The actual mechanisms occurring at interfaces underlying the Dzyaloshinskii-Moriya interaction (i-DMI) remain largely an open question in nanomagnetism. In this study, we investigate the origin of the i-DMI, aiming at estimating how independent the DMI contributions of the two interfaces of a FM layer are and what their relative weight in the effective DMI amplitude is. The effective DMI is measured by the study of the asymmetric domain wall propagation in the presence of an in-plane magnetic field, in Pt|Co|M stacks. These measurements are completed by Brillouin light scattering (BLS) measurements. We then explore the correlation between the effective i-DMI and the properties of metal M, namely, its atomic number, electronegativity, and work function. A clear linear relationship is found between the i-DMI and the work function difference at the Co|M interface (ΔΦ) [1,2]. We define Δφ = φM - φCo. This result is a strong evidence of the independent DMI contributions of the two interfaces for the chosen Co thickness (1 nm). These findings may guide the optimization of the magnetic properties of future spintronic devices.
This work has been supported by DARPA TEE program grant (MIPR HR-0011831554), ANR grant TOPSKY (ANR-17-CE24-0025), FLAG-ERA SographMEM (ANR-15-GRFL-0005), and the Horizon2020 Framework Program of the European Commission, under FET Proactive Grant Agreement No. 824123 (SKYTOP) and under Marie Sklodowska- FQ Curie Grant Agreement No. 754303 for supporting J.P.G together with the LABEX LANEF in Grenoble (ANR-10-LABX-0051). Univ. Paris-Saclay, CNRS INP, Sesame IMAGeSPIN project (nEX039175) and the LABEX NanoSaclay (ANR10 LABX0035, BLS@PSay and SPiCY projects) are acknowledged for the BLS equipment. 
**References** [1] F. Ajejas et al., Phys. Rev. Mat., June 2022
[2] Y.-K. Park et al., NPG Asia Mater. 10, 995 (2018)
 
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Interfacial potential gradient modulates Dzyaloshinskii Moriya interaction in Pt|Co|Metal multilayers

Spin-orbit interaction in metals and its ability to generate spin-current has been the hallmark of spintronics in the last decade. Beyond its fundamental interest as a source of spin-current, the manipulation of magnetization via transfer of the spin angular momentum has proven to be energy efficient for spin-based memory (e.g. SOT-MRAM) and also neuromorphic devices (e.g. using spin Hall nano-oscillators). Therein, charge to spin conversion is believed to be governed essentially by two main mechanisms, spin Hall effect in the bulk of heavy-metals and Rashba effect at interfaces [1], the latter being often considered negligible in all-metallic interfaces. However, in the case of atomically thin metallic layers, the underlying SOT physical mechanisms at play have not been experimentally fully tackled. 
In this study, we examine the impact of the insertion of a light element interface on the nature of the SOT as well as its efficiency in terms of damping-like (HDL) and field-like (HFL) effective fields in ultrathin ferromagnets. Importantly, we observe unexpectedly large HFL/HDL ratio (∼2.5) upon inserting a 1.4 nm thin Al layer in Pt|Co|Al|Pt as compared to Cu instead of Al as shown in Fig. 1. From our modeling (dotted lines in Fig.1), these experimental results strongly evidence the presence of a large interfacial Rashba effect at Co|Al interface producing giant HFL. The occurrence of such enhanced torques from an interfacial origin is further validated by reducing the contribution from SHE in the bottom Pt layer as well as by demonstrating current-induced magnetization reversal at reduced current. We believe that our results are important from the application point of view as they provide a clear route for reaching ultimate spin-torque efficiency for the associated devices[2]. 
**Acknowledgement:** DARPA TEE (MIPR no. HR0011831554), the Horizon2020 Framework Program of the European Commission under FET-Proactive Grant agreement No. 824123 (SKYTOP) and the the Agence Nationale de la Recherche, France, No. ANR-17-CE24-0025 (TOPSKY). 
**References:** [1] Manchon, A. et al., Rev. Mod. Phys. 91, (2019). 
[2] Krishnia S. et al., arXiv : 2205.08486. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d8fd135b8e9157bc0dc4a5f819d2811b.png) 
Co thickness (tCo) dependence of (a) DL-SOT field and (b) FL-like SOT fields in Pt8|Co (tCo)|Al1.4|Pt3 (red ) and Pt8|Co (tCo)|Cu1.4|Pt3 (blue ) samples (c) ζ = HFL/HDL as a function of tCo.

