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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].&lt;br/&gt;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.&lt;br/&gt;&lt;br/&gt;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.&lt;br/&gt;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&amp;lt;2GHz), medium (2&amp;lt;f&amp;lt;7GHz) and high frequencies (f&amp;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).&lt;br/&gt;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, &lt;i&gt;i.e.&lt;/i&gt; 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 &lt;i&gt;et al.&lt;/i&gt;, Nat. Rev. Mater. 2, 17031 (2017)&lt;br/&gt;[2] W. Legrand &lt;i&gt;et al.&lt;/i&gt;, Sci Adv 4, 7, (2018)&lt;br/&gt;[3] M. Garst &lt;i&gt;et al.&lt;/i&gt; J. Phys. D: Appl. Phys. 50, 293002 (2017)&lt;br/&gt;[4] J.-V. Kim, &lt;i&gt;et al.&lt;/i&gt;, Phys. Rev. B 90, 064410 (2014)&lt;br/&gt;[5] G. Finocchio &lt;i&gt;et al.&lt;/i&gt;, Appl. Phys. Lett. 107, 262401 (2015)&lt;br/&gt;[6] F. Garcia-Sanchez &lt;i&gt;et al.&lt;/i&gt;, New J. Phys. 18, 075011 (2016)&lt;br/&gt;[7] Onose &lt;i&gt;et al.&lt;/i&gt; Phys. Rev. Lett. 109, 037603 (2012)&lt;br/&gt;[8] S. A. Montoya &lt;i&gt;et al.&lt;/i&gt; 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).

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 Ferromagnetic resonance of skyrmions in thin film multilayers

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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).

technical paper

Magnetic skyrmions are nanoscale topological spin structures stabilized by chiral interactions and they are promising candidates for realizing brain-inspired computing devices [1,2]. One important prerequisite of such applications is the controlled formation of skyrmions. Skyrmions could form via one of two pathways - nucleation from uniform magnetization or evolution from magnetic stripes. The latter can be further divided into two distinct mechanisms – the reversible shrinking of a stripe into a skyrmion or the irreversible fission of a stripe into multiple skyrmions [3]. In this work, Ir/Fe/Co/Pt chiral multilayers were characterized with first-order reversal curve (FORC) magnetometry in conjunction with Lorentz transmission electron microscopy (LTEM) over the temperature range of 100 - 350 K. With both techniques, we observed a marked increase in stripe-to-skyrmion fission tendency with increasing temperature. FORC magnetometry consists of measuring a series of minor hysteresis loops (M(H,Hr)) and computing the quantity ρ (=-1/2 dM(H,Hr)/dHdHr) which represents the degree of irreversibility of a magnetic process [4,5]. The fission of stripes into skyrmions at intermediate fields and the annihilation of skyrmions at high fields are two processes that are revealed by FORC as ρ≠0 features [3]. The annihilation-fission separation (AFS, indicated by red arrows in Fig. 1e-h) could be used as a proxy of the favourability of the fission process. In Fig. 1i, one can observe the rise of AFS with temperature. LTEM microscopy captures the real-space evolution of magnetic textures as the field is swept. By tallying the stripe and skyrmion densities and tracking their field dependence, we estimate the average number of skyrmions generated by a stripe, η, using the ratio of the maximum skyrmion to stripe densities. As shown in Fig. 2, η increases 3-fold: from ~1 at 100K to ~3 at 350K. We interpret our results as the consequence of temperature-dependent magnetic interactions such as direct exchange, Dzyaloshinskii–Moriya interaction (DMI), and anisotropy. The relative strengths of these competing interactions will determine the energy barrier of the fission process. With theoretical modeling from geodesic nudged elastic band (GNEB) calculations [6], we found that the barrier height is greatly reduced with increasing temperature. These findings establish temperature as an important tuning parameter and provide insights into skyrmion formation, which is crucial to the realization of skyrmionic devices.

