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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.&lt;br/&gt;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.&lt;br/&gt;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.&lt;br/&gt;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.&lt;br/&gt;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.&lt;br/&gt;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.&lt;br/&gt;[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].

INTERMAG 2021

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

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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].

technical paper

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

**References:**

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

**Images:**

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

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

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

Topological magnetic textures such as skyrmions have been extensively studied during the last decade due to their potential application in spintronics devices. In ultrathin films systems, a key parameter to stabilize chiral topological magnetic textures is the Dzyaloshinskii-Moriya interaction (DMI), obtained at the interfaces between ferromagnetic layers and heavy-metals, promoting a unique chirality of the magnetic texture. We focus on an ultrathin epitaxial Au1-xPtx/Co(0.6-0.8nm)/W(110) trilayer, a model system exhibiting perpendicular magnetic anisotropy (PMA) and interface DMI. The epitaxial growth of Co (0001) on W(110) gives rise to a C2v crystal symmetry at the Co/W(110) interface. This symmetry results into a biaxial magnetic anisotropy, with an in-plane easy axis along the W[1-10] direction, and into an anisotropic DMI [1]. In this work, we have used Brillouin light spectroscopy to show the effect of the Pt-to-Au composition on the PMA and DMI of the trilayer. The balance between the different magnetic interactions, give rise to the stabilization in circular nanodots of different magnetic textures such as elliptical skyrmions [2] or magnetic merons [3], which have been observed with X-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM). In this presentation, we will focus on the stabilization of magnetic merons which are radial chiral textures with a topological charge Q=1/2 and topologically equivalent to a circular vortex. We will discuss the stabilization of magnetic merons, and how the topological charge can be switched under the application of an external perpendicular magnetic field as shown with XMCD-PEEM (Figure 1)

**References:**

[1] Camosi, L., et al., Physical Review B, 95(21), 214422. 2017 [2] Camosi, L., Pena Garcia, J. New Journal of Physics, 2021 (accepted) [3] Pena Garcia, J., Camosi, L., et al. (in preparation)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ca98e5ee529cefca6bfaac57ca3bf918.jpg)
Magnetic merons stabilized in a circular nanodot observed with XMCD-PEEM when the x-rays are along the W [1-10]. Under a perpendicular magnetic field, the topological charge has switched from Q=+1/2 to Q=-1/2.

 Stabilization and switching of magnetic merons in AuPt/Co/W(110) epitaxial thin films

Two-dimensional (2D) van der Waals (vdW) materials are a family of quantum materials that have attracted great research attention in the past decade as they possess a diverse range of novel phenomena which are promising for technological applications. Among these materials, Fe3GeTe2 (FGT) is only ferromagnetic metal, exhibiting a strong out-of-plane uniaxial magnetic anisotropy down to atomic-layer thicknesses, [1-4] which is very critical for spintronic applications, typically, magnetic-tunneling-junctions and magnetic random-access-memory devices. In this talk, we will show that a Bloch-type magnetic skyrmion bubble can indeed be realized in the single crystals of 2D vdW FGT. A high-density hexagonally-packed lattice of skyrmion bubbles emerges by a simple field-cooling process and keeps stable after turning off the magnetic field.[5] Besides, we will show that the density of field free skyrmion lattice was tuned by changing the value of the cooling magnetic field. The highest-density skyrmion bubble was obtained when the field was applied at H = 500 Oe. As the value of the magnetic field is increasing, the size of the skyrmion is increasing but the density of skyrmion is decreasing. When the field is higher than 800 Oe, only stripe domain is observed. Finally, we will show the results from the miromagnetic simulations. We found that total energy of the skyrmion lattice is higher than than energy of the stripe domain, which indicates that the field free skyrmions is metastable state compared with ferromagnetic state. We believe the results presented in this talk could be useful for understanding the topological spin textures physics in 2D vdW materials.

