www.acsami.org Research Article Understanding the Magnetic Microstructure through Experiments and Machine Learning Algorithms Abhishek Talapatra,* Udaykumar Gajera,* Syam Prasad P, Jeyaramane Arout Chelvane, and Jyoti Ranjan Mohanty* Cite This: ACS Appl. Mater. Interfaces 2022, 14, 50318−50330 Read Online ACCESS Metrics & More Article Recommendations * sı Supporting Information See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. ABSTRACT: Advanced machine learning techniques have un- furled their applications in various interdisciplinary areas of research and development. This paper highlights the use of Downloaded via 37.29.227.95 on December 7, 2023 at 07:47:20 (UTC). image regression algorithms based on advanced neural networks to understand the magnetic properties directly from the magnetic microstructure. In this study, Co/Pd multilayers have been chosen as a reference material system that displays maze-like magnetic domains in pristine conditions. Irradiation of Ar+ ions with two different energies (50 and 100 keV) at various fluences was used as an external perturbation to investigate the modification of magnetic and structural properties from a state of perpendicular magnetic anisotropy to the vicinity of the spin reorientation transition. Magnetic force microscopy revealed domain fragmentation with a smaller periodicity and weaker magnetic contrast up to the fluence of 1014 ions/cm2. Further increases in the ion fluence result in the formation of feather-like domains with a variation in local magnetization distribution. The experimental results were complemented with micromagnetic simulations, where the variations of effective magnetic anisotropy and exchange constant result in qualitatively similar changes in magnetic domains, as observed experimentally. Importantly, a set of 960 simulated domain images was generated to train, validate, and test the convolutional neural network (CNN) that predicts the magnetic properties directly from the domain images with a high level of accuracy (maximum 93.9%). Our work has immense importance in promoting the applications of image regression methods through the CNN in understanding integral magnetic properties obtained from the microscopic features subject to change under external perturbations. KEYWORDS: magnetic domains, magnetic force microscopy, convolutional neural network, micromagnetic simulation, machine learning ■ INTRODUCTION Magnetic thin films exhibiting perpendicular magnetic ization and the shape of the magnetic structure (important in the case of patterned structures), opposes the single domain anisotropy (PMA) are of technological importance and formation. Thus, in the absence of an external magnetic field (EH = 0), the minimization of the total energy terms leads to promising candidates for spintronic nanodevices in the context the formation of magnetic domains.4 In reality, it is of ultrahigh density magnetic storage, 1 fast memory complicated to predict the simultaneously changing competing applications,2 and nanosensors.3 At favorable atomic ordering, magnetic interactions that result in various domain morphol- ultrathin stacking of Co with Pd or Pt displays PMA. For ogies for perpendicularly magnetized systems.5−7 Now, the magnetic thin films and multilayers with PMA, the information characteristic features of magnetic domains in multilayer (ML) about magnetic microstructure is extremely important to films can be controlled by different factors such as growth understand the magnetization reversal, which is governed by conditions,8 the thicknesses of the constituent layers, as well as energetics. The net magnetic energy (Etotal) for a thin film can the application of external stimuli, viz., magnetic field, heat be represented as Etotal = EK + EA + ED + EH, where EK, EA, ED, treatment,9 laser,10 and ion irradiation.11 Moreover, the and EH represent the anisotropy energy, exchange energy, magnetostatic energy, and Zeeman energy, respectively. The minimization of EK tries to drive the magnetization along the Received: July 18, 2022 easy axis, which can be tuned with thickness, growth Accepted: October 5, 2022 parameters, and route of processing of the materials for a Published: October 21, 2022 real system. EA gets minimized when the spins align in parallel and thus prefer the formation of a single domain. On the contrary, ED, primarily determined by the saturation magnet- © 2022 The Authors. Published by American Chemical Society https://doi.org/10.1021/acsami.2c12848 50318 ACS Appl. Mater. Interfaces 2022, 14, 50318−50330 ACS Applied Materials & Interfaces www.acsami.org Research Article tunable exchange coupling in the exchange spring magnets can ferrimagnetic thin films, the compensation point and magnetic significantly control the magnetic microstructure.12,13 Thus, anisotropy were successfully engineered in Gd−Fe and Tb−Fe modeling of process-induced magnetic modifications has also thin films using He+, and Ne+ ions with various fluences.44 been proven to be important in designing highly controlled Interestingly, magnetic domains were engineered without experiments and predicting new materials and methods. domain walls in Tb/Co ML with the bombardment of He+ In recent times, machine learning techniques have been ions.45 Our recent works on Ar+-induced modifications of proven to be an important tool to understand material systems magnetic properties in the amorphous Tb−Fe−Co thin films46 with interdependent and simultaneously variable material and Tb−Fe/Gd−Fe/Tb−Fe trilayer47 highlighted the tuna- properties. In this paper, we are going to address the bility of magnetic domains correlated with the structural application of the convolutional neural network (CNN) to changes in the vicinity of the spin reorientation transition. understand the modifications of magnetic domains in a The focus of this paper is to understand the modifications of perpendicularly magnetized multilayer, which has been magnetic properties with a special interest in nanoscale observed experimentally by using ion-beam irradiation. Of magnetic domains, displaying a transition from the maze-like late, advanced machine learning techniques have acquired pattern in pristine condition to feather-like domains as a