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

INTERMAG 2021

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

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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.

technical paper

Introduction Spin torque oscillators (STOs) and MRAM devices can exhibit non-linear behaviour which can be exploited to carry out tasks which would otherwise take a long time or require a huge amount of processing power when using conventional, von Neumann computing architecture. Arrays of phase-locked STOs can be used to measure the degree of matching between a test value and a reference value, and this can be used for applications such as image recognition. STOs which are sufficiently close together can be synchronised via the magnetostatic interactions between the devices. The strength of the magnetostatic interactions depends upon the relative location of the STOs, their shape and their magnetic properties. This work examines the requirements for STO synchronisation and ways to extend the correlation time (the time during which the STO magnetisation is phase-locked). The model Arrays of STOs were modelled using micromagnetic simulations. Each STO had a cylindrical shape with a diameter, D, of 60 nm and consisted of a 5 nm thick spin injection layer (SIL) and a 10 nm thick free layer (FL), separated by a 2.5 nm non-magnetic interlayer. The saturation magnetisation, Ms, of the SIL and FL was 637 and 1591 emu/cm3, respectively, with uniaxial anisotropy, Ku, of 8×106 erg/cm3 and zero, respectively. The SIL easy axis was along the z, or vertical axis. An electric current flowing through the STOs exerted a spin torque on the magnetisation, causing the free layer magnetisation to rotate in the x-y plane. In this work the STO diameter was sufficiently small that the free layer magnetisation was largely uniform and no vortices were formed. Results The average free layer magnetisation correlation, 〈M1.M2〉, was calculated for two STOs as a function of their separation and the temperature; the results are shown in fig. 1. When the STOs were very close together (dx &lt; 140 nm) the magnetostatic field was so strong that the electric current could not induce oscillation. As the STO separation increased, the magnetostatic field from one STO acting on the other decayed rapidly, limiting the range of separations over which the magnetisation was synchronised. Increasing the temperature decreased the degree of correlation between the magnetisation. Even when the value of 〈M1.M2〉was high, there were occasions when the magnetisation of the STOs slipped out of phase, i.e. the phase difference exceeded 180°. Such events are referred to as phase slips and the time interval between phase slips is denoted here as the correlation time. For practical applications the magnetisation should remain phase-locked for 1000 - 10000 oscillations, equivalent to correlation times of 200 - 2000 ns in the case of the STOs described here, which had an oscillation frequency of about 5 GHz. The correlation time decreased as the number of STOs in the array increased. Fig. 2 shows the average correlation time for an array of nine STOs in which the angle between the STOs, θ, was varied from zero (STOs arranged in a straight line along the x axis) to 60°. The correlation time was calculated using the magnetisation of the STOs at either end of the array. When the STOs were in a straight line (θ = 0°) the maximum correlation time was about 30 ns for STOs with a separation of 180 nm. Introducing an angle between the STOs increased the correlation time. When θ = 60° the correlation time was increased by more than an order of magnitude compared to θ = 0°. When dx = 180 nm and θ = 60° the correlation time exceeded the maximum simulation time of 10 μs, and for dx = 220 nm the correlation time was about 300 ns. The reason for the increase in correlation time with θ can be understood by plotting the magnetostatic field in the fifth (central STO) as a function of θ for the case when the FL magnetisation was perpendicular to the array of STOs, i.e. along the y axis, as shown in the inset to fig. 2. When θ = 0° the component of Hd along the y axis was negative and the magnetostatic energy favoured an anti-parallel alignment of the magnetisation in adjacent STOs, increasing the probability of a phase slip. As the angle between STOs was increased the magnetostatic field approached zero and became positive for 44° &lt; θ &lt; 61°, i.e. the magnetostatic energy favoured parallel alignment of the FL magnetisation over this range of θ and the correlation time was increased. The total output power of arrays of STOs also increased when an angle was introduced between the STOs. The effect of STO size and position distributions will also be discussed.

**References:**



**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8212c931a853017bc62c0e888bc7f90a.jpg)
Fig. 1 Correlation of free layer magnetisation of two STOs as a function of separation and temperature.

![](https://assets.underline.io/uploads/markdown_image/1/image/2667bb73da57e86310396a6f9eb251e6.jpg)
Fig. 2 Correlation time of STO magnetisation for arrays of nine STOs. T = 300 K. Inset: Hd in centre STO vs. angle between STOs for dx = 200 nm.