**References:**

[1] Y. Deng, Y. Yu, Y. Song, et al, Nature 563, 94 (2018). [2] Z. Fei, B. Huang, P. Malinowski, et al, Nat. Mater. 17, 778 (2018). [3] D. R. Klein, D. MacNeill, J. L. Lado, et al, Science 360, 1218 (2018). [4] V. Y. Verchenko, A. A. Tsirlin, A. V. Sobolev, et al, lnorg. Chem. 54, 8598 (2015). [5] B. Ding, Z. Li, G. Xu, et al, Nano Lett. 20, 868 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c9573c8423b4b6943c8bb7c702dc1bce.jpg)
Figure 1 L-TEM images demonstrating the skyrmion generation and sustainability via fielding cooling manipulation in Fe3GeTe2. L-TEM images acquired at 93K after a magnetic field cooling at (a) 100 Oe, (b) 500 Oe, (c) 700 Oe, and (d) 800 Oe. The corresponding simulation of the field free skyrmion lattice is obtained at (e) 100 Oe, (f) 500 Oe, (g) 800 Oe. (g) The cooling field dependence of the energy terms in the simulations.

 Observation of Magnetic Skyrmion Bubbles in a van der Waals Ferromagnet Fe3GeTe2

The lamellar morphology of chiral spin textures is analogous to liquid crystals and biological systems. Similar to cholesteric liquid crystals, chiral magnets possess a periodic layered structure and form a wide variety of non-trivial topological defects[1,2]. Using magnetic force microscopy (MFM), we resolve 1D and 2D topological defects in the near-room temperature helimagnet FeGe, including disclinations and dislocations with nonzero topological winding number, as well as three fundamental types of helimagnetic domain walls. Interestingly, in addition to their non-trivial structure, all topological defects in FeGe exhibit a pronounced non-linear magnetic response in MFM, which is not observed in regions with perfect lamellar-like order. This magnetic signature is reminiscent of the so-called “lines of flare” in cholesteric liquid crystals, suggesting local variations in magnetic susceptibility. We investigate the origin of the magnetic signature of the topological defects and discuss the possibilities to utilize the anomalous local response as read-out signal in spintronics devices.

**References:**

1. A. Dussaux, P. Schoenherr, K. Koumpouras, J. Chico, K. Chang, L. Lorenzelli, N. Kanazawa, Y. Tokura, M. Garst, A. Bergman, C. L. Degen, and D. Meier, Nature Communications, Vol. 7, p.12430 (2016). 2. P. Schoenherr, J. Müller, L. Köhler, A. Rosch, N. Kanazawa, Y. Tokura, M. Garst, and D. Meier, Nature Physics, Vol. 14, p.465 (2018).

**Images:**

 Non-linear Magnetic Response at Topological Defects in Helimagnetic FeGe

Skyrmions are chiral spin textures, which have gained considerable interest due to their promising applications in memory and synaptic devices [1]. These textures can exist in a low-density state or in a high-density state [2]. A high density skyrmion state is more favourable for high-density memory devices. However, formation of the high density state requires a subtle balance of magnetic properties . One of the key requirements needed for the high density state is a relatively high value of Dzyaloshinskii Moriya interaction (DMI) as compared to the effective magnetic anisotropy (Keff) and exchange coupling energy (Aex) [3]. DMI is an anti-symmetric exchange interaction induced by spin-orbit coupling in the presence of broken inversion symmetry [4]. In a specific thin material system, DMI can be tuned by either changing the thickness of ferromagnet or by varying its stoichiometry. Former has been reported for materials like Pt/Co/AlOx, Pt/CoFeB/AlOx, and Ta/FeCoB/TaOx [5, 6]. In these studies, decreasing the thickness of ferromagnet results in a higher DMI. However, a decrease in thickness also results in an enhanced value of Keff, which limits the skyrmion density to a certain number. In the latter report, which was carried out on Ir/Fe/Co/Pt structures, the thickness and composition of the ferromagnetic layers was varied to modulate skyrmion size and density [7]. However the used material system, because of polycrystalline nature of FM resulting in grains, is inadequate for an unhindered skyrmion motion. Here, we report a reduction of effective anisotropy energy density Keff ,by using post growth 20 keV He+ ions induced interface intermixing, without compromising DMI. We have used Pt/CoFeB/MgO stacks to study the effect of varying ion irradiation dose and carried out Monte Carlo simulations to get the probability of the ions’ distributions and the intermixing in the sample [8]. The displacement of ferromagnetic layer atoms increases linearly with increasing dose (inset of Fig. 1a). To study the effect of such intermixing on magnetic properties, we have used a vibrating sample magnetometer. We have found that Keff is reduced as atomic intermixing at interfaces between the ferromagnetic and non magnetic layers increase, which corroborates the behaviour of Keff from previous reports [9]. Interestingly, even at high dose, Keff still remained positive, indicating an out-of-plane magnetization. (Fig. 1a). Moreover, we have observed an increase in the saturation magnetisation (Ms) (fig 2a), due to increased polarization of the ferromagnetic component . The increase in polarization is caused by formation of CoPt alloy at the Co-Pt interface, which results in the increase of the spin moment at interface up to ~17% [10]. Furthermore, we speculate the increase in magnetisation also includes contribution from the migration of B atoms at interstitial sites between Co and Fe atoms. Besides, we have measured the interfacial Dzyaloshinskii-Moriya interaction (DMI) by the Brillouin light scattering spectroscopy . We have noticed an increase in the DMI values of the irradiated samples. Considering a possibility of change in the effective thickness of FM, we have calculated surface Ms and hence, interface DMI (Fig. 2a inset and 1c). We find that the interface DMI increases under intermixing. Moreover, we have used micromagnetic simulations to estimate the exchange coupling energy (Aex) by assessing the periodicity of equilibrium state achieved at zero field (Fig. 1d). Noticeably, both DMI (interface DMI) and Aex follows a similar trend as Ms. To probe the change in magnetization dynamics due to the modification of the magnetic properties, we have carried out magnetic force microscopy (MFM) as shown in Fig. 2a and 2b. We notice the zero-field periodicity of labyrinthine textures is reduced by ~50 nm, depicting a higher density of striped domains after processing the sample (Fig. 2c). The skyrmion density is increased up to six folds as compared to the pristine sample (Fig. 2d). We speculate that the increase in skyrmion density and reduction in periodicity is due to the reduction of domain wall energy. Furthermore, we have also measured the skyrmion size and we observe a reduction by ~50 nm, down to 75 nm for large intermixing (Fig. 2d). Besides, we have carried out a comparatively low energy treatment (annealing) of deposited stack to explain the physical phenomena of skyrmion density enhancement. Our study demonstrates that post growth He+ irradiation can achieve a high density skyrmion state, which is promising for memory, logic and neuromorphic applications.

**References:**

[1] A.Fert, N. Reyren, and V. Cros, Nature Review Materials., Vol. 2, p.1 (2017) [2] X. Yu, Y. Onose, and N. Kanazawa, Nature., Vol. 465, p.901 (2010) [3] A. Bogdanov and A. Hubert, Journal of magnetism and magnetic materials,. Vol. 138, p.255 (1994) [4] A. Fert, Materials Science Forum (Trans Tech Publ), p.439 (1990) [5] J. Cho, Nam-Hui Kim, and Sukmock Lee, Nature communications,, Vol. 6, p.1 (2015) [6] T. Srivastava, W. Lim and I. Joumard, Physical Review B., Vol 100, p.220401 (2019) [7] A. Soumyanarayanan M Raju and AL Gonzalez Oyarce, Nature materials., Vol. 16, p.898 (2017) [8] M. Bonder, N. Telling and P. Grundy, Journal of Applied Physics., Vol. 93, p.7226 (2003) [9] M. S. El Hadri, M. Hehn and G. Malinowski, Journal of Physics D: Applied Physics., Vol. 51, p.215004 (2018) [10] B. Zimmermann, W. Legrand and D. Maccariello, Applied Physics Letters., Vol. 113, p.232403 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0cf69cced73dbfa4a69615ab43d5deef.jpg)
Fig.1 Effect of He+ irradiation induced interface intermixing on magnetic properties of CoFeB. Variation in (a) Keffective, (b) Saturation Magnetization (Ms), (c) Interface DMI (DMIint) and (d) Exchange coupling (Aex) energy due to varying dose of He ions. Inset of (a) shows a linear relation of atoms intermixing and varying dose. Inset of (b) shows varying surface magnetization due to the irradiation dose. The trend of Ms influences the DMIint and Aex.

![](https://assets.underline.io/uploads/markdown_image/1/image/3b447b4953a37f1cdbe4f095cd4514c9.jpg)
Fig.2 Effect of interface intermixing on magnetization dynamics of CoFeB. (a) and (b) MFM images depicting change in skyrmion density (top image) and size (bottom image) due to the interface intermixing. (c) Periodicity of magnetic textures as function of irradiated dose. Inset shows 2D FFT of pristine sample, used to calculate the periodicity. (d) Variation of skyrmion density (up to six folds) and reduction of skyrmion size (up to ~50 nm) due to varying dose.

 Enhancement of Skyrmion Density Achieved via Interface Engineering

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

Magnetic skyrmions are quasiparticle-like chiral textures that appears in materials with broken inversion symmetry. Implementation of skyrmions in data storage technologies requires the ability of stabilizing them at room temperature and efficiently driving the textures under spin-orbit torque (SOT). Skyrmion stabilization at zero field, as per the requirement of application, can be realized by controlling the interplay between the anisotropy energy, Dzyaloshinski-Moriya interaction (DMI), exchange interaction, and dipolar coupling [1]. Here we show the formation of stable magnetic skyrmions at remanence following the application of an external perpendicular field. We also control the size and density of the skyrmions by manipulating the strength of the applied magnetic field. Further, we observe motion of the skyrmions in nanotrack under the influence of SOT. We chose asymmetric superimposition of two magnetic layers with appropriate combination of materials and thicknesses to satisfy the energy requirements to constrict skyrmions. When the thickness of the ferromagnetic layer is near the spin-reorientation transition (SRT), the effective anisotropy vanishes and the ferromagnetic ground state is the stripe phase [1]. In order to stabilize skyrmion phase in absence of any bias field, we increase the stability of the homogeneous state using a reduced ferromagnet thickness to enhance the anisotropy of the system. Hence we chose the following thin film heterostructure: Si/SiO2/Ta(3 nm)/Pt(5 nm)/Co(1.4 nm)/Au(1 nm)/Pt(5 nm)/Co(1.4 nm)/Au(2.5 nm), where the SRT of Co is ~1.6 nm. FIG 1 (a) shows the PMOKE hysteresis with minor loops for the sample. While major loops show a 100% remanence, minor loop show the possibility to demagnetize the sample, through the creation of textures. As shown by magnetic force microscopy in FIG 1 (b) and (c) at remanence after application of perpendicular magnetic field of 48, and 31 mT, the resulting magnetic state strongly depend on the maximum applied field. The larger the maximum field, the smaller the textures and their density. Therefore, after the application of sufficiently large magnetic field, skyrmions are stable even at remanence. The longevity of the magnetic textures has been confirmed by performing MFM imaging at different times after application of the external field. We have observed motion of these skyrmions in a patterned nanotrack under the influence of SOT by applying 10 ns wide pulses with a current density of ~ 6×1011 A/m2, which opens a perspective toward skyrmionic spintronics devices at zero field.

**References:**

[1] A. Hrabec et al, Nat. Comm. 8, 15765 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/70fb3e0992cff11d4ec7b151d31b17d3.jpg)
FIG 1: (a) Polar magneto-optic Kerr effect (PMOKE) Hysteresis with minor loops in the asymmetric bilayer sample. MFM images of the same sample at remanence after application of perpendicular magnetic field of: 48 mT (b), and 31 mT (c), respectively.

 Stable zero-field skyrmions in magnetic bilayers

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.

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.

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

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