Large interfacial Rashba interaction and giant spin orbit torque in atomically thin metallic multilayers

Magnetic topological textures could serve as powerful tools in the development of next-generation spintronics devices, especially in terms of stability and energy consumption. Two-dimensional (2D) magnetic solitons such as chiral domain walls or skyrmions were mostly under focus for the last decade. Beyond these 2D textures, a new interest has risen for more complex quasi-particles that display variations over the thickness, i.e., three-dimensional (3D) objects. Examples include different skyrmion phases [1], bobbers [2] or even hopfions [3]. In this work, we show how by engineering Pt/Co/Al based multilayers with variable Co thickness, we observe the signature of new textures, called skyrmionic cocoons [4] that are only present in a fraction of the magnetic layers. Interestingly, these cocoons can coexist with more standard ‘tubular’ skyrmions going through all the multilayer as evidenced by the existence of two very different contrasts in the magnetic force microscopy (MFM) images recorded at room temperature (Fig. 1a). Moreover, the field dependence of skyrmionic cocoons has also been studied with Fourier transform holography measurements (FTH) with similar observations (Fig. 1b). FTH additionally puts forward various magnetic phase transitions as well as the existence of an attractive interaction between cocoons. The presence of these novel skyrmionic textures has also been investigated by micromagnetic simulations (Fig. 1c). The relaxed states can easily be identified with the different experimental contrasts: the columnar skyrmion tubes (resp. cocoons) corresponds to the strong contrast (resp. weak contrast). Thus, this coexistence of various magnetic textures in multilayers and the discovery of a novel magnetic texture are particularly interesting as they can open new paths for three-dimensional spintronics. 
**References** [1] A.O. Mandru et al. Nature communications 11,1 (2020)
[2] F. Zheng et al. Nature Nanotechnology 13, 451 (2018)
[3] N. Kent et al. Nature communications 12, 1 (2021)
[4] M. Grelier et al. arXiv: 2205.01172 (2022). 
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Skyrmionic 3D cocoons in magnetic multilayers

Spintronic nano-oscillators can provide energy efficient solution to realize neuromorphic applications. They have been shown to emulate biological neurons and perform
machine learning tasks with an accuracy similar to that of state-of-the-art neural networks [1]. Moreover, they can serve as synapses when operated as a spin diode [2]. In this context,
systems with compensated anisotropy could offer key advantages. For instance, an easy plane geometry achieved by compensating the anisotropy can produce spikes as an output, a
phenomenon, recently demonstrated via micromagnetic simulations for a spin Hall nano-oscillator (SHNO) geometry [3]. Moreover, an SHNO with a compensated or near zero effective
magnetization would require low operating current and exhibit extremely low phase noise, making it suitable to realize large chain of synchronized neurons [4]. A synapse or a spin diode
with a compensated anisotropy would also resonate at a relatively fixed frequency, which is an essential requirement for frequency multiplexing and transmitting data from the SHNO
based neurons. This motivates us to study spin Hall systems with compensated anisotropy. Here, Pt/CoFeB based thin films are used as the spin Hall system. The anisotropy has been tuned
by varying the thickness of the magnetic layer. The thin films have been fabricated into micro-strip waveguides and nano-constrictions to study the magnetization dynamics in these
systems which emulate the behaviour of an SHNO. Spin-torque ferromagnetic resonance (ST-FMR) technique is employed to evaluate the effective magnetization of the fabricated devices.
The measurements indicate the fabricated devices achieve compensation when the starting thin films have perpendicular anisotropy, implying the effects of post-fabrication anisotropy
reduction and shape anisotropy. Different nano-constriction geometries have been studied to evaluate the effect of shape on the compensation point. We also demonstrate frequency
tunability of the nano-synapses and thereby its weights by anisotropy modification. We then propose a non-volatile method to control the synaptic weights via electric fields which would
enable realization of compact and energy efficient neuromorphic chips. 
**References** [1] J. Torrejon et al., “Neuromorphic computing with nanoscale spintronic oscillators”, Nature 547, 428 (2017).
[2] N. Leroux et al., “Radio-Frequency Multiply-and-Accumulate Operations with Spintronic Synapses”, Phys. Rev. Appl. 15, 034067 (2021).
[3] D. Markovic et al., “Easy-plane spin Hall nano-oscillators as spiking neurons for neuromorphic computing”, Phys. Rev. B 105, 014411 (2022).
[4] A.A. Awad et al., “Long-range mutual synchronization of spin Hall nano-oscillators”, Nat. Phys. 13, 292 (2017).

