/Heavy-Metal magnetic trilayers via atomistic spin dynamics (ASD) simulations using the software package Vampire[6]. Quasi-static simulations by increasing temperature above the Curie one and cooling down the system in a timescale of few nanoseconds produce a stable ground state in the form of stripe domains, as is usually found in these kind of systems. Next, we model the dynamics under ultrafast non-polarized femtosecond laser pulse varying the pulse duration and intensity. We present phase diagrams of the magnetic states after the laser pulse action revealing the possibility of accessing final metastable skyrmionic states for a proper window of laser parameters. The same protocols have been studied adding external static fields pointing both, parallel and antiparallel to the initial magnetization. Under these conditions, slow field-cooling processes now leads to stable ground states in the form of skyrmion lattices. As a result, the window of laser parameters leading to final skyrmionic states is substantially increased. Interestingly, the results show that applying a laser pulse and under the effect of external fields it is possible to access both, metastable and stable skyrmionic states, being even possible to nucleate skyrmion lattices with different polarizations. Our results unambiguously demonstrate the necessity of following a highly non-equilibrium dynamical path in order to reach a final metastable skyrmion lattice in the absence of external fields.

**References:**

[1] A. Fert, N. Reyren and V. Cros, Nature Reviews Materials, Vol. 2, p.17031 (2017) [2] S.-G. Je, P. Vallobra, T. Srivastava et al., Nano Letters, Vol. 18(11), p.7362-7371 (2018) [3] F. Büttner, B. Pfau, M. Böttcher et al., Nature Materials, Vol. 20, p. 30-37 (2021) [4] R. Moreno, R. Evans, S. Khmelevskyi et al., Physical Review B, Vol. 94, p. 104433 (2016). [5] H. Yang, A. Thiaville, S. Rohart et al., Physical Review Letters, Vol. 115, p. 267210 (2015). [6] R. F. Evans, W. J. Fan, P. Chureemart et al., Journal of Physics: Condensed Matter, Vol. 26, p. 103202 (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f65deb21d80e86a03c6c6aee01f7217d.jpg)
Fig.1 Light-induced nucleation of metastable skyrmion lattices. a) Initial saturated state. b) Ground state of the system obtained after a slow zero-field cooling process. c) Nucleated metastable skyrmion lattice obtained after applying an ultrafast laser pulse. d) Temperature profile following a slow zero-field cooling process. e) Temperature profile of the laser-induced nucleation of skyrmion lattice.

 Nucleation of Metastable Skyrmion Lattices following a Non-Equilibrium Laser-Induced Heating Path

Electrical current remains one of the simplest and most accessible tools for the control of magnetic skyrmions. However, it can be challenging to only perform the intended operation among all the possible current-induced effects such as deformation, nucleation, and propagation [1-3]. While current-induced skyrmion nucleation has been demonstrated [1,2], its equally important complementary operation of current-induced skyrmion annihilation remains elusive. Our investigation on the current-induced skyrmion effects revealed an additional regime at low current densities where skyrmion annihilation can be performed via skyrmion-stripe transformation [4]. In this work, an experimental study of current-induced skyrmion-stripe transformation in a Pt/Co/Fe/Ir magnetic bilayer was performed. Using a Hall cross device shown in Fig. 1(a), a slow evolution of the magnetization after current injection was observed and showed distinct features in the high and low current density regimes. High current density injection induced a sharp negative change in magnetization followed by a continuous decay back to equilibrium while low current density induced a gradual positive change in magnetization from equilibrium before decaying back to equilibrium forming a peak as shown in Fig. 1(b). In situ observation under magneto-optical Kerr (MOKE) imaging showed that at high current densities, additional magnetic skyrmions were nucleated as shown in Fig. 2(e-h). In contrast, at low current densities, skyrmions expanded into stripes. The resulting competition for space annihilates skyrmions. Eventually the stripes contract into skyrmions with a lower overall density as shown in Fig. 2(a-d). The mechanism for the skyrmion-to-stripe transformation was further investigated by analyzing the MOKE images of the stripe domains over many runs. The stripe domains were found to nucleate at predictable spots on the wire which can be attributed to pinning sites. Together with the additional requirement of a long current pulse duration of several milliseconds for the transformation to occur, the transformation was concluded to be occurring as the result of a skyrmion-pinning site interaction and creep motion. A skyrmion at a pinning site undergoes slow creep elongation into a stripe due to the weak propagative being insufficient to fully depin the skyrmion. By utilizing the combination of skyrmion nucleation at high current density and skyrmion annihilation at low current density, skyrmion density control was demonstrated purely by current density modulation. In addition, the volatile nature of these current-induced stripes offers interesting possibilities for neuromorphic computing applications such as artificial leaky-integrate fire neurons which requires a continuous decaying property after an excitation, and artificial synapses with short-term plasticity which requires a temporary retention of state after excitation. In conclusion, our work revealed additional current-induced magnetic texture transformations which can be exploited for skyrmion density control using solely current modulation. In addition, our findings establish an additional requirement of a minimum operating current density in the design of skyrmionic devices to avoid unintended skyrmion deletion.

