Synthetic antiferromagnets (SAFs) are of interest in a wide variety of spintronic applications owing to their net zero magnetisation and inherent tunability arising from control over complex stacking sequences [1]. They show very fast domain wall (DW) motion in response to spin torques [2]. Here we describe current-driven DW motion in an SAF with stack structure Ta/[Ru/Pt/CoB/Ru/Pt/CoFeB]×5/Ru/Pt which displays both perpendicular magnetic anisotropy (PMA) and the Dzyaloshinskii-Moriya interaction (DMI). The alternating CoB and CoFeB layers had their thicknesses adjusted to give net zero magnetisation (as determined by SQUID-VSM) for applied fields up to ~500 Oe. They were patterned into 2 µm wide wires with Cu leads attached to each end. These were fabricated on Si3N4 membranes to permit imaging of DW motion using scanning x-ray transmission microscopy. The distinct chemical composition of the two sublattices means that we could use the element specificity of this technique to observe the CoFeB separately whilst imaging at the Fe L3 edge, whilst contrast at the Co L3 edge is dominated by the other sublattice. Inverted domain structures observed at these two edges, as shown in Fig. 1, confirm the SAF ordering of the layers. Current pulses drive domain wall motion, as shown in Fig. 2, with velocities up to ~ 20 m/s achieved at current densities as low as 4 × 1011 A/m2.

![](https://assets.underline.io/uploads/markdown_image/1/image/d87de30dbef334ff75e4447e90cf2feb.jpg)

Fig. 1: STXM images acquired at zero field the Co and Fe L3 edges, which probe different sublattices of the SAF. A finger-shaped Cu lead is visible on the left. 1 µm scale bar.

![](https://assets.underline.io/uploads/markdown_image/1/image/04b915124bc7866fb80c310fb03a761b.jpg)

Fig. 2: DW velocity against current density measured using 5 ns current pulses.

Current-Driven Domain Wall Motion in a Synthetic Antiferromagnet Multilayer

Skyrmions in magnetic thin films are solitonic excitations that could open new possibilities for spintronic devices. The recent successes obtained in ferromagnetic films have shown some limitations, with dipolar-coupling induced large skyrmion sizes and topology induced gyrotropic deflection. Antiferromagnetic films and their artificial equivalents that are ferrimagnets and synthetic antiferromagnets could overcome these limitations. In this talk, we explore the skyrmion dynamics in such materials. Separating them into two antiferromagnetically coupled sublattices, we show that the dynamics can be described by two coupled Thiele equations. This framework is used to address the consequences of the small skyrmion size and the angular momentum compensation. It provides a simple approach to describe this problematic. Small skyrmions, that are possible due to the vanishing total magnetization, are shown to be significantly slower (velocity proportional to radius) than larger ones (size independent velocity). This result is a direct consequence of the skyrmion topology, which induces an excess of dissipation per size unit at small sizes. Angular momentum compensation is shown to cancel the gyrotropic deflection, without the need to modify the topology and maximizes the velocity. In a track, where the edge repulsion cancels the gyrotropic deflection, the angular momentum compensation has no effect and skyrmions travel faster that non confined skyrmions. From an applied perspective, the data rate is given by the velocity to radius ratio and correspond to the inverse of the time needed for a skyrmion to jump from one site to another. This shows that small skyrmions in ferrimagnetic films would still be preferable to large ones, providing fast and dense devices.

**References:**



**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/255c7d94b2bc6cbde230f79959b9396a.jpg)
(a) Variation of the skyrmion velocity in a CoGd thin film and (b) variation of the skyrmion velocity to skyrmion radius ratio (proportionnal to an application data rate), when the skyrmion is confined in a track, as a function of the alloy compostion, close to the angular momentum (LS) composition (79.4%), and for different DMI values. The points are the results of simulations, and the lines are the result of the model. Note that the skyrmion size increases with DMI at a given composition, and that the size is minimual at the magnetic moment compensation (77.5%).