**References:**

1. Fert, A. et al. Nat. Rev. Mater. 2, natrevmats201731 (2017). 2. Soumyanarayanan, A. et al. Nat. Mater. 16, nmat4934 (2017). 3. Tan, A. K. C. et al. Phys. Rev. Mater. 4, 114419 (2020). 4. Pike, C. R. et al. J. Appl. Phys. 85, 6660 (1999). 5. Davies, J. E. et al. Phys. Rev. B 70, 224434 (2004). 6. Bessarab, P. F. et al. Comput. Phys. Commun. 196, 335–347 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/75d2d0e93437b24489d3975ae58dedb6.jpg)
Fig. 1: Temperature dependence of annihilation-fission separation (AFS). (a-d) Out-of-plane (OP) hysteresis loops of a multilayer sample from 100K to 350K. (e-h) Irreversibility ρ(H,Hr) derived from FORC magnetometry at the same temperatures. Hr, the reversal field, is the starting point of each minor loop. AFS are indicated by red arrows. (i) AFS plotted against temperature, showing a remarkable temperature dependence.

![](https://assets.underline.io/uploads/markdown_image/1/image/e3a535a7a6251b9e645ce19e5a74fc92.jpg)
Fig. 2: Texture density evolution imaged by LTEM. (a-d) Field evolution of stripe (St) and skyrmion (Sk) densities of a multilayer sample from 100 K to 350 K. While the stripe densities remained relatively constant, the skyrmion densities appreciated significantly with temperature. Accompanying LTEM images show the field evolution of stripes into skyrmions over selected fields. White dot lines enclose a typical magnetic domain for 100K and 300K. (e) η, estimated by ratio of maximum skyrmion to stripe densities, increases with temperature.

 Thermal Evolution of Magnetic Skyrmion Formation Mechanism in Chiral Multilayers

The Dzyaloshinskii-Moriya interaction (DMI) plays a key role in the formation and motion of chiral domain walls and magnetic skyrmions. Traditionally, DMI has been generalized to two forms - bulk-like DMI in single crystal chiral magnets lacking inversion symmetry, and interfacial DMI, formed as a result of inversion symmetry breaking at the interface of bilayer and multilayer systems, such as the extensively studied ferromagnet/heavy metal heterostructures. In these bi- and multilayer structures, it is widely believed that interfacial DMI is limited to asymmetric structures and will result solely in a Néel chirality, imposing challenges, such as a significant skyrmion Hall effect, for further development of spintronic devices. Here, we present our recent results in Co/Pd multilayers which challenge this understanding [1,2,3]. Systematic observations of domain structure and response to externally applied magnetic fields was performed using in-situ Lorentz transmission electron microscopy. For samples with a total magnetic thickness less than 6.7 nm, a pure Néel spin structure was observed [1]. However, in thicker samples, the competing demagnetization energy results in a mixed chiral Néel/achiral Bloch domain boundary. By comparing the observed Lorentz intensity to image simulations and micromagnetic modeling, key material parameters such as the exchange stiffness and domain mixing angle, found to be between 55 and 60 degrees, are measured and an interfacial DMI of nominally 1.0 mJ/m2 is extracted from a sample consisting of 10 x Co(0.7 nm)/Pd(0.5 nm) layers [2]. These results are agreement with values extracted from Kerr microscopy on lower repetition samples, indicating a saturation of DMI with increasing layer repetition. For a larger net magnetic thickness we observe a large asymmetry in the chirality of the Bloch component of these domain walls. For the largest thicknesses, only clockwise Bloch chiralities are observed, indicating a complete asymmetry. Further, as samples are relaxed from saturation with a magnetic field applied at an angle to the film normal, domain nucleation and expansion is characterized by propagation of the domain wall along the in-plane field component with the internal domain wall spin structure oriented along the magnetic field. These 360-degree domains are characterized by one clockwise and one counterclockwise Bloch domain wall. During the relaxation process, these domains may also expand via branching. This branching occurs predominantly through expansion of the clockwise wall, with little branching along the counterclockwise region. This is in disagreement with expected behavior, wherein branching from either side would be equally probable. We term this behavior chiral branching. We develop a model accounting for an interlayer contribution to the Dzyaloshinkii-Moriya interaction which, in combination with a large demagnetization field, can break the degeneracy between Bloch chiralities, showing qualitative agreement with a systematic investigation across a range of repetitions and layer thicknesses [3]. These results open a new avenue in which to modulate the internal domain wall spin texture and new means in which to control the skyrmion Hall angle, and add to recent results finding that interlayer DMI plays a key role in determining spin structure and dynamics in magnetic multilayers.