**References:**

[1] W. Jiang, P. Upadhyaya, W. Zhang, Science 349, 283 (2015). [2] F. Büttner, I. Lemesh, M. Schneider, Nat. Nanotech. 12, 1040 (2017). [3] W. Legrand, D. Maccariello, N. Reyren, Nano Lett. 17, 2703 (2017). [4] C. C. I. Ang, W. Gan, G. D. H. Wong, and W. S. Lew, Phys. Rev. Appl. 14, 054048 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a3717886e8df859abbd62b4fff284cdc.jpg)
Fig. 1 (a) Measurement setup consisting of a Hall cross with widths of 20 and 10 μm. (b) Time evolution of Hall resistance change △RHall after 30 current pulses of 10 ms are injected for a range of current densities. Error bars are omitted from the graph for clarity, and the data have a standard deviation of 6ms or less.

![](https://assets.underline.io/uploads/markdown_image/1/image/a4abf908ca6581b85f8680db6164d0c6.jpg)
Fig. 2 MOKE images of current-induced magnetic states and their relaxation process back to equilibrium. (a) Magnetization state at equilibrium. Magnetization state at (b) t = 0.4 s, (c) t = 12.1 s, and (d) t = 41.4 s after injection of 2.21 × 1010 A/m2 current pulses. (e) Magnetization state at equilibrium with skyrmion density of 0.645 μm-2. Magnetization state at (f) t = 0.4 s, (g) t = 12.1 s and (h) t = 41.3 s after injection of 7.20 × 1010 A/m2 current pulses. Skyrmion density are stated below the respective MOKE images.

 Skyrmion Density Modulation via Current-induced Skyrmion-to-stripe Transformation

Magnetic skyrmions [1,2], with their small size, topological stability and low driving-current density, hold promises for high-density and energy-efficient information storage devices [3,4]. Here, we demonstrate the creation of individual skyrmions at zero-field in an exchange-biased magnetic multilayer with exposure to soft X-rays. In particular, a single skyrmion with 100-nm size can be created at the desired position using a focused X-ray spot of sub-50-nm size. This single skyrmion creation is driven by the X-ray-induced modification of the antiferromagnetic order and the corresponding exchange bias. And artificial skyrmion lattices with various arrangements can be patterned using X-ray [5]. Furthermore, by exploiting the fact that the antiferromagnetic order can also be reconfigured by local thermal excitations, a focused electron beam with a graphic pattern generator to “print” skyrmions is used, which is referred to as skyrmion lithography [6]. These works provide a route to design arbitrary skyrmion patterns, thereby establishing the foundation for further exploration of topological magnetism.

**References:**

[1] S. Mühlbauer, B. Binz and C. Pfleiderer, et al., Science 323, 915 (2009). [2] X. Z. Yu, N. Nagaosa, and Y. Tokura, et al., Nature. 465, 901 (2010). [3] N. Romming, J. E. Bickel and K. V. Bergmann, et al., Science 341, 636 (2013). [4] A. Fert, N. R. Ren, V. Cros. Nat. Rev. Mater. 2, 17031 (2017). [5] Y. Guang, L. Bykova, Y. Z. Liu, G. Q. Yu* and X. F. Han, et al., Nat. Commun. 11, 949 (2020). [6] Y. Guang, Y. Peng, Z. R. Yan, G. Q. Yu* and X. F. Han, et al., Adv. Mater. 32, 20003003 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a435a181ee49a2c2127ddfd0d93213b7.jpg)
Fig. 1 (a) Sketch of X-rays measurement. (b) Single domain with IOP pattern. (c) Initial magnetic domain pattern imaged by STXM at zero field, and zero-field magnetic domain after scanning the central area (dashed lines) using circular X-ray under magnetic field of 2000 Oe and -2000 Oe. (d) Creating single skyrmion. (e)-(f) Triangular and Square skyrmion lattice.