 Increasing the Correlation Time of Spin Torque Oscillators Synchronised by Magnetostatic Interactions

Over the last decade, magnetization manipulation based on spin-orbit torque has attracted wide research attention as it shows tremendous potential for the next generation ultrafast and power efficient nonvolatile memories. Very recently, centrosymmetric L10 FePt is reported to achieve the room temperature SOT switching in single layer and a new type of inversion asymmetry called composition gradient is responsible for the observed SOT. Due to its inherent superior perpendicular magnetic anisotropy (PMA), the FePt in L10 phase enables high thermal stability when device size reduced to nanoscale, which may provide a simple structure towards industry application. In this work, current-induced perpendicular magnetization switching is obtained in 6 nm thick L10 FePt single layer and in Ta/6nm FePt bilayer, respectively. The switching ratio of L10 FePt single-layer (Figure 1 (e)) in the optimum applied magnetic field (500Oe) is relatively small, about 3.3%. However, the Ta/FePt bilayers have a slightly larger switching ratio (about 4.3%) than the L10 FePt single-layer. In addition, the stability of the switching loop of the Ta/FePt bilayers film is relatively better and the critical current density is reduced in the case of a Ta/FePt bilayer. Moreover, we found that the SOT effective fields become smaller in FePt/Ta bilayer compared to that in single FePt layer by measuring the harmonic Hall voltages, which may attribute to the combined effect of the opposite spin current generated by Ta HM layer and the smaller perpendicular anisotropy. The SOT efficiency βDL of the Ta/FePt bilayers is 3.2×10-10 Oe m2A-1, which is several times of the traditional Ta/CoFeB/MgO structure reported before. The results indicate a new scheme of current-induced magnetization switching for high PMA and high coercive materials, which is expected to be applied to spintronics devices with high thermal stability and ultra-high storage density in the future.

**References:**

Fukami S, Zhang C, DuttaGupta S, et al, Nature materials, 2016, 15(5): 535-541. Liu L, Yu J, Gonzalez-Hernandez R, et al, Physical Review B, 2020, 101(22): 220402. Manchon A, Zelezny J, Miron I M, et al., Reviews of Modern Physics, 2019, 91(3): 035004. Tang M, Shen K, Xu S, et al , Advanced Materials, 2020, 32(31): 2002607. R. Ramaswamy, J. M. Lee, K. Cai, et al, Appl. Phys. Rev. 5, 031107(2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c8bb1f4b27f941b96b8e5a272593f346.jpg)
Fig.1 (a) A schematic of Ta/FePt bilayer structure.(b) Schematic of Hall bar structure (c)Schematic illustration of Hall device together with the measurement circuit.(d) R-H hysteresis characteristic measured by AHE. Positive RAHE corresponds to“upward” magnetization, whereas negative RAHE corresponds to “downward” magnetization.(e)and (f) SOT switching loops obtained under varying Hx for (e) 6-nm FePt single layer and (f) 5-nm Ta/ 6-nm FePt bilayer. (g)-(j) Field dependence of first and second-harmonic signals for 6-nm FePt film (Iac = 6mA).

 Current induced magnetization switching in L10 FePt and Ta/FePt films with large perpendicular magnetic anisotropy through spin-orbit torque

Magnetic skyrmions are topologically-nontrivial spin textures with particle-like properties [1]. Their size, topological stability, and mobility suggest their use in future generations of spintronic devices, the prototype of which is the skyrmion racetrack [2]. To realise a racetrack requires three basic operations: the nucleation (writing), propagation (manipulation), and detection (reading) of a skyrmion, all by electrical means. Here we show that all three are experimental feasible at room temperature in Pt/Co/Ir or Pt/CoB/Ir multilayers in which the different heavy metals above and below the magnetic layer break inversion symmetry and induce chirality by means of the Dzyaloshinskii-Moriya interaction, defining the structure of Néel skyrmion spin textures [3]. We show deterministic nucleation on nanosecond timescales using an electrical point contact on top of the multilayer [4] (Figure 1), current-driven propagation along a wire in which the skyrmions are channelled by defects in the multilayer [5], and their detection by means of the Hall effect (Figure 2) that reveals an unexpectedly large contribution to the Hall signal that correlates with the topological winding number [6].

**References:**

[1] N. Nagaosa & Y. Tokura, Nat. Nanotech. 8, 899 (2013). [2] A. Fert et al. Nature Nanotech. 8, 152 (2013). [3] K. Zeissler et al. Sci. Rep. 7, 15125 (2017). [4] S. Finizio et al., Nano Lett. 19, 7246 (2019). [5] K. Zeissler et al., Nature Comm. 11, 428 (2020) [6] K. Zeissler et al. Nature Nanotech. 13, 1161 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e2d829c356fc36105eeb0bb2e9c2db72.jpg)
Figure 1. STXM images (a) before and (b) after electrical nucleation of a skyrmion at a 500 nm wide injector contact to a Pt/CoB/Ir multilayer.

![](https://assets.underline.io/uploads/markdown_image/1/image/031a069098aadac7fb343bb1f3bd715d.jpg)
Figure 2. STXM image of two skyrmions in an electrically-connected 1 µm diameter Pt/Co/Ir multilayer dot. 500 nm scale bar.

 Skyrmions in chiral magnetic multilayers

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.

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

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

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