Machine-learning-based detection of spin structures

One of the most important magnetic spin structures is the topologically stabilized skyrmion quasiparticle. Its interesting physical properties make it a candidate for memory and efficient neuromorphic computation schemes. For device operation, the detection of the position, shape, and size of skyrmions is required and magnetic imaging is typically employed. A frequently used technique is magneto-optical Kerr microscopy, in which, depending on the sample’s material composition, temperature, material growing procedures, etc., the measurements suffer from noise, low contrast, intensity gradients, or other optical artifacts. Conventional image analysis packages require manual treatment, and a more automatic solution is required. We report a convolutional neural network specifically designed for segmentation problems to detect the position and shape of skyrmions in our measurements. The network is tuned using selected techniques to optimize predictions and, in particular, the number of detected classes is found to govern the performance. The results of this study show that a well-trained network is a viable method of automating data preprocessing in magnetic microscopy. The approach is easily extendable to other spin structures and other magnetic imaging methods.

Figure 1

Two-class model predictions. The pictures on the left show MOKE measurements, which are difficult to mask using traditional methods; the middle column shows the labels of these measurements; and the right column shows predictions made by these two-class models. (a) A sample with few defects. The inset visualizes the spin structure of a skyrmion. The centre of the skyrmion with the magnetization “down” leads to black contrast and the surrounding area with the magnetization “up” leads to light gray contrast. Note that the colored Bloch domain wall in the inset is not visible in the experimental image due to the limited spatial resolution. (b) Label of (a). (c) Prediction of (a). (d) This sample has defects and a slight brightness gradient. (e) Label of (d). (f) Prediction of (d) where the green square indicates an example of how these models predict defects. (g) This sample is particularly noisy and the black square indicates an enlarged area. (h) A 4 times enlargement of the label of (g). (i) A 4 times enlargement of a prediction of (g) (note the small speckles indicating incorrect detection). The inset skyrmion sketch in (a) is adapted from Ref. [1].

Figure 2

Network topology for the CNN used in this study. The left side is the contraction path and the right side is the expansion path. The gray arrows connecting both paths indicate the skip connections. Figure is adapted from Ref. [22].

Figure 3

Inverted data predictions. (a) Color-inverted sample. (b) The prediction. This figure shows that any dark pixel is nearly always automatically classified as a skyrmion for the two-class case. The splash in the bottom left corner is likely caused by the fact that the sample has a color gradient where the image gets progressively darker from the bottom left to the top right corner. (c) Grayscale pixels ranging from 0 to 88 are predicted to be skyrmions 100% of the time.

Figure 4

Three-class model predictions. The pictures on the left (a),(d),(g) show MOKE measurements; those in the middle column (b),(e),(h) show the labels (note the defects labeled in green); and those on the right (c),(f),(i) show predictions made by these three-class models. (c),(d) show that this model architecture can tell the difference between skyrmions and defects. As can be noted in (i), this kind of model no longer predicts small skyrmion speckles in noisy images.

Figure 5

Performance statistics of the benchmark and master models on the three sets. Plot comparing the average MCC and MCC standard deviation of the three-class benchmark model and the master model on all three datasets. The average value is written next to the respective distribution.

Figure 6

Predictions on the size of the skyrmions in the test set, normalized per image to account for skyrmion densities varying strongly throughout the set images. This figure shows the skyrmion size distributions of the test set skyrmion labels and the master model predictions on this test set. The total numbers of labeled (45 707) and predicted (45 779) skyrmion objects coincide well.

Figure 7

Inverted data predictions from the master model and model trained on inversion data augmentations. (a) The inverted sample. (b) The master model prediction. (c) The inversion model predictions.