Smaller and faster skyrmions in compensated ferrimagnets and synthetic antiferromagnets

In this last decade, experimental results and their understanding have led to magnetic skyrmions becoming promising candidates for the storage and processing of digital information [1]. However, some key barriers such as reducing their size, enhancing their stability at room temperature, or their low-power manipulation under electrical current have not yet been overcome, meaning that they are rarely integrated in actual devices [2]. To surmount these limitations, it has been proposed to study these magnetic textures in antiferromagnets or synthetic antiferromagnets (SAFs) instead of the conventional ferromagnetic layers that are usually considered [3,4]. In this more complex system, multiple ferromagnetic layers are coupled antiferromagnetically through a non-magnetic spacer layer via the RKKY interaction (Fig a) [4,5]. By switching to these systems, two crucial points need to be addressed. First, a drastic reduction of stray fields is expected in SAFs due to the anti-alignment of magnetization, which should reduce the size of the skyrmions [6]. Second, it is not possible to manipulate a conventional skyrmion in the driving force direction in a ferromagnet due to its topology that intrinsically induces a deflection known as the skyrmion Hall effect [7]. In SAF systems, since the magnetisation of the skyrmions in each magnetic layer are opposite, it is expected that the two deflections cancel each other out and the two skyrmions move in the current direction [3]. Even if skyrmions have recently been observed in SAFs [4,8,9], a clear and simple micromagnetic description of both the static and dynamic properties of such skyrmions is so far lacking to further understand this phenomenon. In order to improve the description of these properties and highlight the expected benefits of using SAFs rather than conventional ferromagnets, we simulate numerically the behavior of skyrmions in bilayer SAFs for a large range of parameters. We also adapt the ferromagnetic analytical formalism [10] to SAF systems. This leads to results that are in good agreement with the numerical simulations whilst also highlighting the underlying mechanisms. First, we investigate the stability region of SAF skyrmions and how their radii r evolve with micromagnetic parameters. We show that they are only slightly smaller than for ferromagnetic systems (Fig b), but that they exist for a larger range of parameters. Second, we study the dynamics of these skyrmions under spin currents. We find, as expected, that SAF skyrmions move at a faster velocity v than in a conventional ferromagnet (Fig c) for a given current density J, and move in the applied current direction (Fig d) with zero skyrmion Hall angle θSky. By using the analytical model based on the Thiele equation, we are able to recover these dynamics (Fig c and d) and identify the required condition for the vanishing of the topological deflection. Finally, we unbalanced the SAF by asymmetrizing the skyrmions in each layer in different ways in order to verify the condition for vanishing deflection. The results obtained highlight the qualitative benefits of SAF skyrmions and propose some methods for more quantitative optimizations.

**References:**

[1] The 2020 skyrmionics roadmap: C. Back et al., J. Phys. D: Appl. Phys. 53 (2020) [2] Magnetic skyrmions: advances in physics and potential applications: A. Fert, et al. Nat. Rev. Mat. 2, 17031 (2017) [3] Static and dynamical properties of antiferromagnetic skyrmions in the presence of applied current and temperature: J. Barker, et al. Phys. Rev. Lett. 116, 147203 (2016) [4] Room-temperature stabilization of antiferromagnetic skyrmions in synthetic antiferromagnets. W. Legrand et al., Nat. Mat. 19, 34–42 (2020) [5] Oscillatory magnetic exchange coupling through thin copper layers: S. S. P. Parkin, et. al . Phys. Rev. Lett. 66, 2152–2155 (1991) [6] Theory of isolated magnetic skyrmions: from fundamentals to room temperature applications: F.Büttner, et al,. Sci. Rep. 8 4464 (2018) [7] Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures: J. Sampaio, Nat. Nano. 8, 839-844 (2013) [8] Imaging non-collinear antiferromagnetic textures via single spin relaxometry: A. Finco et al., arXiv:2006.13130v1 (2020) [9] Exploring different facets of magnetic skyrmion nucleation and dynamics in ultra-thin films: R. Juge, PhD Thesis, Université Grenoble-Alpes (2020) [10] The skyrmion-bubble transition in a ferromagnetic thin film: A. Bernand-Mantel et.al. SciPost Phys. 4, 027 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/060a538fb9d9988c2db214e60cb7057e.jpg)
(a) Sketch of the skyrmion structure and motion under current in ferromagnetic and SAF systems. Radii (b), velocity (c) and deflection (d) for a ferromagnetic skyrmion (in blue) and a SAF skyrmion (in red) with the same micromagnetic parameters versus the current density J. Points correspond to the micromagnetic numerical simulations and lines to the analytical model.