**References:**

[1] J. A. Garlow, et al., Phy. Rev. Lett 122, 237201 (2019). [2] S. D. Pollard, et al., Nat. Comm. 8, 14761 (2017). [3] S. D. Pollard, et al., Phys. Rev. Lett 125, 227203 (2020)

**Images:**

 Chirality control in ferromagnetic multilayers through intra- and interlayer DMI INVITED

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.

Recently, the Dzyaloshinskii-Moriya (DM) interaction, which emerges at the interface of ferromagnetic layer and non-magnetic layer with strong spin-orbit interaction, has attracted much attention in spintronics. To evaluate the strength of the DM interaction (the DM exchange constant), a number of approaches have been proposed. As many of the approaches make use of the dynamics of the magnetic system, for example, current- or field-induced motion of domain walls, propagation of spin waves, and current/field dependence of the magnetization reversal processes, there are difficulties in accurately extracting the DM exchange constant. In this study, we present that the DM exchange constant can be simply extracted from a magnetic domain image using machine learning[1]. Magnetic domain structure is determined by minimization of magnetic energy of the system, which typically includes magneto-static, magneto-elastic, anisotropy, Heisenberg exchange, and DM exchange energies. The pattern of the magnetic domain structure, therefore, includes information of the DM exchange constant. A convolutional neural network is used to characterize the magnetic domain pattern with high sensitivity. To train the neural network, a large number of images with different patterns that derive from a magnetic system with fixed material parameters are required. As such image acquisition using existing experimental setup is typically cumbersome, here we use micromagnetic simulations to generate the images for supervised learning. We use the trained system to estimate the DM exchange constant from experimentally obtained magnetic domain images in Fig. 1. The training data set is generated using a homemade micromagnetic simulation code. We first generate training images where parameters other than the DM exchange constant are fixed. The DM exchange constant (D) is varied from 0 to 1.00 mJ/m2. The initial condition and the pattern of magnetic-anisotropy distribution are varied to generate 100,000 images of the equilibrium magnetic state for a given parameter set with various values of D. Exemplary images of the equilibrium magnetic state with different D are shown in Fig. 2(a). Model validation is performed with 10,000 testing images with different values of D created using the same code. D^set corresponds to D used in the simulations to generate the testing images. The testing images are studied by the trained system: the estimated D returned from the system is denoted as D^est. The relation of D^set vs. D^est is shown in Fig. 2(b). When D^set is larger than ~0.05 mJ/m2, we find a linear relation between D^set vs. D^est with a root mean square error of ~0.046 mJ/m2. We next use the trained system to estimate D from experimentally obtained magnetic domain images. The film stacking of the samples used is: Si sub./Ta (d)/Pt (2.6 nm)/Co (0.9 nm)/MgO (2 nm)/Ta (1 nm). The thickness of the Ta seed layer (d) is varied to change D of the films via modification of the (111) texture of the Pt layer. The DM exchange constant is estimated using magnetic field induced switching of magnetization[2]. A Hall bar is patterned from the films using conventional optical lithography. We use the Hall voltage to probe the magnetization via the anomalous Hall effect. The magnetic domain images of the films are acquired using a magnetic microscope equipped with a magnetic tunnel junction sensor. The value of D the trained system returned for each image is plotted against d in Fig. 2(c). Interestingly the d dependence of the estimated D is consistent with that of the experiments (red circles in Fig. 2(c)). Note that the magnitude of K_eff does not significantly influence estimation of D. In summary, we have demonstrated that machine learning can be applied to extract the DM exchange constant (D) from a single magnetic domain image. The accuracy of the supervised learning in estimating D is found to be ~0.05 mJ/m2, which is significantly better than conventional experimental approaches. This approach can be extended to estimate all relevant material parameters at once from a single magnetic domain image, which will significantly simplify materials research for magnetic memory and storage technologies. Acknowledgements: This work was partly supported by JSPS Grant-in-Aid and the Center of Spintronics Research Network of Japan.