immense importance in interdisciplinary research, such as in function of the fluence (F) and energy (E) of Ar+ ions. microstructure optimization,14 prediction of a magnetic field,15 Micromagnetic simulations were performed to record the phase transition,16 magnetic grain size study,17 modeling variations of magnetic domains with micromagnetic input magnetic domains,18,19 relation between different magnetic parameters. Furthermore, we have proposed a model using a chiral states,20 prediction of effective magnetic spin config- CNN-based image regression technique to identify and urations,21,22 2D metal−organic frameworks with high recognize various features of magnetic domains correlated magnetic anisotropy,23 and different components of Hamil- with the magnetic properties (micromagnetic input parame- tonian including the Dzyaloshinskii−Moriya interaction ters). A large set of simulated domain images was used to train (DMI),24 using different deep learning and machine learning and test the neural network (NN) which determines the methods. From the point of view of atomistic magnetism, magnetic properties of the unknown (out of the sets used for researchers21,22 have tried to estimate and analyze various training) domain images with higher accuracy. Our work components of Hamiltonian, such as exchange constant, directs a novel route for the quantitative analysis of anisotropy constant, and DMI, using different CNNs.25 The microscopic domain images using artificial intelligence. advanced CNN methods showed effectiveness and accuracy in different research domains. However, these methods generally require a large data set26 to properly train and test the model, ■ METHODS Experiments. Co/Pd ML films with the configuration of Si which might stand in the way of directly using these methods (substrate)/Ta (30)/Pd (30)/[Co (tCo)/Pd (8)]×50/Pd (12) (the in analyzing regular experimental data. numbers in parentheses indicate thicknesses in Å) have been From the experimental point of view, ion-beam irradiation is deposited by ultrahigh vacuum DC magnetron sputtering at a a popular and viable technique to tune magnetic properties, working pressure of 1.35 × 10−3 Torr of Ar. The ion-beam irradiation associated with a locally induced structural imperfection or was performed on the films with maximum PMA, obtained with a specific tCo. The ion-irradiation process was carried out under high intermixing, relevant in the context of magnetic MLs.27 The vacuum (2 × 10−6 Torr), normal to the film surface using Ar+ ions of ion energy and fluence (number density) can be separately energies 50 and 100 keV with varying fluences, ranging from 0.5 × adjusted to control the depth and lateral extent of the 1014 to 3.3 × 1016 ions/cm2. The time of irradiation (t) controls the irradiation-induced effects, which leads to the modification of F g ion-fluence following the relation t = 1 , where σ represents the area magnetic properties. The ions lose energy during their passage I e through the material, which is either spent in displacing the of irradiation (1 cm2), g denotes the charge state of the ion (+1), I target atoms by elastic collision (nuclear stopping) or exciting denotes the beam current (2 μA), and e is the electronic charge. Table the atoms by inelastic collisions (electronic stopping).28 A 1 describes the nomenclature of the films with different values of large variety of studies exists on ion-beam induced fluence. Simultaneous atomic and magnetic force microscopy (AFM and MFM) were carried out to observe the topography and magnetic modifications in magnetic ML, either in the context of domains. Magnetization reversal has been studied with a vibrating patterning29 or depth-resolved structural modifications.30,31 sample magnetometer (VSM) by applying the external magnetic field The creation of graded anisotropy media by domain wall along the in-plane (IP) and out-of-plane (OOP) directions with positioning has also been reported using ion irradiation.32 Ion- respect to the film surface. Cross-sectional transmission electron induced modification of magnetic properties with depth- resolved structural studies in Co/Pt ML has been reported.33,34 Table 1. Nomenclature of the Samples and Comparison of An interesting study on the investigation of magnetic domains MR, Hc, Keff, and Rq with Variable Ion Fluences after ion beam irradiation was performed by Trassinelli et al., where local microscopic features of domains were highlighted MR in Keff in in the vicinity of the ferromagnetic to paramagnetic phase F in emu/cm3 OOP Hc in Oe erg/cm3 Rq in ions/cm2 name (IP) OOP (IP) (×106) nm transition temperature for Mn−As thin films.35 Co/Pt ML36 and soft magnetic FeCoSiB thin film37 systems have also been 0 pristine 1200 (120) 880 (440) 3.5 0.4 investigated in order to study the behavior of magnetic 0.5 × 1014 A1 260 (395) 243 (244) −0.9 0.5 domains in response to light ions. Swift heavy ion-induced 1 × 1014 A2 47 (424) 188 (268) −2.7 0.5 modification of magnetization dynamics,38 lattice distor- 3.3 × 1014 A3 56 (921) 201 (80) −5.3 0.4 tion 39,40 and spin reorientation 41 are also topics of 1.0 × 1015 A4 68 (68) 230 (226) −0.2 1.0 contemporary research interest. Of late, deterministic gen- 3.3 × 1015 A5 86 (783) 245 (75) −5.0 1.4 eration42 and precise tunability of skyrmion density43 have 1.0 × 1016 A6 98 (779) 234 (85) −4.9 1.0 been achieved using energetic ions. From the point of view of 3.3 × 1016 A7 58 (483) 162 (88) −3.3 2.2 50319 https://doi.org/10.1021/acsami.2c12848 ACS Appl. Mater. Interfaces 2022, 14, 50318−50330 ACS Applied Materials & Interfaces www.acsami.org Research Article microscopy (XTEM) was carried out for selective samples employing • The third group was used to test the model, using 30% (288) high voltage (1250 kV) electron microscopy. Spatial mapping of the of the total images. corresponding elements was performed using energy-dispersive It is worth mentioning that the images used for validating were also spectroscopy (EDS) of the X-ray associated with the FEI Titan used during the training process. However, the images used for testing scanning transmission electron microscope. The depth-resolved the model were never exposed to the machine during training. structural investigation was complemented by X-ray reflectivity (XRR) measurements. Micromagnetic Simulation. Micromagnetic simulations of magnetic domains were performed using MuMax3 software.48 The ■ RESULTS AND DISCUSSIONS Pristine Co/Pd Multilayers. Co/Pd ML films were Co/Pd ML is considered as a single magnetic layer with an effective deposited with three different tCo to observe the variation in anisotropy constant (Keff) and effective thickness (teff) of the magnetic PMA. Figure 1a−c represents the OOP and IP hysteresis loops layers, comparable to the multilayer. The input parameters are close to the values reported in the literature,49 that is, exchange constant (Aex) = 2.3 μerg/cm, saturation magnetization (Ms) = 1 kemu/cm3, and Keff = 10 Merg/cm3. The simulation temperature (T) and damping constant (α) were 300 K and 0.9, respectively. Cubic meshes of volume (4 nm)3 are used for the discretization of the total area of simulations (∼2 μm × 2 μm) with teff = 16 nm. The simulations started from arbitrary initial spin configurations and run for 100 ns to obtain energy-minimized stable configuration of magnetization following Landau−Lifshitz−Gilbert equation.50,51 Here our main focus is to analyze the domain images which essentially signify the spatial variation of the overall magnetization (M). Building and Training of CNN. In this article, the CNN-based image regression technique is used. We have used different popular deep learning (DL) models as mentioned below. • Cutsom multilayer perceptron model using Tensorflow.52 • Residual NN architectures ResNets with and without pretrained models.53 • VGG16 with improved (3 × 3) convolution filters54 • DenseNet, which utilize dense connections between layers through dense blocks.55 • One of the classic DL algorithms: AlexNet56 • EfficientNet uniformly scales all dimensions of depth, width, and resolution using compound coefficients.57,58 The custom architecture of CNN contains a multilayer perceptron with a batch normalization layer followed by a dense NN. For optimization, during the training of CNN, the default function Adam is used, which is the first-order gradient-based optimization of stochastic objective functions. For the pretrained ResNets models, we have used Fastai and PyTorch libraries to train and predict the different magnetic properties from the simulated domain images. We have also compared the performance using different models such as ResNet-18 and ResNet-34 comprising 18 and 34 layers, respectively. Overfitting is prevented by employing the default early-stopping Figure 1. The in-plane and out-of-plane hysteresis loops for Co/Pd algorithm. The learning rate is set to 0.001 with a strategy to reduce ML at different tCo are shown in (a−c) along with the corresponding the learning rate when the error stops decreasing with several steps. MFM images of magnetic domains in the as-deposited state, shown in Furthermore, early stopping is implemented in a way that it decides to (d−f) for tCo = 3, 5, and 8 Å, respectively. stop training based on accuracy improvement. The fit one cycle method was used for the dynamic learning rate implemented in PyTorch. We have also checked our model using pretrained weights. for the values of tCo of 3, 5, and 8 Å, respectively, with a fixed In order to create a large data set for training the NN, we have used Pd layer thickness of 8 Å and number of Co/Pd repeats of 50. 960 simulated images, obtained by realistic variations of four Additionally, Ta and Pd were used as the buffer layers to aid micromagnetic input parameters, viz., Aex (range: 0.1−2.7 μerg/ the PMA. For tCo = 3 Å (Figure 1a), an almost square cm), α (range: 0.825−0.925), Keff (range: within the order of 104 to hysteresis loop can be observed with high remanence (MR) 109 erg/cm3), and T (range: 300−1000 K). The considered range of and coercivity (Hc) along the OOP direction, which is the parameters makes the data sets versatile by incorporating various indication of strong PMA. On the other hand, slanted types of magnetic domains of different characteristic length scales and spatial features. Physically, the variation of Aex and Keff results in a hysteresis loops are observed with the increase in tCo, as shown in Figure 1b,c, which indicate the onset of nucleation of change in domain wall energy (proportional to Aex · Keff ). The reversed domains at comparatively higher magnetic fields. A variation in temperature introduces thermal agitation that results in fluctuation of magnetization near the boundary between two quantitative comparison shows that the OOP Hc is 884 (±10) oppositely magnetized domains. α controls the relaxation of Oe for tCo = 3 Å and decreases to 161 (±10) Oe and 205 magnetization. The entire data set was divided into three different (±10) Oe for tCo = 5 and 8 Å, respectively, whereas the OOP groups, as mentioned below. saturation field (Hs) varies to 5, 5.5, and 7 kOe, as shown in • The first group was used for training the model, using 63% Figure 1a−c, respectively. The value of the nucleation field (605) of the total images. (HN) is closely related to the ratio of saturation magnetization • The second group was utilized for the validating and (Ms) to MR, as both the quantities play a decisive role in rearrangement of weights, using 7% (67) of the total images. magnetization reversal. A high MR/Ms of 90% and HN of 50320 https://doi.org/10.1021/acsami.2c12848 ACS Appl. Mater. Interfaces 2022, 14, 50318−50330 ACS Applied Materials & Interfaces www.acsami.org Research Article around −200 Oe in Figure 1a clearly indicate that the magnetization reversal is dominated by the rapid domain wall motion.59 The values of HN are close to 2.4, and 4.5 kOe along with weak MR/Ms of 4 and 2.9% for Figure 1b,c, respectively, which confirm that nucleation, propagation, and annihilation of the reverse domains lead to the magnetization reversal of these films. The IP loops for all three films cannot be brought up to saturation within the limited field of the VSM measurements. Thus, the magnetization studies confirmed that all the ML displays a predominant easy axis along the OOP direction among which the strongest PMA can be observed with tCo = 3 Å. Microscopic investigation of tCo-induced variation of PMA was performed using MFM. All the pristine Co/Pd ML displays a uniform featureless surface (not shown) with a root mean square roughness (Rq) of less than 1 nm, and the domain imaging has been performed in the as-deposited condition of the films before exposure to an external magnetic field. Periodic, nanoscale magnetic domains can be observed in Figure 1d−f for tCo = 3, 5, and 8 Å, respectively. Maze-like domains with strong OOP contrast with an average lateral size of 434 (±12) nm can be observed in Figure 1d. The domain Figure 2. Hysteresis loops of the irradiated films with the applied field size reduces to 176 (±2) nm, and 88 (±2) nm for Figure 1e,f, along the (a) out-of-plane and (b) in-plane directions. respectively. The reduction in the OOP contrast is also clear from the normalized MFM images with a transition to thinner Hc, and Keff have been recorded in Table 1 for all the irradiated stripes domains for the highest tCo. The effective magnetic films. Although the variations of the parameters are not very anisotropy (Keff) for magnetic multilayers can be expressed as systematic, a huge increase in IP MR is to be noticed with K respect to its OOP counterpart. The IP loops gain squareness Keff = K v + 2 tint , where Kv and Kint represent the volume and with a decreased IP coercivity, which shows variation close to interface anisotropy constants, respectively, with t as the the error limit of ± 5 Oe at higher F values. This behavior is effective thickness of the magnetic layers. The magnetic also reflected in the Keff values. Most importantly, the negative properties of the ML can be modified with the variation of the values for Keff essentially indicate the presence of easy-plane number of stacking or by varying the thickness of the anisotropy, originating due to the SRT induced by ion constituent materials.60,61 The increase in the effective irradiation. The hysteresis loops for the irradiated samples at thickness reduces the contribution of interfacial anisotropy various fluences with E = 100 keV are presented in Figure S1 energy and simultaneously increases the volume anisotropy of the Supporting Information. energy. In this competition, whenever both the interface and The simultaneously recorded normalized AFM and MFM volume anisotropy energies become comparable, the system images are depicted in Figure 3a,b, respectively, for the breaks into multiple domains. From the results of Figure 1, it irradiated films. The Rq values, listed in Table 1, are can be confirmed that the domain nucleation is more favorable determined from the AFM images and show an overall at higher tCo, which essentially reduces the PMA of the increasing trend with the increase in F. This can be connected systems, and hence, the highest contribution of interface with the ion-induced surface damage with irradiation for longer anisotropy energy at the lowest tCo is considered to play a times at higher F. In addition to that, the growth of irregularly major role behind the strong PMA. distributed granular topographic features has been observed Effect of Ion Irradiation. Magnetic Characterizations. with high-resolution AFM imaging (not shown here), where Owing to the possession of strong PMA, the films with tCo = 3 the maximum grain size appears to be 141 nm with a Å have been used for the ion irradiation studies. The integral distribution error of ±50% for the A6 film. The MFM images magnetic response of the irradiated films has been charac- (Figure 3b) for A1 and A2 display a maze-like domain pattern terized with the OOP and IP hysteresis loops, as depicted in with alternate dark-bright contrast, reduced with respect to Figure 2a,b, respectively, for the selected samples. It can be that of the pristine film, as shown in Figure 1d. The average clearly understood from Figure 2 that the maximum magnitude domain size is estimated to be 150 (±4) nm and 126 (±3) nm of magnetization detected in the IP mode is larger than that in for A1 and A2, respectively. A3 is seen to be the threshold the OOP mode, in contrast to the case of the pristine film, where a domain pattern with this in-plane correlation length shown in Figure 1a. This essentially indicates that irradiation no longer exists. Instead, feather-like domains are observed for with 50 keV ion energy triggers a spin reorientation transition A3 and A4. Finally, the magnetic contrast drops significantly (SRT) from OOP to IP with respect to the film surface. The for A6 and topographic interference starts to appear in the OOP loops become slanted with reduced MR/Ms and a higher MFM images due to the increased height of the topographic saturation field, whereas the IP loops gain MR with a lower features. Two distinct factors are relevant for this domain saturation field. At higher fluence of irradiation, the collision transformation. The first one is ion energy which determines between the larger number of energetic ions and the film the penetration depth of the ions inside the film. This gives rise surface may result in the formation of surface defects that act to intermixing at the interfaces by modifying the periodicity of as the pinning sites for the domain wall and restrict the rapid the ultrathin stacking. Hence, the effective anisotropy is domain wall motion, as interpreted from the hysteresis loops expected to decrease,33 causing a reduction in the domain size (Figure 1a) of the pristine film. The values of IP and OOP MR, and the associated magnetic contrast, as observed in the case of 50321 https://doi.org/10.1021/acsami.2c12848 ACS Appl. Mater. Interfaces 2022, 14, 50318−50330 ACS Applied Materials & Interfaces www.acsami.org Research Article (8 Å)]×50 multilayer (with highest PMA) in Figure 4a, which shows a multilayer film on top of the single-crystalline Si substrate. A high-resolution (HR) TEM image is depicted in Figure 4b, clearly displaying the presence of lattice fringes. Inverse Fourier filtered transform (IFFT) was performed selectively at different regions (regions 1 and 2 are indicated by yellow boxes for clarity) of Figure 4b. The average value of the d-spacing was estimated from the line scans over the IFFT images shown in Figure 4c and turned out to be around 2.43 (±0.02) Å. This lattice spacing can be attributed to the fcc(111) crystal orientation of the Co/Pd system that appears due to the lattice averaging of Co and Pd, and therefore, can be tuned with tCo.64,65 It is always intriguing to analyze the depth- resolved elemental mapping for the case of ultrathin multilayer stacks, which provides information about the interfaces. The EDS technique was used to perform the elemental mapping of the constituent elements along the specified region (box), shown in the high-angle annular dark-field scanning trans- mission electron microscopy (HAADF-STEM) image in the extreme left of Figure 4d. Thereafter, the mappings for Ta, Co, and Pd are shown from left to right which well justifies Ta as the buffer layer. However, Co and Pd are observed everywhere in the selected region of mapping, which suggests the possibility of alloying at the interfaces of the corresponding ultrathin layers in the pristine state. Yang et al. reported the absence of the multilayer feature when thicknesses of both Co, and Pd layer reach around 5 Å.66 The XTEM and HRTEM images of the sample, irradiated at the maximum fluence (A7), are shown in Figure 4e,f, respectively. Unlike the pristine sample, Figure 4e displays the presence of irregular and aperiodic stripes that could probably be the footprint of the bombarded ions. Two regions with different textures have been indicated in Figure 4f, where the position of the dotted line could be the grain boundary in the polycrystalline film. The average d-spacing estimated from the IFFT images of Figure 4g is around 2.37 (±0.06) Å, indicating no change in the fcc(111) growth direction. The estimations of d-spacing are comparable to those values, mentioned by Barton et al.67 The HAADF- STEM image of Figure 4h shows the presence of bubble-like Figure 3. Normalized (a) AFM images with simultaneously captured features, which might be the Ar bubbles, appearing after (b) MFM images for the films irradiated with 50 keV of Ar+ ions at irradiation. However, we could not confirm the presence of Ar various fluences (specified by the nomenclature). The scale bar is the with EDS due to its lighter atomic weight. The alloying of Co same for all the images. and Pd is clear from the EDS mapping, shown in Figure 4h, which also suggests the possibility of the diffusion of Ta in the A1 and A2. The other effect is fluence, which is responsible for multilayer. the extent of modification of surface properties such as defects The XTEM studies on the depth-resolved microstructure and pinning sites for domain walls. The observed feather-like have been complemented with XRR. Comparative XRR domains can be explained based on the IP magnetization spectra for the pristine Co/Pd ML and the irradiated films distribution and transport of the magnetic charge toward the with minimum (A1) and maximum (A7) fluence are presented surface, which is achieved by a small deviation from the IP in Figure 5. All the spectra have been fitted with multilayer magnetization, similar to the formation of cross-tie walls.62 The models, relevant to the experimentally prepared samples. The modified domain morphologies can be different for different best-fitted data along with the experimental spectra for the material systems and choice of ions.63 The surface roughness pristine film are shown in Figure 5a, which confirms the of the films increases with higher ion energy, and the presence of interfacial diffusion of Co and Pd, as explained fragmented maze-like domains could not be observed for the from the elemental mappings in Figure 4d. The fitted model irradiated samples with E = 100 keV; the corresponding AFM suggests the formation of the [Co (1.8 Å)/CoPd (1.13 Å)/Pd and MFM images are presented in Figure S2 of the Supporting (7.1 Å)]×50 ML in the pristine state (Figure 5a), and [Co (1.3 Information. Thus, variation in the domain size and pattern Å)/CoPd (3.16 Å)/Pd (5.96 Å)]×50, and [CoPd (10.82 Å)/Pd can be tuned via locally competing anisotropies, which create a (3.34 Å)]×50 for A1 and A7, respectively, in Figure 5b. The strong force for the SRT toward the IP direction. highest ion fluence in A7 results in complete diffusion of Co Depth-Resolved Structural Characterizations. The depth- along with higher interfacial and surface roughnesses, and resolved structural studies were performed with XTEM. First, consequently, the XRR intensity falls rapidly at lower 2θ values. we have shown the TEM image for the pristine [Co (3 Å)/Pd The XRR results follow similar trends when the ion energy 50322 https://doi.org/10.1021/acsami.2c12848 ACS Appl. Mater. Interfaces 2022, 14, 50318−50330 ACS Applied Materials & Interfaces www.acsami.org Research Article Figure 4. (a,e) cross-sectional TEM images, (b,f) HRTEM images, and (c,g) IFFT images for the pristine Co/Pd ML and A7 films, respectively. (d,h) EDS mapping of the distribution of the corresponding elements in the pristine and A7 films, respectively. SiO2 above the Si substrate makes the fitting model more accurate and viable with the real samples. Simulated Domain Configurations. Detailed analysis of magnetic domains for the pristine and irradiated films has been presented in Figures 1 and 3, respectively. The MFM imaging (Figure 3) along with the integral magnetic measurements (Figure 2) confirmed the modification of magnetic anisotropy, which triggers a spin reorientation transition from OOP to the plane of the film after irradiation. In this section, we are going to discuss the possible changes in domain pattern as a function of Keff, and Aex and qualitative comparison between the Figure 5. Experimental and fitted XRR spectra for (a) pristine and simulated and experimental results. It is well known that (b) irradiated A1 and A7 multilayer. domain walls (DW) represent the net in-plane component of magnetization, ( Mx2 + My2 ), acting as the boundary between the out-of-plane magnetized (±Mz) domains. The width of the increases to 100 keV at the same fluences (Figure S3 of the Aex DW is proportional to , and hence, the SRT phenomenon Supporting Information). Thus, the XRR studies explain the Keff broadening of interface width and roughness with increasing can be well understood in terms of the parameters controlling energy and fluence of Ar+ ions.68 The interface quality and the width of the DW. The simulated domain images are magnetic properties change significantly due to reduced presented in Figure 6a,b for different Aex values of 2.3, and 1.15 symmetry breaking at the Co/Pd interfaces.67 It is worth μerg/cm, respectively, for four different Keff values, as mentioning that consideration of a thin native oxide layer of mentioned in the left column of the images. For all the 50323 https://doi.org/10.1021/acsami.2c12848 ACS Appl. Mater. Interfaces 2022, 14, 50318−50330 ACS Applied Materials & Interfaces www.acsami.org Research Article IP magnetization can be marked at Keff = 5 Merg/cm3, where the OOP components shrink to a thread-like region bounded by IP magnetization in a different direction. Further reduction of Keff leads to a symmetric vortex configuration. Thus, with the combination of variables Keff and Aex, we can explain tunability in the magnetic domain structure, which is qualitatively similar to the experimentally observed domain images in terms of the extended maze-like pattern in the pristine condition, fragmented thinner domains with reduced OOP magnetization after irradiation at lower fluences, and finally, feather-like structure with dominant IP magnetization in response to the irradiation at higher ion fluences is formed. In view of the experimental and simulated results, it is evident that a proper understanding of magnetic domain patterns provides a direct route to understanding the change in micromagnetic energetics in response to the physical processes. Thus, it urges to establish a reliable path for proper estimation of important parameters controlling the energetics, which we visualize in the form of magnetic domains. It is important to mention that recognizing the modifications in the micromagnetic parameters from the domain images become extremely difficult with the human eye when the change in parameters does not lead to a significant change in the images, or domain patterns obtained by simultaneous changes in two or more parameters. In this regard, we propose different CNN architectures to identify the micromagnetic parameters from the domain images, which also help immensely to complement the experimental results. As mentioned earlier, training the CNN requires a large and homogeneous data set, which is not easy to obtain through modifications of experimental process conditions. Therefore, in this article, we are using only 960 domain images obtained through micromagnetic simulations considering different combinations of Keff, Aex, T, and α. The tuning of the domain size and net magnetization can arise from the modification of the abovementioned parameters, but pinpointing the exact parameters with higher accuracy from Figure 6. Simulated domain images with different Keff (mentioned in the entire parameter space is not straight forward. In order to the left column) with Aex of (a) 2.3 and (b) 1.15 μerg/cm. The scale reduce the expense of simulation time and increase accuracy, bar is the same for all the images. we have reduced the simulation area to around 1 μm × 1 μm. However, the CNN model is not limited to the size of the domain images of Figure 6, the white and black colors indicate images, which we have confirmed by verifying our model with two mutually opposite OOP components of magnetization, different sizes of images. and the other colors indicate the IP components, the Overview of the CNN. In order to predict the micro- orientations for which are shown by the arrows. The domain magnetic properties (parameters) directly from the domain image in Figure 6a with Keff = 10 Merg/cm3 (top) displays images, we have used advanced numerical deep learning extended maze-like domain structure with strong perpendicular methods, such as CNN. As we have mentioned in the previous anisotropy. With the reduction in Keff to 8 Merg/cm3, the section, CNN consists of a convolutional part associated with a domain size decreases, and the pattern appears as extended fully or partially connected NN.69 Here, we will briefly discuss periodic stripes with no preferential orientations and higher in- the fundamental working principle of CNN. plane contrast. With further reduction in Keff, the extended First, we are going to explain different components of the stripe patterns shrink to circular stripes (not shown) to NN and the generally used terminologies. NN primarily minimize the magnetostatic energy. Interestingly, strong in- consists of node layers that include the input and output layers plane contrast leading to asymmetric vortex structure with an and hidden layers, which are the dense layers between the out-of-plane magnetized core can be observed with Keff = 5 input and output layers. Each neuron is connected with other Merg/cm3. Further reduction in Keff results in a feather-like neurons through weights in between and the threshold values. structure with multiple vortices (bottom). The domain features If the output value of a neuron reaches the threshold values, display significant changes with the reduction of Aex to 50% for that particular neuron is activated and sends information to the the same Keff. Unlike extended maze-like patterns, worm-like next layer. In general, the weights between different domains without preferential orientation can be observed with connections can be adjusted by various methods following Aex = 1.15 μerg/cm, as shown in Figure 6b. Stronger OOP the back-propagation or forward-propagation algorithms to contrast with reduced domain sizes can be observed with minimize the error in the output node layer. The simplest respect to the corresponding domain images of Figure 6a with model is to consider a NN of 3 input layers and 1 output layer, the same Keff. Here, the threshold for transition from OOP to as shown in the schematic of Figure 7. In this case, we can 50324 https://doi.org/10.1021/acsami.2c12848 ACS Appl. Mater. Interfaces 2022, 14, 50318−50330 ACS Applied Materials & Interfaces www.acsami.org Research Article artificial NN with zero input. Once the weights wi are determined, we can also investigate the contribution of different input properties. In general, larger weights for the input values with comparable magnitude represent a higher contribution to the prediction. Then, the summed function will pass through the activation function, which determines the output. If the output values are higher than the threshold values, the neuron will be activated. This leads to the propagation of the data to the next layer. In this way, finally, we calculate and minimize the cost function or error function, n Figure 7. Schematic of an artificial NN with three input and one fe (x) = 0 (y y )2 , by adjusting the weights. output neurons. Here, wi, x, and f i are the weights, input values, and threshold function, respectively. Now, while investigating with images, we do not have the exact numerical values of the parameters, mentioned above. Therefore, convolutional layers are used to extract those write the equations for the input layer and the simple threshold features from the images.70 Thus, in addition to the dense or activation function (f i(x)) as layers, the CNN model contains convolutional layers and y= wx pooling layers, which are utilized to extract important features i i + b = w1x1 + w2x 2 + w3x3 + b (1) from the images. The schematic for the distribution of different l o layers in a typical custom CNN is shown in Figure 8a, where o o1, if ( wxi i + b ) 0 three convolution layers and four dense layers were used. In fi (x) = m o o o 0, otherwise order to extract the features, the convolution layer transforms n (2) the input image using the different convoluted filters. A filter is where wi, xi, and b are the weights, input values, and bias, a small matrix with a dimension smaller than that of the image respectively. A bias vector is an additional set of weights in a to be convoluted. A single convolution layer contains a series NN with no input, and thus, it corresponds to the output of an of filters as shown in Figure 8c. Following the convolution Figure 8. Details of the custom NN with different descriptions: (a) schematic for the reduction in dimension of the input image in each layer of CNN, (b) flow chart of a custom CNN model, and (c) qualitative working principal of the CNN. 50325 https://doi.org/10.1021/acsami.2c12848 ACS Appl. Mater. Interfaces 2022, 14, 50318−50330 ACS Applied Materials & Interfaces www.acsami.org Research Article Figure 9. Evolution of images with the application of different filters on the input image and feature extraction from different layers, (a) distribution of out-of-plane magnetization, (b) domain boundaries, and (c) curvature or branching. layer (Conv2D), we have also used the pooling layer branching. However, the information extracted in the last (MaxPooling2D) to reduce the dimensions of the feature layer (4th Conv2D layer and higher) from a specific filter in maps (Figure 8a), which is helpful in reducing the number of Figure 9 becomes too complex to understand with the human parameters to learn and the amount of computation performed eye. Several other filters were also used to produce this higher in the network. A reduction in the lateral dimension of the dimensional information, which was further fed to the NN to input image can be observed after getting filtered through each identify particular features inside the image, where we use layer. While the convolution layer increases the depth effect different functionalities mentioned above to predict the with a little reduction in the lateral dimension, the pooling magnetic properties. It is important to notice that the lateral layer only contributes to the reduction in lateral dimension. dimension of the images decreases from 256 × 256 to 15 × 15 After getting filtered through a series of convolution and after passing through all the filters, as observed from Figure 9. pooling layers, the images pass through the global average Now, we will look into the training process of the CNN pooling layer and various dense layers. The sequence of model. For the training, we use particular images, grouped with different filters in our custom model and the corresponding batch sizes of 32 images. Batch size decides the number of changes in dimension at each layer has been well illustrated in images trained at a time. We trained the CNN model on the the flow chart of Figure 8b. The machine essentially entire training data set, also known as epochs. After training understands and compares the “higher dimensional images” the model, we checked the prediction of the model to validate obtained after filtering through all the layers of the CNN images and calculated the mean squared error (MSE) for each model. The features, extracted using the filters, were further epoch. Based on the errors, the model tries to adjust the used for the prediction or classification. The entire process of weights to reduce the MSE. We have used different models for working principal of CNN can be understood through the training, and their comparative performances are shown in schematic of Figure 8c. However, in practice, substantially Figure 10, where the MSE has been plotted at different epochs. more convolutional and pooling layers are used in a CNN to A large MSE difference between the trained and validation data extract different features from the images. In order to sets indicates overfitting in the model. As observed from Figure understand the effect of filters inside different convolution 10, the difference between the validation data set and the and pooling layers, we have shown an example of image trained data set is small, which implies that the models are regression in Figure 9, illustrating the action of filtering three learning different features from the images. Further, the three important features when the simulated domain image of Figure different models are converging with comparable values of 6a pass through different filters in different convolution and MSE (close to 5%) for higher epochs. We have tried to pooling layers. In Figure 9a, the first filter (top row) is estimate the magnetic properties from an experimental domain extracting the distribution of the out-of-plane magnetization, image, which has been shown in Figure S4 of the Supporting whereas the second filter (middle row) in Figure 9b marks the Information. domain walls, which are the boundaries between the two Comparison with Pretrained CNN Architectures. We have oppositely magnetized areas, and