 Statics and Dynamics of Skyrmions in Synthetic Antiferromagnets : Benefits and Micromagnetic Understanding

Magnetic layers interfaced with materials with strong spin-orbit coupling (SOC) (such as Pt, Ta) manifest several fascinating phenomena when the inversion symmetry is broken1. One direct consequence of SOC is the interplay between charge and spin transport via spin Hall effect (SHE) in heavy metals, which leads to non-equilibrium spin accumulation at the surfaces2. Another mechanism, the Rashba effect, arises when the electrical carriers move in an interfacial electric field and experience the resultant magnetic field that couples with their spins3. Both mechanisms give rise to spin-orbit torques (SOTs) in the magnetic layer, with damping-like and field-like components4. The SOTs are an efficient way to manipulate chiral magnetic textures, such as Néel domain walls (DWs)5,6 and skyrmions, whose chirality is induced by another product of SOC, the Dzyaloshinskii-Moriya interaction (DMI)7. However, up to now, the SOC was mainly studied in 3d-transition-metals (TM) (Co, Ni, Fe)/5d-heavy-metal (Pt). Very recently, interfacial DMI has been observed in TmIG/Pt and TbIG/Pt garnets thin films grown on Gd3Ga5O12 (GGG) substrates, which was attributed to the orbital moment in rare-earth (RE) material8. On the other hand, experiments on [Co/Tb]n multilayers did not show any SOT contribution from the RE9. The underlying origin of SOC and role of RE (specially Gd, which has no atomic orbital momentum) on SOC in ferrimagnets hence remain to be understood and need to be addressed by sophisticated experimental evidence. Here, we demonstrate that the effects of SOC can be obtained without any need of additional nonmagnetic heavy metal in a single layer GdFeCo ferrimagnet (RE-TM alloy). For this study, a Si/SiOx(100nm)//GdFeCo(5nm)/Al(5nm) film was grown by co-evaporation in ultra-high vacuum with a controlled stoichiometry. The ferrimagnet is composed of two sub-lattices of Gd (RE) and FeCo (TM) which are coupled antiferromagnetically. At the magnetic compensation temperature, TM ≈ 275K for this sample, the net magnetization vanishes (MS) and the anisotropy and the coercive fields diverge. To investigate the existence of SOC inside the ferrimagnetic layer, first we quantify the two components of current-induced effective fields, damping-like (HDL) and field-like (HFL) by using second harmonic Hall voltage measurement technique. The temperature dependence of HDL and HFL per current density in GdFeCo layer are shown in Figure 1(a) and 1(b). Both HDL/J and HFL/J diverge at , showing the expected scaling with 1/MS. Another phenomenon induced by SOC is the DMI, which favours chiral magnetic textures. In the single layer GdFeCo ferrimagnet, we observed chiral Néel domain wall structures of width (Δ) = 20 ± 10 nm, using photoemission electron microscopy combined with X-ray magnetic circular dichroism (XMCD-PEEM) as shown in Figure 2(a), which further indicate the presence of internal DMI or SOC in GdFeCo. The DMI is quantified using Brillouin light scattering (BLS) technique in Damon-Eshbach geometry and the DMI constant ( is obtained from the slop of frequency shifts (Δf) of nonreciprocal spin waves vs wave vector (figure 2(c)). Though the DMI amplitude is much smaller in GdFeCo if compared with Pt/Co and Ta/Co systems, the chiral DWs are stabilised due to lower net magnetization of GdFeCo, as the threshold Dc for Néel DW stabilisation is proportional to Ms. The occurrence of these phenomena also requires a broken inversion symmetry. Electron Energy-Loss Spectroscopy (EELS) studies in a scanning transmission electron microscopy (STEM) reveal an inhomogeneity in Gd concentration along the film thickness. This elemental inhomogeneity breaks the spatial inversion symmetry and the combination of broken inversion asymmetry and electronic hybridization of RE-5d and TM-3d electrons favors the emergence of net SOC effects (SOTs, DMI and chiral Néel DWs) inside the GdFeCo layer. These results show that phenomena that can only exist in systems with broken inversion symmetry and strong SOC -- spin-orbit torques, chiral textures, and DMI -- can occur in a ferrimagnetic thin layer without a heavy metal adjacent layer. This should be taken into account when analysing these phenomena even in bi-layers, and may be very useful for applications as it may allow removing the requirement for a heavy-metal layer and improving the efficiency of SOT-driven magnetisation switching.

**References:**

1. Soumyanarayanan, A. et al. Nature 539, 509–517 (2016). 2. Stamm, C. et al. Phys. Rev. Lett. 119, 087203 (2017). 3. Sánchez, J. C. R. et al. Nat. Commun. 4, 1–7 (2013). 4. Garello, K. et al. Nat. Nanotechnol. 8, 587–593 (2013). 5. Emori, S. et al. Nat. Mater. 12, 611–616 (2013). 6. Ryu, K.-S. et al. Nat. Nanotechnol. 8, 527–533 (2013). 7. Thiaville, A. et al. Epl 100, (2012). 8. Caretta, L. et al. Nat. Commun. 11, 1–9 (2020). 9. Yu, J. et al. Nat. Mater. 18, 29–34 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/906aed22f1aa90a30aad88a7fc2c9d8a.jpg)
Figure 1. (a) HDL and (b) HFL effective fields per current density as a function of temperature. Purple points correspond to an up saturated film state and khaki to down one. The diagrams represent the direction and magnitude of Gd (black) and FeCo (red) magnetic moments. The dotted lines are guides to the eyes.