**References:**

[1] M. Kawaguchi, K. Tanabe, K. Yamada et al., npj Computational Material, in press. [2] S. Kim, P.-H. Jang, D.-H. Kim et al., Phys. Rev. B., Vol. 95, p.220402(R) (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f4f5a41d04f3e6f96c2b7dba22465bdf.jpg)
Concept of the study. Micromagnetic simulations are used to generate thousands of training images. There are five relevant material parameters: M_s, K_eff, A_ex, D, and σ. Here we vary D and σ in the simulations so that the system can learn domain patterns with different D and σ. After the supervised training, we feed the system with an experimentally obtained image of magnetic domains to extract D and σ. Images taken from Ref. [1].

![](https://assets.underline.io/uploads/markdown_image/1/image/e554449d0724b35eb4ec0e3a28fd1436.jpg)
D obtained from pattern recognition and machine learning. (a) Typical magnetic domain images calculated using micromagnetic simulations. Dark and bright contrast represents the magnetization direction along the film normal. The DM exchange constant is varied from 0 to 0.90 mJ/m2: the corresponding value is indicated at the bottom right corner of each image. (b) The DM exchange constant (D^est) estimated from the testing images are plotted as a function of D set in the simulations (D^set). (c) DM exchange constant (D) estimated from the measured domain images using the trained system. Two different values of K_eff are used in the simulations to generate the training images: the estimated values obtained from the two trained systems are denoted using open and solid squares. Images taken from Ref. [1].

 Determination of the Dzyaloshinskii-Moriya interaction from a single magnetic domain image using machine learning

Magnetic multilayer films are known to host a variety of novel magnetic configurations such as topological magnetic skyrmions with potential nano-electronic applications. However, characterizing these material systems at film and device-level typically involves a combination of several magnetometry, microscopy, and spectroscopy experiments. Some of these techniques can be time-consuming and expensive, or even inaccessible to materials scientists. Therefore, to rapidly characterize these material systems, it is crucial to maximize the information extracted from results of experiments that are more accessible, such as domain images obtained from magnetic force microscopy (MFM). We show that deep convolutional neural networks are able to extract magnetic parameters, in particular the exchange interaction (A), Dzyaloshinskii-Moriya interaction (D), effective anisotropy (Keff), and the thermodynamic stability (κ), from images of domain configurations. Experimentally realistic training and validation input images, as shown in Fig. 1, were generated through micromagnetic simulations with MuMax3 [1]. The magnetic parameters and structures used in the simulations are based on Ir/Fe/Co/Pt multilayers with tunable magnetic properties [2, 3]. The neural network architecture, implemented with the Keras package [3], consists of multiple convolutional layers followed by a fully connected network with 4 outputs corresponding to the magnetic parameters of interest. The trained models were consistently able to reach R2 values greater than 0.9 on validation data, as shown in Fig. 2. By inspecting the intermediate feature maps of the neural network, we find that the network is able to learn features such as domain boundaries. Notably, testing the models on experimentally obtained MFM images yield magnetic parameters that were consistent with our knowledge of the material systems. Our work thus demonstrates the utility of developing machine models trained on simulation data as a means to accelerate the characterization of magnetic systems.

**References:**

[1] A. Vansteenkiste, J. Leliaert, M. Dvornik et al, AIP Advances 4, 107133 (2014). [2] A. Soumyanarayanan, M. Raju, A. L. Gonzalez Oyarce et al., Natural Materials 16, 898-904 (2017). [3] A. K. C. Tan, J. Lourembam, X. Chen et al., Phys. Rev. Materials 4, 114419 (2020). [4] F. Chollet et al., https://keras.io (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fb4ee2b3d9e20e768e23cfca8d572833.jpg)
Representative micromagnetic images used as input for the training and validation of neural networks.

![](https://assets.underline.io/uploads/markdown_image/1/image/f46694e5bfcc6346ff1b6bf794d5f03e.jpg)
Parity plots showing the predicted micromagnetic magnetic parameters (exchange stiffness A, Dzyaloshinskii-Moriya interaction D, effective anisotropy Keff, and thermodynamic stability κ) vs the actual parameters on the validation data.