the third filter (bottom) in constructed our custom CNN architecture and compared it Figure 9c brings information about the domain curvature, with different available CNN architectures. Many numerical which is physically related to domain nucleation and methods, such as Pearson correlation coefficient, mean squared 50326 https://doi.org/10.1021/acsami.2c12848 ACS Appl. Mater. Interfaces 2022, 14, 50318−50330 ACS Applied Materials & Interfaces www.acsami.org Research Article run each pretrained model in two parts: (1) using the freeze (unchanged) weights and (2) using the unfreeze weights, as suggested in the model manual.53 It is a general practice to decrease the load on the computer and preserve the prefixed weights in pretrained models since these CNN architectures have around half a million parameters to adjust. We can see significant improvement when we increase the layers from the custom model to ResNet18, after which the improvement is not significant while increasing the number of layers in ResNet34. A larger number of layers generally captures higher- dimensional features from the images; however, after some threshold number of layers in the model, the possibility of overfitting increases. ■ CONCLUSIONS This paper explains a detailed understanding of modifications Figure 10. Evolution of the loss function for different CNN models as of magnetic domains in the perpendicularly magnetized Co/Pd a function of epochs. Here losses for training and validation images ML. Sputtered ML films with tCo = 3 Å show the highest PMA are shown by solid and dashed lines, respectively. The blue solid line with maze-like magnetic domains in pristine condition. The represents a reference level at 5%. integral magnetic properties and magnetic domains are influenced significantly by the irradiation of Ar+ ions at 50 error (MSE), R2 score, and so forth, are used to check the keV of energy. The magnetic contrast decreases, and the accuracy of the prediction. In our case, we have checked the domain size reduces to almost one-third of that in the pristine accuracy of each model by the goodness parameter, R2 score, state after the bombardment of ions with a fluence of 1014 as defined in the eq 3. It is a measure of fit that indicates the ions/cm2. Irradiation with a higher ion fluence renders the variation of a dependent variable, explained by the effective anisotropy to reorient along the plane of the film. As a independent variable(s) in a regression model. Furthermore, result of that, no definite periodic domain configurations were we also report different R2 scores for different methods in observed. Instead, feather-like domain patterns with localized Table 2. Here, it is worth mentioning that the reported R2 vortices could be seen. The changes in magnetic properties can be corroborated by the structural modifications in terms of Table 2. Comparison of the R2 Scores and Time of Training diffusion and alloying at the interfaces of the ultrathin Co and for 1000 Epochs (500 Epochs with Each of Freeze and Pd layers. In this context, we felt an urge to establish a reliable Unfreeze Weights) for Different CNN Modelsa and automated way to predict the magnetic properties directly name of the model R2 score (%) training time (s × 103) from the microscopic investigation. Advanced machine custom model [Figure 8] 81.8 5 learning algorithms, in the form of a CNN, were found to be ResNet18 90.2 130 the best route to achieve our goal. In order to produce a large ResNet34 93.4 145 data set of images to train the CNN, micromagnetic simulation VGG16 93.9 72 was used, which acts as a bridge between microscopy and the EfficientNet 92.9 65 CNN, as the simulated domain images showed good AlexNet 89.1 35 qualitative agreement with the MFM images. The CNN DenseNet 91.1 75 architecture, trained through 960 simulated images, success- a fully predicts the micromagnetic parameters with a maximum The time for training is based on an Intel i5 quad core processor. efficiency of 93.9%, which is quite high and well comparable with the recently reported results. However, the model requires scores are calculated using the test images, which were never the same lateral dimension of images and similar color exposed to the model during the training process. information while comparing the trained and validation data sets. From the point of view of a realistic change in magnetic SSresidual R2 = 1 properties correlated with the experimental results, we have SStotal (3) considered here the variations of Keff, Aex, T, and α to create the data set for training. In the future, the CNN model can be In eq 3, SStotal = i (yi y )2 and SSresidual = i (yi fi )2 , extended to a more complex form, extending to the variations where f i are the predicted values; xi and yi are values of input of Ms, external magnetic field, DMI constant, and spin- and output properties, respectively; and x̅ and y̅ are the mean polarized current, encompassing the aspect of predicting novel of the input and output values, respectively. In general, the magnetic materials with chiral domain wall/skyrmion config- values of R2 score should lie between 0 and 1, where 0 urations, to be manipulated using the current.. indicates no dependency of input parameters on output properties (least accuracy), while 1 shows the 100% depend- ence (maximum accuracy). Negative values of R2 score are also ■ * ASSOCIATED CONTENT sı Supporting Information possible, indicating the worst performance by selecting the The Supporting Information is available free of charge at mean value from the data set. https://pubs.acs.org/doi/10.1021/acsami.2c12848. In addition to that, we refer to Table 2, which shows that the pretrained models that have a significantly large number of Hysteresis loops, AFM and MFM images, and XRR layers than the custom model work comparatively better. We spectra of the samples irradiated at an energy of 100 keV 50327 https://doi.org/10.1021/acsami.2c12848 ACS Appl. Mater. Interfaces 2022, 14, 50318−50330 ACS Applied Materials & Interfaces www.acsami.org Research Article of the Ar+ ions and estimation of magnetic properties from the MFM image (PDF) ■ REFERENCES (1) Hellwig, O.; Marinero, E. 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