![](https://assets.underline.io/uploads/markdown_image/1/image/4b4afae03c3181e42876985bb777aa9a.jpg)
Figure 2. (a) Multidomain XMCD-PEEM images at the Gd M4,5 edge (1178.7 eV) at T = 230 K. The green arrow shows the direction of the X-ray beam at a grazing angle of 16°. The dark (bright) contrast corresponds to a down (up) magnetic domain. (b) Intensity profiles (black lines) averaged over the yellow regions in (a). The thick yellow line is a fit to the experimental data using the theoretical profile. The presence of a peak or a dip in the line scan is an evidence of chiral Néel DWs. (c) The DMI induced frequency shifts (𝛥f) of nonreciprocal spin waves vs wave vector magnitudes |ksw| for GdFeCo thin film

 Direct Observation of Spin-Orbit Torques, Dzyaloshinskii-Moriya Interaction and Chiral Spin Textures in Single Layer Ferrimagnets

Magnetic skyrmions are a peculiar kind of chiral magnetic textures stabilized by chiral interactions like the Dzyaloshinskii-Moriya interaction (DMI) [1]. Their topological properties offer interesting robustness qualities but, as a counterpart, add a complexity to their dynamics. Since their first observation in a bulk chiral magnet in 2009 [2], rapid experimental advances demonstrated their stability at room temperature without any magnetic field in ferromagnet/heavy metal bilayers and multi-stacks [3]. The experimental demonstrations of smaller and smaller skyrmions at room temperature (down to few 10s of nm) suggest that they are the perfect candidates for information storage and logic devices. Before building such devices, we first need to master skyrmions' static and dynamical properties, namely the nucleation and stabilization of small skyrmions that can move at high speed inside tracks. One significant issue with skyrmion dynamics is the topological deflection. Also known as Skyrmion Hall effect, it is caused by the topological charge of skyrmion and consists in a deflecting force proportional and perpendicular to the skyrmion velocity. Deflection can lead to the expulsion of skyrmions from the tracks that contain them, and thus imposes a limit to the skyrmion velocity. Experiments and calculations found that the deflection angle varies with skyrmion velocity and diameter probably due to its interaction with pinning disorder [4]. It has been suggested that antiferromagnetically-coupled systems, such as antiferromagnets, synthetic antiferromagnets (SAFs) or ferrimagnets, may be used to overcome these issues. The low net magnetization of these systems reduces the size of the skyrmions, and their low angular momentum density should suppress the troublesome topological deflection. Ferrimagnetic Rare-Earth/Transition Metal alloys possess two anti-parallel sublattices whose relative magnetic moments can be changed by temperature or alloy composition. Ferrimagnets share properties from ferromagnets and antiferromagnets (at the magnetic compensation) with which they present many similarities. They are perfect systems to study the advantages of antiferromagnetically-coupled materials, while preserving the effects that have already been used to stabilize and drive skyrmions in ferromagnets. Recent results on SAF showed the promising advantages of using multi-lattices coupled antiferromagnetically [5], and in 2018 a huge breakthrough was achieved in Rare-Earth/Transition Metal ferrimagnets where the smallest skyrmions were observed (10-30nm) [6] as well as a reduced topological deflection [7]. Using co-evaporation in Ultra-High-Vacuum [8], we grew ferrimagnetic thin film of Ta(1nm)/Pt(5nm)/Gd0.3Co0.7(5nm)/Ta(5nm) with an amorphous structure that decreases pinning of skyrmions. By optimizing the material stack and the process conditions, we were able to strengthen the interfacial DMI while keeping a balanced interfacial anisotropy to obtain out of plane magnetized samples (around room temperature) that can host skyrmions. We then observed the skyrmions by Magneto-Kerr Microscopy with sizes smaller than the technique’s resolution limit (around 500 nm) (Fig. 1). After saturating the sample, we were able to nucleate skyrmions in the tracks and to tune their overall density by applying magnetic fields. Skyrmions were also nucleated on the edges of the track by nanosecond-long current pulses. Thanks to the tunability of the magnetic properties of the ferrimagnet, we studied the sample in a range of magnetic field and temperature (0–40 mT, and 295–320 K). We observed different regimes: saturated magnetic textures, skyrmions with different densities, and stripes textures. Skyrmions were observed between ~295-310 K. The field necessary for nucleating skyrmions increased with temperature (8 mT at 295 K, 15 mT at 305 K), probably due to a decreasing Ms (as the compensation temperature of this sample is above the tested range). We also observed their dynamics under the application of nanosecond current pulses. The current going through the adjacent Pt layer generates a spin orbit torque (SOT) due to the spin Hall effect, which drives the skyrmions. We observed speeds higher than 150 m/s (for ~10 GA/m2) in a denser skyrmion regime and up to 40 m/s in the most diluted regime (Fig. 2), limited for higher current density by edge nucleations. The speed seems to follow a linear dependence with current. In the conditions of higher density, the velocity was higher and the depinning current lower, probably due to a change of the skyrmion diameter. We also studied the evolution of the deflection angle of the skyrmions, which increased from 40° at low current to finally saturate around 60°. This work shows that ferrimagnetic skyrmions can be nucleated, stabilized and propagated by SOT in amorphous rare earth/transition metal thin films. In these results, we stabilized skyrmions far away from the magnetic compensation of the sample (also far away from the angular compensation). We have since prepared new samples with accessible magnetic and angular compensation in order to study the dynamical properties of our sub-micron skyrmions in these very peculiar regimes.