Compensation of anisotropy in spin Hall systems for realizing neuromorphic applications

Room-temperature skyrmions have been presented as potential candidates for encoding information bits in several types of new spintronic devices [1]. There have been many recent progresses allowing to stabilize sub-100 nm skyrmions at room temperature in crystalline ferromagnetic thick layers or in (amorphous) thin magnetic multilayers (MML) [2]. In most case, at least in extended films or large structures, the application of relatively large perpendicular field (a few 10 mT) is needed which might be unfavorable for most of the anticipated skyrmion based devices. Hence, the stabilization of zero-field isolated skyrmions or skyrmion lattices is an important step towards application. There are recent works demonstrating isolated zero-field skyrmions stabilized due to interlayer exchange in polycrystalline [3], epitaxial [4] or exchange biased [5] trilayers. Here we demonstrate a new approach showing that room-temperature zero-field skyrmion lattices can be stabilized in MML. We develop a system in which perpendicular magnetic anisotropy, chiral order and bias field strength, through a non-magnetic spacer, can be adjusted simultaneously. Typical stacking sequence is schematically presented in Figure 1 (a). The samples have been characterized first by standard magnetometry (Fig. 1b). Relying on the interlayer electronic coupling to an adjacent bias magnetic layer with strong perpendicular magnetic anisotropy (uniform configuration), we demonstrate by Magnetic Force Microscopy that the remnant wormy-stripe “as-grown” domains (Fig. 1d) can be turned into skyrmion lattice phase (Fig. 1c). The skyrmion density and size can be modified by finely tuning the thicknesses of the layers allowing the control of the parameters related in the stabilization of the lattices. ANR TOPSKY (ANR-17-CE24-0025), DARPA TEE program (MIPR#HR0011831554) and EU SKYTOP (H2020 FET Proactive 824123) are acknowledged for financial support. 
**References** [1] A. Fert, N. Reyren, V. Cros, Nat. Rev. Mat. 2, 17031 (2017)
[2] C. Moreau-Luchaire et al., Nat. Nanotechnol. 11, 444 (2016)
[3] G. Chen et al., Appl. Phys. Lett. 106, 242404 (2015)
[4] R. Loconte et al., doi : 10.1021/acs.nanolett.0c00137
[5] K. G. Rana et al., Phys. Rev. Applied 13, 044079 (2020)
 
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Zero field room

In nanomagnetism and spintronics, magnetic multilayers continue to thrive as pivotal structures to engineer complex non-trivial spin textures thanks to the tunability of their composition and their properties. Two-dimensional magnetic textures such as skyrmions or chiral domain walls were mostly under focus for the last decade, but recently interest has surged for more complex objects which display an inhomogeneous behavior over the vertical dimension [1,2]. Interesting examples include bobbers which could become remarkable assets for the development of logic devices [3] or the recently observed hopfions [4] or even different skyrmions phases [5]. Our own efforts to engineer and explore three-dimensional textures in Pt/Co based multilayers allows us to observe the signature of new textures, which we name skyrmionic cocoons. At low magnetic field, they resemble tubular skyrmions but upon an increase of the out-of-plane field, they shrink and disappear in the outer layers (Fig 1.b,c), becoming elongated ellipsoids. To observe such textures, we grew multilayers displaying variable thicknesses of a ferromagnetic material, thereby introducing a non-uniform effective anisotropy. By carefully tuning the thickness of each magnetic layer, it was possible to observe in a single sample two distinct types of objects, as shown by the strong difference in the Magnetic Force Microscopy (MFM) contrasts (Fig 1.a). With the support of micromagnetic simulations (Fig 1.b), we identify them as two vertically coupled cocoons (large contrast) and single cocoons only present in half of the layers (weak contrast). The existence and field-dependent behavior of such textures could represent interesting possibilities for potential applications.

![](https://assets.underline.io/uploads/markdown_image/1/image/e2c9cf21f889d9f4fd7c83a4aa3ac691.jpg)

Fig 1. a) MFM measurement at 265 mT on a multilayer with variable thickness of Co. b) Corresponding micromagnetic simulations at different fields displayed with isosurfaces, mz=0 (white) and mz=-0.8 (red), with plane cuts identified by the coloured lines. The yellow dotted ellipses evidence the two kinds of objects correlated with the MFM image: coupled cocoons (left) and single cocoons (right). c) Simulated vertical cuts showing the evolution of a cocoon at different out-of-plane magnetic fields.

Non-Collinear Three-Dimensional Textures In Magnetic Multilayers: Hatching of Skyrmionic Cocoons

Microwave response of magnetic textures in ferromagnets offers rich physics and has been intensively investigated over the past decades for their potential application in magnonics. Eigenexcitations of films featuring bubble domains [1,2] and stripes [3] have been accounted for, broadly consisting of acoustic, optical and domain wall oscillation modes. Recently, topologically non-trivial chiral magnetic structures called skyrmions [4] have gathered a lot of interest owing to their robust, tiny and particle-like nature. They exhibit unique spectral signatures which have been observed mainly in bulk systems below room temperature [5,6]. The experimental observation and interpretation of their resonant dynamics in thin films remain elusive owing to high damping coefficients. Here we report room temperature investigation of resonant skyrmion dynamics in [Pt/CoFeB/AlOx]×20 multilayers. We optimize our sample by tuning the different layer thicknesses to host magnetic skyrmions at room temperature, along with a fairly low damping parameter α= 0.02. We use magnetic force microscopy to observe the static magnetic domain configuration consisting of randomly distributed skyrmions and dense skyrmion lattice as a function of an out-of-plane magnetic field. Broadband ferromagnetic resonance measurements are performed to study the dynamic response with an in-plane excitation field. Besides the Kittel mode (KM) above saturation, three distinct modes, a low frequency mode (LFM), an intermediate frequency mode (IFM) and a high frequency mode (HFM), appear with unique frequency-field dispersions in the non-saturated state (see Fig). Micromagnetic simulations reveal the characteristics of these modes, where the LFM features a mode localized in the skyrmion edges, while for the IFM skyrmion edge dynamics couples with the uniform background. In the HFM, the precession of skyrmion cores emits omnidirectional spin waves into uniform background, producing interference patterns in the lattice. Our results thus open up new avenues for skyrmion-based magnonic devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/20e701a47ef97bc8c284fee76af80155.jpg)

Fig : Frequency-field dispersion map measured by FMR over a frequency range of 0.1 GHz to 20 GHz with an out-of-plane magnetic field swept from -500 mT to 500 mT.

Localized and propagating spin-wave modes in thin film multilayers hosting skyrmions

Current-induced spin-orbit torques (SOTs) provide a unique mechanism to manipulate the magnetization of diverse class of magnetic multilayers and devices. The core of the phenomenon is charge to spin-current conversion in ferromagnetic/heavy-metal heterostructures which is governed by spin-orbit interactions mainly through spin Hall effect in heavy metals or Rashba effect at interface with broken inversion asymmetry1. The non-equilibrium spin-current (of spin σ) interacts with local magnetic moments (m) via exchange interaction and creates two different components of spin-transfer torques: damping-like and field-like , where HDL and HFL are damping-like and field-like effective fields2. In the macrospin approach of spin-orbit torque induced dynamics, the magnetization reversal in systems with perpendicular magnetic anisotropy is governed by damping-like torque and Dzyaloshinskii-Moriya interaction3. However, recent micromagnetic studies predict a unique reversal path which is determined by interplay between damping-like and field-like torques4. In this work, we will show how the ratio of field-like torque to damping-like torque is affected by the thickness of magnetic layer. A series of samples Pt 8|Co x|Al 1.4|Pt 3 with x = 0.7, 0.9, 1.2, 1.4 (numbers are thicknesses in nm) is deposited using magnetron sputtering. 5-μm-wide Hall bar structures were fabricated using optical lithography and Ar ion-milling technique. All the devices show perpendicular magnetic anisotropy. We used AC harmonic Hall voltage measurement technique to quantify current-induced effective fields. This technique exploits a sinusoidal current (IAC) of frequency 727 Hz and simultaneous measurement of the first and second harmonics of the Hall voltage as a function of an in-plane field (H) applied along or transverse to the current direction (H || IAC and H ⊥ IAC), and extract HDL or HFL effective fields. The measured HDL and HFL increase linearly with the current for all the Co thicknesses as shown in Figure 1(a) and 1(b), respectively. Furthermore, the HDL (= m×σ) changes sign with magnetization direction whereas HFL (= σ ) is independent of magnetization direction, in agreement with literature2. Figure 2 shows the HDL and HFL for an estimated current density JPt=1011 A/m2 in seed Pt layer as a function of Co thickness. The measured HDL and HFL increase with decreasing the Co thickness. The observed behavior confirms the interfacial nature of spin-orbit torques5. Interestingly, here we observe a clear increase in the ratio of HFL/HDL with decreasing the Co thickness. To corroborate the phenomenon, we next quantify the SOTs in Pt 8|Co x|Al 1.4|Ta 5 series and the similar increasing trend in HFL/HDL is observed when the Co thickness is decreased. The results suggest for additional mechanisms of spin-current generation which will be discussed in details during the conference. Acknowledgement-French ANR grant TOPSKY (ANR-17-CE24-0025), DARPA TEE program grant (MIPR#HR0011831554) and EU grant SKYTOP (H2020 FET Proactive 824123) are acknowledged for their financial support.

**References:**

1. Garello, K. et al. Nat. Nanotechnol. 8, 587–593 (2013). 2. Hayashi, M., Kim, J., Yamanouchi, M. & Ohno, H. Phys. Rev. B 89, 1–15 (2014). 3. Lee, O. J. et al. Phys. Rev. B 89, 1–8 (2014). 4. Baumgartner, M. et al. Nat. Nanotechnol. 12, 980–986 (2017). 5. Park, Y. K. et al. NPG Asia Mater. 12, (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ea959e15ad0cfb2ba720f28f9d4b4f37.jpg)
Figure 1. Current-induced SOT effective fields (a) HDL and (b) HFL as a function of current density in seed Pt layer for various Co thicknesses.

![](https://assets.underline.io/uploads/markdown_image/1/image/883262de168f440ae01eb8bce55a8174.jpg)
Figure 2. Plot of HDL and HFL per 1011 A/m2 current density in seed Pt layer with respect to the Co thickness.

 Magnetic Layer Thickness Dependence of Spin-Orbit Torques in Pt / Co / Al / (Pt | Ta) Skyrmion Magnetic Multilayers.

Magnetic multilayers (MML) with large perpendicular magnetic anisotropy (PMA) and Dzyaloshinskii-Moriya interaction (DMI) have attracted great attention in recent years owing to the possibility of stabilizing non-collinear magnetic textures such as chiral domain walls (DW) [1], spin spirals [2] or skyrmions [3-4] with chiral Neel magnetization rotation. The latter are promising candidates as carriers of information for next-generation race-track magnetic memories or logic devices. The accurate experimental determination of the DMI is an important challenge as it is necessary to tailor the properties of future devices. The determination of the effective DMI amplitude D is still a current subject of active research since the origin of the DMI is not well known. Beyond the three-sites Fert-Levy model [5], first principle calculations for the common Pt|Co|M systems were carried out [6], aiming at finding a simple relation between the DMI and the intrinsic properties of the metallic element that would be easily accessible to the experimentalist, providing guidance to design systems with a required D value. In this study, we perform thorough measurements to determine DMI strength by asymmetric expansion of domains in the presence of an in-plane magnetic field, using Kerr microscopy [7-8]. Results are shown in Figure 1 for all the different materials selected to build asymmetric trilayers with the general structure is Pt|Co|M, with M = Ni, Pd, Ru, Al, Al|Ta and MoSi. The symmetric (asymmetric) expansion of Néel-type bubble without (under the presence of) an external in-plane magnetic field of Pt|Co|Al trilayer is displayed in panel (a). In panels b-g are plotted the expansion velocities of the up and down domain branches as function of the in-plane field for all the studied systems. The minima of the plotted curves correspond to the field which compensates HDMI, which is related to D by , is the DW parameter. From the D, we estimate the effective interfacial DMI (summing Pt and M contributions), Ds = D*t, with t the Co thickness. We look for correlation between Ds and three material properties in Fig. 2. In Fig. 2a is presented in log-log scale the absolute value of Ds as function of atomic number (Z). As DMI is proportional to spin-orbit coupling, Z scales with different power laws e.g. Z2 and Z4 for 3d and 4d elements, becoming more complex for the heaviest elements. Fig. 2b shows Ds as function of Pauling electronegativity (χ) [6]. Here we found a linear correlation in good agreement with theoretical calculations (Pearson-r dispersion index of 0.74). Finally, in panel c is presented Ds as a function of the work function difference (ΔΦ) [9] at the Co|M interfaces. We find a striking linear relationship between Ds and ΔΦ (Pearson-r dispersion index of 0.93). This strong correlation points to Rashba-like interfacial fields, leading to the modulation of the effective interfacial DMI.