 Estimation of Magnetic Parameters from Domain Images with Convolutional Neural Networks in Chiral Multilayers

While for many years magnetic domain walls (DWs) were considered to be Bloch type in ultra-thin magnetic layers with perpendicular anisotropy and particularly in stacks lacking inversion symmetry, the observation of the Dzyaloshinskii Morya interaction (DMI) in these stacks combined with the use of advanced imaging techniques have shown that these DWs were in fact of the Neel type and that they also had a precise chirality. These discoveries have led to significant advances in understanding the mechanisms governing the current induced motion of these DWs and to the reinterpretation of many past experimental results. These discoveries and reinterpretation have also allowed the demonstration of skyrmionic bubbles (Sk) and the development of their current induced dynamics. By analogy with DMI, which is a chirality dependent energy, we have demonstrated the existence of a chirality dependent dissipation: the chiral damping (αC) 1,2. As their chirality is altered, the induced variations of the damping parameter modify the DWs and Sk dynamics. Nevertheless, as this phenomenon shares with DMI the same origins, spin-orbit interaction and symmetry breaking, and as their effects and consequences are often confused, the influence of chiral damping on the dynamics of Sk and chiral DW has remained elusive so far, even though the understanding of this influence is crucial both for the understanding of chiral phenomena in the field of magnetism but also with the aim of developing innovative memory, logic or neuromorphic devices based on these chiral magnetic objects. In this study, we clearly separate the effects of DMI and αC in Sk and DW dynamics and, by focusing on the flow regime, which is both simpler to unambiguously interpret the experimental results and more relevant for the application objectives, we show that the effects of chiral dissipation are ubiquitous: they occur in all possible types of DW and SK motion: i) field-driven DW motion, ii) current induced DW motion, iii) current induced dynamics of skyrmionic bubbles. For each of these experiments, the observed asymmetries cannot be explained by considering either only DMI or only αC. A simple numerical modelling including these two mechanisms and using a single set of parameters makes it possible to reproduce the relevant features of these experimental results (Figure). Finally, these numerical simulations allow us to show the importance of αC for the stability and dynamics of skyrmionic bubbles in the regime of high spin-orbit torques and strong DMI sought for the applications: when they are distorted under the action of an electric current, αC can increase or decrease these distortions. These results show the importance of the chiral damping in the dynamics and stability of DW and Sk and the need to understand and control it in the objectives of applications using these chiral magnetic objects.

**References:**

1. Jué, E. et al., Nat. Materials, 15, 272–277 (2016). 2. Akosa, C. A., Miron, I. M., Gaudin, G. & Manchon, A. Phys. Rev. B, 93, 1–5 (2016).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/344f02225ea9513667ef104df38bf7ea.jpg)
a. Measured DW velocity vs. Hip (red for down/up DW, blue for up/down DW) at constant HZ= -82 mT. b. When only DMI is considered, numerical simulations cannot reproduce the crossing of curves: the up-down DW velocity is always higher than that of down-up DW for positive in-plane fields. c. When DMI and αC are taken into account, experimental results are well reproduced by numerical simulations.

 Effect of Chiral Damping on the dynamics of chiral domain walls and skyrmions INVITED

Recently, an ever-growing interest of the community of solid-state physics has been captured by the promising potentials of the magnetic skyrmions [1]. The skyrmion chiral property is generally driven by an additional anti-symmetric term in the exchange energy, namely the Dzyaloshinskii-Moriya interaction (DMI), induced by the lack of structural inversion symmetry and the spin-orbit coupling. As they have a high stability, small size and they can be moved by very small currents densities, skyrmions are considered as the ultimate magnetic storage bit for a new generation of devices of ultra-dense information storage and low power consuming spintronic logic and neuromorphic computing devices [2]. One of the major advantages of using interfacial DMI in thin films is that several materials parameters, that define not only the existence of skyrmions but also their dimensions, can be experimentally tuned, such as the magnetic anisotropy, or the DMI strength, which can be efficiently tailored. Here, we show a novel method to control interfacial effect in thin films with DMI using He irradiation. We compare SQUID, Ferromagnetic resonance (FMR), Magnetic force microscopy (MFM) as well as Brillouin light scattering (BLS) results on Ta(4.7 nm)/[Pt(4nm)/Co(1.4nm)/Ta(1.9nm)]20 stacks as a function of He irradiation dose to study the behaviour of the magnetic properties and interfacial effect of the stacks, such as magnetic anisotropy, intrinsic damping, effective magnetization, exchange stiffness as well as DMI. Our results show clear evidence of i) tailoring interface ii) different magnetic properties in thin film with different irridiation dose. These results can open novel way to manipulate skyrmions, as well as control of interface of spin-orbit torque devices and spin injection into a thin film, for example using spin pumping. Figure 1 (a) shows typical magnetization measurements while sweeping the external magnetic field in the direction perpendicular (out-of-plane) and parallel (in-plane) to the substrate at room temperature. Figure 1 (b) shows anisotropy energy density K and anisotropy field Hk with different Helium irridiation dose IR. As IR is increased further, a significant IR dependent diminishment of K and Hk occurs that is explained by the tailoring interface of the samples via IR. Figure 2 (a) show typical two-dimensional color plots of microwave absorption as a function of microwave frequency f and perpendicular magnetic field B. We determined the effective magnetization Meff from out-of-plane fits of the resonance Hres as different frequency using frait equation [3]. We show that Meff decrease with increasing IR (Fig. 2 (c)). The linear dependence of FMR linewidth ΔH on frequency f (Fig. 2(b)) allows the computation of the Gilbert-type damping constant α [4]. We see the clear enhancement of α with IR (Fig. 2(d)), suggesting of high rates of spin injection in the non-magnetic layers by spin pumping. Funding from the EMPIR project TOPS “Metrology for topological spin structures” (#17FUN08)) is acknowledged.

**References:**

[1] A. Fert et al. Nat. Nanotech. 8, 152 (2013)] [2] J. Grollier et al. Nat. Electronics, 3, 360–370(2020)) [3] S Klingler et al. J. Phys. D: Appl. Phys. 48 015001 (2015) [4] J.-C. Rojas-Sanchez, M. Cubukcu et al. Phys. Rev. B. 88, 064403 (2013)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f89f26dd8da5338caf4117406cbcea1c.jpg)
Figure 1. SQUID measurements. (a) Normalized magnetization M/Ms versus applied magnetic field B plots for out-of-plane and in-plane configurations for sample with He irridation dose IR=8.1014 cm-2. (b) Anisotropy energy density K and anisotropy field Hk plots as a function of He irridation dose IR.

![](https://assets.underline.io/uploads/markdown_image/1/image/b4ac438e8762f4a8c4d6fb0e3d228d84.jpg)
Figure 2. FMR measurements. (a) Two-dimensional colour plots of microwave absorption as a function of microwave frequency f and magnetic field B for the out-of-plane configuration for sample with IR=8.1014 cm-2. We can clearly identify two modes; n=0 FMR uniform mode and n=1 spin wave mode. The solid line is fit to used to deduce the Meff. (b) FMR linewidth ΔH as a function of frequency f for the out-of-plane configuration for sample with IR=8.1014 cm-2. The solid line is fit to used to deduce the Gilbert damping constant α. Meff (c) and damping α (d) as a function of IR.

 Tailoring interfacial effect in thin films with DMI by He irradiation

Chiral magnets hosting non-collinear spin textures such as skyrmion lattices (SkL) [1] provide novel functionality in magnonics because of the formation of bandgaps in the magnon band structure and asymmetric magnon dispersion relations [2]. Multiple SkL phases were observed in the bulk chiral magnet Cu2OSeO3, e.g. high temperature SkL near TC, low temperature SkLs when the magnetic field was applied along an easy axis and meta-stable SkL when Cu2OSeO3 was quenched by fast cooling down [3-5]. Their dynamic modes are hard to be discriminated in large bulk samples because they coexist with conical and helical phases. Conventionally detected spin excitations (magnons) show complex spectra with a multitude of resonances due to multiple domains of different phases and boundary conditions. It is challenging to understand the one-to-one correspondence between an individual SkL phase and its magnon spectra. Here we report the local spectroscopy of magnons by scanning Brillouin light scattering (BLS) microscopy on Cu2OSeO3 in SkL phases. Thanks to the high sensitivity of BLS, we resolved the dynamic behavior of all reported SkL phases. Clockwise, counterclockwise and breathing modes of hexagonal SkL were detected by BLS proving simultaneous thermal excitation of all three modes which exhibit different polarization characteristics. Using the magnon modes, we were able to locate SkL phases and investigate the stabilization mechanism of non-collinear multi-domains. Our observations of locally excited thermal magnons in Cu2OSeO3 deepen the understanding of the SkL dynamics in chiral magnet. They pave the way for further design of magnonic devices based on chiral magnets. We acknowledge the finical support from Swiss National Science Foundation (SNSF) via Sinergia Network NanoSkyrmionics CRSII5 171003.

**References:**

[1] S. Mühlbauer, B. Binz and F. Jonietz, etc. Science, 323, 915 (2009). [2] M. Garst, J. Waizner and D. Grundler, J. Phys. D. Appl. Phys., 50, 293002 (2017). [3] A. Chacon, L. Heinen, M. Halder, etc. Nat. Phys. 14, 936-941 (2018). [4] F. Qian, L.J. Bannenberg, H. Wilhelm, etc. Sci. Adv. 4, eaat7323 (2018). [5] R. Takagi, Y. Yamasaki, T. Yokouchi, etc. Nat. Commun., 11, 5685 (2020).

**Images:**

 Spin Dynamics of Skyrmion Lattices in a Chiral Magnet Resolved by Micro-Focus Brillouin Light Scattering



The use of spin waves (SWs) as data carriers in spintronic and magnonic logic devices offers operation at low power consumption, free of Joule heating. Nevertheless, the controlled emission and propagation of SWs in magnetic materials remains a significant challenge. Here, we propose that skyrmion–antiskyrmion bilayers form topological charge dipoles and act as efficient sub-100 nm SW emitters when excited by in-plane ac magnetic fields. The propagating SWs have a preferred radiation direction, with clear dipole signatures in their radiation pattern, suggesting that the bilayer forms a SW antenna. Bilayers with the same topological charge radiate SWs with spiral and antispiral spatial profiles, enlarging the class of SW patterns. We demonstrate that the characteristics of the emitted SWs are linked to the topology of the source, allowing for full control of the SW features, including their amplitude, preferred direction of propagation, and wavelength.

**References:**

[1] S. A. Diaz, T. Hirosawa, D. Loss, and C. Psaroudaki, Nano Letters 20, 6556 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/227a77e02f052fbbadd7732d22309280.jpg)
Skyrmion-antiskyrmion bilayers form topological charge dipoles and act as efficient sub-100 nm spin wave emitters when excited by in-plane ac magnetic fields.