**References:**

 [1] – A. Fert et al., Nature Nanotechnology, Vol 8, p 152–156 (2013) [2] – X. Z. Yu et al. Nature, Vol 465, p 901–904 (2010) [3] – A. Hrabec et al., Nature Com. Vol 8, 15765 (2017) [4] - Joo-Von Kim et al. Appl. Phys. Lett., Vol 110, 132404 (2017) [5] – W. Legrand et al., Nature Materials, Vol 19, p 34–42 (2020) [6] – L. Caretta et al., Nature Nanotechnology, Vol 13, p 1154–1160 (2018) [7] – S. Woo et al. Nature Communications Vol 9, 959 (2018) [8] – E. Haltz et al. Physical Rev. Materials Vol 2, 104410 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4deb0696a0fd43f90ed46a6cc224f887.jpg)
Fig.1 : Magneto-Kerr Microscopy image of skyrmions in GdCo micro-structured sample.

![](https://assets.underline.io/uploads/markdown_image/1/image/25864383d3eb7d0bd0916c7804a27862.jpg)
Fig. 2 : SOT-driven velocity at room temperature in diluted and denser regime.

 Spin Orbit Torque Dynamics of Magnetic Skyrmions in GdCo Ferrimagnetic Thin-Films

**Session chair:** Jean-Yves Chauleau, CEA-SPEC


HOF - Dynamics in AF-coupled Materials

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

2022 Joint MMM-INTERMAG

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

*Session Co-Chair: Daria Gusakova, SPINtronique et Technologie des Composants*

*Session Co-Chair: Joo-Von Kim, Université Paris-Saclay*

These on-demand presentations are available to view at your leisure. 

AE: Micromagnetic Modelling

INTERMAG 2021 Welcome Video



	
<figure class="video_container">
 <iframe src="https://screencast-o-matic.com/player/crflqFVnUpZ?v=6&ff=1&title=0&controls=1" width=640 height=360 frameborder="0" allowfullscreen="true"> </iframe>
</figure>

Want to buy a ticket? 

Register for INTERMAG 2021 here

[![](https://assets.underline.io/uploads/markdown_image/1/image/17ce76e7960db633258024eef8d6da7f.png)](https://intermag.org/register)

Got your ticket, but still can’t access the event?

Contact us and our team will look into it.

INTERMAG 2021

*Session Chair: Vito Puliafito, Universita degli Studi di Messina*

These on-demand presentations are available to view at your leisure.

FH: Antiferromagnetic Spintronics II

*Session Chair: Sebastian Diaz, Johannes Gutenberg Universitat Mainz*

These on-demand presentations are available to view at your leisure.

Eloi Haltz

5

25

SHORT BIO

Presentations

Current-Driven Domain Wall Motion in a Synthetic Antiferromagnet Multilayer

Smaller and faster skyrmions in compensated ferrimagnets and synthetic antiferromagnets

Statics and Dynamics of Skyrmions in Synthetic Antiferromagnets : Benefits and Micromagnetic Understanding

Direct Observation of Spin-Orbit Torques, Dzyaloshinskii-Moriya Interaction and Chiral Spin Textures in Single Layer Ferrimagnets

Spin Orbit Torque Dynamics of Magnetic Skyrmions in GdCo Ferrimagnetic Thin-Films

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES