Authors:
(1) VINÍCIUS YU OKUBO, Dept. Electronic Systems Engineering, Polytechnic School, University of São Paulo, Brazil;
(2) KOTARO SHIMIZU, Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan;
(3) B. S. SHIVARAM, Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA;
(4) HAE YONG KIM, Dept. Electronic Systems Engineering, Polytechnic School, University of São Paulo, Brazil. Authors: Authors: (1) VINÍCIUS YU OKUBO, Dept. Electronic Systems Engineering, Polytechnic School, University of São Paulo, Brazil; (2) KOTARO SHIMIZU, Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan; (3) B. S. SHIVARAM, Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA; (4) HAE YONG KIM, Dept. Electronic Systems Engineering, Polytechnic School, University of São Paulo, Brazil. Table of Links Abstract and I. Introduction Abstract and I. Introduction II. Related Work II. Related Work III. Methodology III. Methodology IV. Experiments and Results IV. Experiments and Results V. Conclusion and References V. Conclusion and References IV. EXPERIMENTS AND RESULTS A. PERFORMANCE EVALUATION A. PERFORMANCE EVALUATION A. PERFORMANCE EVALUATION Evaluating TM-CNN poses a certain challenge because there are no benchmarks or published results for direct comparison. So, we defined that junction and terminal detections reviewed by human observers as the gold standard and compared the algorithms against this standard. For testing purposes, we annotated 5 independent images from varying experiments, using the same procedure as the training images (subsection III-E). False detections were excluded since they do not contribute to the detection evaluation. In total, the test set contained 3,551 junctions and 3,653 terminals. B. RESULTS FROM A PHYSICS PERSPECTIVE B. RESULTS FROM A PHYSICS PERSPECTIVE B. RESULTS FROM A PHYSICS PERSPECTIVE In Bi:YIG films, it is known that a perfect stripe pattern is the most energetically favorable and stable configuration of magnetic moments [4]. In this structure, the magnetic moments exhibit stripes aligning straight in one direction throughout the entire structure, resulting in large spatial coherence. Meanwhile, the experimentally obtained structures often manifest labyrinthine patterns, as illustrated by dark and bright stripes in Fig. 1. In these labyrinthine patterns, stripes are aligned within small domains but propagate in different directions between different domains, and thus the spatial coherence of stripes is smaller than the perfect stripe. Notably, junctions and terminals are defects emerging in the formation of these labyrinthine patterns, intricately linked to the growth of spatial coherence in the system. Introducing such defects into the perfect stripe structure leads to the bending and branching of the initially aligned stripes, eventually reducing spatial coherence accompanied by the transformation to labyrinthine patterns. Indeed, a plethora of defects are observed in the labyrinthine patterns shown in Fig. 2. Conversely, the elimination of these defects plays a crucial role in the transition from a quenched state to an annealed state, where the system increases the spatial coherence. Each of these defects cannot be eliminated alone by continuous deformation of the stripes due to their topological properties. They can be removed through the pair annihilation. For instance, in Fig. 2, terminals are branched from junctions and they can be removed pair wisely by reducing the branching distance. These defects, known as topological defects, are widely recognized for playing a crucial role in the formation of periodic structures. By detecting the positions of defects, the evolution of the labyrinthine patterns would be systematically quantified. Specifically in the context of magnetic labyrinthine patterns, a much smaller dataset was used to detect these defects manually [4]. Recently, persistent homology has been used to extract the topological features of the labyrinthine patterns in a systematic way [38]. However, it is still difficult to detect the positions of defects and classify them into junctions and terminals. In this article, we achieved the systematic detection. To quantify the evolution of the labyrinthine patterns, we applied the TM-CNN technique to the 444 images and investigated how the number of defects and their locations changes step by step. Fig. 6 illustrates the step dependence of the number of junctions and terminals during the demagnetization process. Results from 6 different experimental runs were averaged to estimate the number of defects. In the initial stages of the demagnetization process, there are approximately 800 defects. The number of defects sharply decreases around step 5 and remains nearly unchanged from step 10 onward. Consequently, the transition to the quenched state is inferred to start before step 5 and be completed by step 10. The reduction in the number of defects during the demagnetization process is compatible with the naive expectation based on the physical argument of a decrease in the number of defects associated with the increased spatial coherence of the stripes. Furthermore, the number of junctions and terminals are close, which is consistent with the topological argument that junctions and terminals are paired. Further quantification of the evolution of the labyrinthine patterns based on the spatial distribution of the defects (and not only on their number) is discussed in another article [6]. V. CONCLUSION In this work, we presented a new algorithm named TMCNN to detect defects in magnetic labyrinthine patterns, contributing to a pioneering analysis in material science. Our study characterized the evolution of junctions and terminals in magnetic stripes during demagnetization procedures, aiming at better understanding defect arrangement in magnetic materials [6]. TM-CNN employs a two-stage detection procedure, combining template matching for initial detection and a convolutional network classifier for refining misdetections. This approach ensures a high detection accuracy and facilitates dataset annotation through a semi-automatic procedure. In our experiments, TM-CNN exhibited performance superior to other techniques, achieving an impressive F1 score of 0.988. This high performance is mainly due to TMCNN’s ability to locate small and clustered objects. TM-CNN achieves almost 100% accuracy with a simple CNN classifier with less than half a million parameters and can be used even on computers without GPUs. While TM-CNN was developed for defect detection in labyrinthine magnetic patterns, its potential applications are not limited to this field. 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