![](https://assets.underline.io/uploads/markdown_image/1/image/4933c887d5795aafc272c95a85696fa7.jpg)
Fig. 2 (a) Sketch of electron beam measurement. (b) A schematic of sample structures. (c) Demonstration of the created antiferromagnetic domain with time sequence of applying the magnetic field and imaging process. (d) MFM images of EBL-patterned artificial skyrmion lattices with square, kagome, and honeycomb configuration.

 X-Ray and Electron Beam Lithography of Zero-Field Magnetic Skyrmions

In Heavy-Metal/Ferromagnet/Metal-Oxide (HM/FM/MOx) magnetic trilayers, the Structural Inversion Asymmetry (SIA) together with the Spin-orbit Coupling (SoC) is at the origin of an additional exchange interaction, the interfacial Dzyaloshinskii-Moriya Interaction (iDMI) [1]. In thin films with Perpendicular Magnetic Anisotropy, this additional exchange, together with the dipolar interaction, stabilizes non-collinear chiral magnetic spin textures such as Néel Domain Walls (DWs) with a given chirality and interestingly, magnetic skyrmion bubbles [2]. The control of iDMI amplitude and sign is thus of great importance, as it determines the DW internal structure and chirality, and their direction of motion driven by Spin-orbit Torques [3]. In most of the existing studies, the iDMI has been controlled by tuning the deposition parameters, such as the FM thickness, the nature of the bottom HM and top oxide or, as recently found, the oxidation state at the top interface [4,5]. Contrary to these approaches, voltage control of the interfacial magnetic properties enables a local and dynamical tuning of iDMI. In Srivastava et al. [6] we have shown that a 130% variation of the iDMI amplitude in Ta/CoFeB/TaOx can be obtained by biasing the sample with a gate voltage [6]. However, a voltage control of skyrmion chirality is still much awaited, since it would enable highly-controllable magnetic skyrmions. In this study, we report on the observation of voltage-controlled chirality switch of magnetic skyrmion bubbles in a Ta/FeCoB/TaOx trilayer heterostructure. The use of polar-Magneto-Optical Kerr-Effect (p-MOKE) microscope through a transparent Indium Tin Oxide (ITO) electrode allowed us to directly observe the current-induced motion of the spin textures and its inversion under or after the application of a gate voltage (see Fig. 1). In addition to skyrmion bubbles, we also demonstrate the voltage-effect on the chirality of magnetic labyrinthine domains. We show that successive voltage pulses of opposite sign reverse the DW chirality back and forth by tuning the oxidation state at the top FeCoB/TaOx interface. Micromagnetic simulations show that such a chirality reversal is also feasible on nanometer scale magnetic skyrmions without their annihilation. This local and dynamical control of the chirality paves the way to an efficient control of magnetic skyrmions enabling new functionalities for spintronic logic devices and memories.

**References:**

[1] I. E. Dzyaloshinskii, J. Exptl. Theoret. Phys., (U.S.S.R.), vol. 46, p 960 (1964) [2] A. Fert, N. Reyren and V. Cros, Nature Review Materials, vol. 46, p. 6 (2017) [3] A. Thiaville et al., EPL (Europhysics Letters), vol. 100, p. 57002 (2012) [4] R. Kumar et al., ArxiV, 2009.13136, p. 11 (2020) [5] M. Arora, J. M. Shaw, and H. T. Nembach, Physical Review B, vol. 101, p. 4 (2020) [6] T. Srivastava et al., Nano Letters, vol. 18, p. 4871 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6e4ca4c30678ab32da05c5a3609e15a9.jpg)
Fig. 1 : Voltage induced chirality switch on magnetic skyrmion bubbles measured through their current-induced motion under p-MOKE microscope. The dark rectangular region corresponds to the ITO transparent electrode below which voltage is applied. Under the ITO (resp. around it), black (resp. grey) regions correspond to magnetization pointing up, and white (resp. black) regions to magnetization pointing down. The current density (white arrow) is the same on (b) and (d). (a)-(b) Initially, the skyrmion bubbles are moving along the current density as depicted by the solid red arrow, consistent with a ClockWise (CW) chirality, schematically represented in the inset of (b). (c)-(d) Under the application of a positive gate voltage on ITO, an inversion of the skyrmion bubbles motion occurs below it, consistent with a CounterClockWise (CCW) chirality, as schematically represented in the inset of (d).

Real-time detection of Hall effects: measuring current-induced magnetization switching in the time domain

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