**References:**

[1] A. Thiaville et al. EuroPhys. Lett, 100, 57002 (2012) [2] P. Ferriani et al. Phys. Rev. Lett. 101, 27201 (2008). [3] A. Fert, N. Reyren, V. Cros, Nat. Rev. Mat. 2, 17031 (2017). [4] C. Moreau-Luchaire et al. Nat. Nano. 11, 444 (2016); O. Boulle et al, Nat. Nano 11 (5), 449 [5] A. Fert and P.M. Levy, Phys. Rev. Lett., 44,1538 (1980) [6] H. Jia et al. Phys. Rev. M 4, 024405 (2020) [7] F. Ajejas et al. Appl. Phys. Lett. 111, 202402 (2017); [8] T. Ha Pham et al EPL 113 67001 (2016) [9] Y.-K. Park et al. NPG Asia Materials 10, 995 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d71e7f7debc02e5ad49cf2c4362d6ece.jpg)
a) Expansion of Néel-type bubble in Pt|Co|Al trilayer for different external in-plane magnetic field Bx. b-g) Domain wall velocity vs. Bx for up/down and down/up DWs.

![](https://assets.underline.io/uploads/markdown_image/1/image/24662d410e7c5046f766007ae55890dc.jpg)
Parameter relationships. Ds as function of, a) Atomic Number (Z); b) Electronegativity (χ); and c) work function difference (ΔΦ), for Pt|Co|M samples with different M values, as denoted in the figure.

 Experimental correlation of Interfacial Dzyaloshinskii-Moriya interaction amplitude and Work Function in magnetic multilayers and its relation with Rashba effect at metallic interfaces.

Magnetic skyrmions are chiral whirling textures of magnetization with a non-trivial topology. Their nanometric size and particle-like behavior has engendered huge interest for their potential applications in memory and logic devices. The observation of magnetic skyrmions at room temperature has triggered extensive research to decipher their various static and dynamic properties which is crucial for their eventual implementation in spintronic devices [1]. In the case of ultra-thin multilayer films consisting of heavy metal_(HM)/ferromagnet_(FM)/insulator_(I), skyrmions are primarily stabilized by interfacial Dzyaloshinskii-Moriya interaction (iDMI) in combination with perpendicular anisotropy, dipolar, exchange and Zeeman energies, where each of these contributions can be finely tuned [2]. The non-trivial skyrmion topology and its emergent electrodynamics is at the heart of phenomena like the skyrmion Hall effect and the topological Hall effect. Another interesting consequence of the skyrmions topology is reflected in their unique spectral signatures given by the gyrotropic rotational modes [3] (clockwise and counter-clockwise) and the breathing mode [4], when excited by an in-plane or an out-of-plane rf magnetic field. These unique dynamics open up new prospects for skyrmion-based microwave detectors [5] and nano-oscillators [6]. However, the experimental observation of skyrmion resonance dynamics remains limited. So far, skyrmion eigen modes have been mainly observed at low temperature in bulk systems [7]. Only few studies have been carried out in thin films, but with zero iDMI [8]. The experimental observation of the excitation modes of homochiral skyrmions stabilized by iDMI at room temperature remains elusive and challenging owing to usually elevated damping parameter and material inhomogeneities in HM/FM/I systems. Here, we study the magnetization dynamics in a [Pt/CoFeB/AlOx]×20 multilayer deposited by sputtering. First, the system is optimized by tuning the Pt and CoFeB thicknesses to host magnetic skyrmions at room temperature, along with a minimized damping parameter α ~ 0.02, measured by ferromagnetic resonance (FMR). The quasi-static magnetic domain configuration is observed by magnetic force microscopy (MFM) where on sweeping an out-of-plane (OP) magnetic field from saturation to zero, random skyrmion nucleation occurs, forming a lattice structure which then breaks into a mixture of skyrmions and stripes at lower fields; finally transforming into labyrinthine domains as shown in Fig. 1. The dynamic response of the system is measured by Vector Network Analyser (VNA) FMR with an rf field applied in-plane and varied over a frequency (f) range of 0.1-20 GHz, and an OP dc magnetic field swept from -0.55 T to +0.55 T. The frequency-field dispersions indicated in Fig. 2 (a) show several resonant modes corresponding to the domain configurations observed by MFM at the respective applied fields. At fields above the saturation, the well-known Kittel mode is observed, pertaining to uniform precession. Below saturation, distinct modes arise in the resonance spectrum with both positive and negative dispersions at low (f&lt;2GHz), medium (2&lt;f&lt;7GHz) and high frequencies (f&gt;7). The low frequency mode is observed on increasing the field towards saturation as can be seen on comparing Fig. 2 (a) and (b). Micromagnetic simulations further give an insight into the mechanisms involved in the subsequent dynamic behavior of the skyrmions. We observe that the low frequency mode (LFM) is due to the excitations localized at the skyrmion edges, corresponding to the breathing dynamics. The medium frequency mode (MM), on the other hand, arises due to the localized excitations in the inter-skyrmion region, i.e. the non-reversed magnetic zone, and has a negative dispersion. The origin of the high frequency mode (HFM) lies in the excitations across the skyrmion lattice and corresponds to the spin waves travelling across both the reversed and non-reversed regions. These latter modes (MM and HFM) are hence attributed to the magnonic cystal modes of the skyrmion lattice. This observation opens up new possibilities of creating and designing dynamically modulable skyrmion-based magnonic crystals at room temperature.

**References:**

[1] A. Fert et al., Nat. Rev. Mater. 2, 17031 (2017) [2] W. Legrand et al., Sci Adv 4, 7, (2018) [3] M. Garst et al. J. Phys. D: Appl. Phys. 50, 293002 (2017) [4] J.-V. Kim, et al., Phys. Rev. B 90, 064410 (2014) [5] G. Finocchio et al., Appl. Phys. Lett. 107, 262401 (2015) [6] F. Garcia-Sanchez et al., New J. Phys. 18, 075011 (2016) [7] Onose et al. Phys. Rev. Lett. 109, 037603 (2012) [8] S. A. Montoya et al. Phys. Rev. B 95, 224405 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/85f55608a7a181b99a46e77d5eb4df88.jpg)
Fig. 1. Magnetic domain configurations: randomly distributed skyrmions, skyrmion lattice, skyrmion-stripe mix, and labyrinthine domains, measured by MFM under the application of OP magnetic field swept from negative to positive values. The OP hysteresis curve in blue is plotted below. The solid blue curve corresponds to the OP field sweep from negative to positive (NtoP) values and the dashed curve from positive to negative (PtoN). The corresponding skyrmion density (red spheres) determined from the MFM images is also plotted. A dense skyrmion lattice is seen to be stable between 0.18T and 0.32T. The dashed grey line indicates the possible extrapolation of the observed skyrmion density at higher field values in accordance with the OP hysteresis curve (NtoP).

![](https://assets.underline.io/uploads/markdown_image/1/image/d3c6b3fe1ca9c66501cb406ed6122b5f.jpg)
Fig. 2. (a) Frequency-field dispersion map (with dashed curves at HFM as a guide to the eye) measured by VNA-FMR by scanning over a frequency range of 0.1 GHz to 20 GHz with an applied OP field swept from -0.55 T to +0.55 T. (b) and (c) Zoom of the areas indicated by white squares in (a).

 Ferromagnetic resonance of skyrmions in thin film multilayers

Generation of spin-current and its transport across interfaces, as well as its interaction with magnetic moments, are the central themes of spintronic community to enable fast and efficient magnetization dynamics for data storage devices. There are two main mechanisms to produce the spin-current in non-magnetic materials: (a) spin Hall effect (SHE) in heavy metals such as Pt or Ta and (b) Rashba effect (RE) at the interfaces1. Irrespective of the origin, the spin-current exerts torques on adjacent ferromagnetic layer with two components: damping-like (DL) & field-like (FL)2. However, disentangling properly SHE from RE remains highly challenging. In this experimental study we identify the mechanisms of spin-transport in ultrathin magnetic multilayer whose thicknesses range from less to above the characteristic spin- decoherence length. To this aim, we quantify the different SOT contributions in series of samples Pt8|Cox|Al1.4|Pt3 and P8|Cox|Cu1.4|Pt3 (as a reference ) with x varying from 0.4 to 1.4 nm. We extract, in each case, a spin decoherence length to be around 1.1 nm. Surprisingly, SOT investigation in the Pt8|Cox|Al 1.4|Pt 3 reveals a dominating FL torque (HFL/HDL&gt;1), which is a signature of a strong Rashba interface in Al-based systems. As a comparison, we find that the Rashba interaction is small in Pt8|Cox|Cu1.4|Pt3 samples. Moreover, we determine the SOTs characteristics in Pt(x)/Co(0.9)/Al(5) by varying the Pt thickness (tPt). The bulk spin Hall angle of Pt(θSHE) and ratio of HFL and HDL as a function of tPt are shown in Figure 1(a) and (b). The increase in HFL/HDL in the range of Pt thickness where the bulk SHE of Pt started decreasing, strongly favors our argument of the presence of Rashba interface3, exhibiting thus the specific role of Al insertion layers to enhance spin-orbit effects. Financial support from the Agence Nationale de la Recherche, France, No. ANR-17-CE24-0025 (TOPSKY), the Horizon2020 Framework Programme of the European Commission under FET-Proactive Grant agreement No. 824123 (SKYTOP), FLAGERA SOGRaphMEM and the DARPA TEE programme through grant MIPR no. HR0011831554 are acknowledged

![](https://assets.underline.io/uploads/markdown_image/1/image/ae330d77631623209411e1c48a048ff1.jpg)

Figure 1(a) θSHE vs tPt in Ta(5)/Pt(x)/Co(0.9)/Al(5). (b) Ratio of HFL/HDL as a function of tPt.

Rashba Spin-Orbit Torque in Interface Engineered Ultrathin Metallic Multilayers

Magnetic skyrmions are localized magnetic textures in magnetic films, behaving as particles and topologically different from the uniform ferromagnetic state, which have been identified to be extremely promising for applications, as well as of fundamental interest [1]. The magnetism community has provided a great effort in the last years to stabilize them at room temperature, most often by designing magnetic and heavy-metal multilayers combining perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI) [2]. The DMI promotes a unique chirality of the skyrmionic spin textures and, combined with spin-orbit torques generated in the heavy-metal layer(s), allows efficient current-induced motion of skyrmions [3]. However, recent observations have revealed that multilayered skyrmions are prone to present a hybrid chirality, due to the competition between dipolar interaction and DMI, which can negatively influence their current-induced motion [4] and also their size and stability [6]. We will discuss how those effects can be reduce thanks to synthetic antiferromagnets (SAF) based systems that allow the stabilisation of smaller antiferromagnetic skyrmions, due to the cancellation of the long range dipolar effects [7]. We will mainly focus on Pt/Co/Ru and Pt/CoFeB/Ru based systems and present the optimization process that has been done on the thicknesses of the different layer in order to maximize the antiferromagnetic RKKY coupling without cancelling the perpendicular magnetic anisotropy, needed to stabilize skyrmions. Those optimizations enabled for example the observation at room temperature of spin spiral, predicted by micromagnetic simulations, by reaching an effective anisotropy close to zero. We will then describe how, combined to a bias layer structure, multi-repeats SAF can host antiferromagnetic skyrmions and present their observation by MFM techniques without needs to go under vacuum. Those observations will also be completed by NV center microscopy images. The ANR grant TOPSky TOPSKY (ANR-17-CE24-0025), the SESAME Ile de France IMAGeSPIN (EX039175), the DARPA TEE program grant (MIPR#HR0011831554) and EU grant SKYTOP (H2020 FET Proactive 824123) are acknowledged for their financial support.References: [1] A. Fert, N. Reyren, V. Cros, Nat. Rev. Mat. 2 (2017), 17031. [2] C. Moreau-Luchaire et al, Nat. Nanotech, 11 (2016), 444 ; S. Woo et al, Nat. Mater. 15 (2016), 501 ; A. Soumyanarayanan et al, Nat. Mater. 16 (2017), 898 ; A. Hrabec et al, Nat. Comm. 8 (2017), 15765. [3] K. Litzius et al, Nat. Phys. 13 (2017), 170 ; S. Woo et al, Nat. Comm. 8 (2017), 15573. [4] W. Legrand et al, Sci. Adv. 4 (2018), eaat0415 ; Y. Dovzhenko et al, Nat. Comm. 9 (2018), 2712. [5] F. Büttner et al, Sci. Rep., 8 (2018), 4464 ; A. Bernand-Mantel et al, SciPost Phys. 4 (2018), 027. [6] W. Legrand et al, Phys. Rev. Applied 10 (2018), 064042. [7] W. Legrand et al, Nat. Mater. 19 (2019), 34–42.

Room-temperature magnetic imaging of antiferromagnetic skyrmions in multi-repeats synthetic antiferromagnets

EOE: Spin-Orbitronics I

technical paper

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FOB: Spin Hall and Spin-Orbit Torque I

EOD: Skyrmions II

GOE: Magnetization Dynamics V

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**Session Chair:** Yue Li, *Argonne National Laboratory*

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CC: Spin Orbit Torques

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HC: Skyrmions: DMI and Dynamics

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GPC - Fundamental Spintronics II

I3: Skyrmion Imaging

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