 Spin Wave Radiation by a Topological Charge Dipole

Magnetic skyrmions are magnetic quasi-particles with a number of interesting properties for possible future applications in, memory storage devices, or non-conventional computing [1-7]. We have shown that in low energetic landscapes of thin film magnetic multilayers, skyrmions show Brownian-like diffusion [7], which can be influenced by magnetic fields, temperature, and the magnetic properties of the pinning site [8,9]. While the diffusive dynamics have experimentally been studied in the continuous film [7,8,10], the device application requires a fabrication process in general, which means that skyrmions move rather in confined geometry. Here we show that the diffusive dynamics of skyrmions can be significantly modified for the geometry of the confined system and the skyrmion density. It is experimentally shown that the critical factor to unravel the underlying physics is the commensurability effect which is corroborated with Molecular dynamics simulations, as well as the pinning effect. The combination of experiment and analysis enables us to reveal the intriguing behavior that pinning sites for magnetic skyrmion depends on the magnetic field strength of the order of μT. Our findings could pave the way to control the thermal dynamics of skyrmions and the pinning effect to realize novel skyrmionic device applications. Stable skyrmions are nucleated by applying a magnetic out-of-plane (OOP) field while pulsing once an in-plane field [10]. We study the skyrmion diffusion in confined geometries varying both the symmetry of the geometry as well as the number of skyrmions from a sparse population to a fully lattice-like situation [11]. Basic geometries like triangles and circles are used. By measuring the mean squared displacement (MSD) of the trajectories of the skyrmions in the structures, the diffusion coefficient is calculated. Figure 1 shows the thermal behavior of skyrmions as a function of the skyrmion density in triangular geometry [11]. As can be seen in Fig. 1(a), The number of skyrmions can be precisely controlled by varying the OOP field to allow us to investigate the skyrmion density dependence of the skyrmion diffusion in confined geometries. Figure 1(b) presents the time-averaged configurations over 9600 Kerr images, where some configurations exhibit blur skyrmions which move with arbitrary time scale. It is shown that the diffusion qualitatively depends on the commensurability of the skyrmion number. Also, we find that the states for skyrmion numbers of 1, 3, 6, and 10 commensurate with the geometry and lead to a saturation of the MSDs as a function of time. The MSDs for an incommensurate state exhibit a non-monotonic relation and do not saturate over the experimental timescale. As shown in Fig. 1(c), molecular simulations agree qualitatively with the experimental findings that corroborating the basic dependence of skyrmion numbers on the motion in triangular confinement [11]. The quantitative difference from the simulation could be related to the pinning effect on the magnetic skyrmion. To explore the behavior closely, we investigate the magnetic field dependence of the skyrmion diffusion under a simplified environment. Figure 2 shows the OOP magnetic field dependence of histograms of skyrmion center positions in the circular geometry. For eliminating the commensurability effect, and the symmetry breaking of magnetic potential, we nucleate a single skyrmion in a circular geometry. We can see not only the modification of the depth of the pinning potential but also the pinning site transition with a small magnetic field of the order of μT, where the size of the skyrmion is modified. More intriguingly, the behavior shows hysteresis to a magnetic field, on the other hand, the reproducibility confirmed after applying a large magnetic field of 8 T suggests that the pinning sites themselves are not linked with the magnetic origin of pinned spins. Thus, the possible origin could arise from the topological spin texture itself. In conclusion, we reveal that the skyrmion diffusion is governed by the commensurability in confined geometry, as well as the magnetic field-dependent skyrmion pinning. The results show that for any potential skyrmionic device based on thin magnetic layers the numbers of skyrmions in the structured geometry as well as the geometry itself influence not only the arrangement but also the thermal diffusive motion of the skyrmions. Also, the pinning effect remains significant however, our findings indicate that magnetic skyrmions could be a new useful tool for experimentally exploring the pinning effect, which is a critical factor for any magnetic objects, and the possibility that the pinning sites are able to be tailored even after film deposition and fabrication process.

**References:**

[1] A. Fert et al., Nat. Nanotechnol.8, 152 (2013). [2] X. Zhang et al., Sci. Rep. 5, 7643 (2015). [3] X. Zhang et al., Sci. Rep. 5, 9400 (2015). [4] F. Garcia-Sanchez et al., New J. Phys. 18, 075011 (2016). [5] S. Zhang et al., New J. Phys. 17, 023061 (2015). [6] D. Prychynenko et al., Phys. Rev. Appl. 9, 014034 (2018). [7] J. Zázvorka et al., Nat. Nanotechnol. 14, 658 (2019). [8] T. Nozaki et al., Appl. Phys. Lett. 114, 012402 (2019). [9] N. Kerber et al., preprint arXiv:2004.07976 (2020). [10] J. Zázvorka et al., Adv. Funct. Mater. 30, 2004037 (2020). [11] C. Song et al., preprint arXiv:2009.03995 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3767ae61748fcafeb8f7fd6ebb2d7005.jpg)
Fig. 1 Thermal behavior of skyrmions as a function of the skyrmion density in triangular geometry. (a) The initial state of the skyrmion configurations. (b) The time-averaged configurations over 9600 Kerr images. (c) Simulations of the histograms of skyrmion center positions for configurations of 1 to 10 skyrmions inside the triangle containing positions from 1 million independent frames.

![](https://assets.underline.io/uploads/markdown_image/1/image/4f7ce9fe1971db64496cd0232ff4f441.jpg)
Fig. 2 The OOP magnetic field dependence of histograms of skyrmion center positions at 341.5 K in the circular geometry, where we plot and integrate the position where skyrmion exists at each frame in a 60 minutes video (57600 frames) on a two-dimensional map. A brighter contrast means that the skyrmion dwell time is longer at these points corresponding to an energy minimum.

Ferromagnetic resonance of skyrmions in thin film multilayers

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