Machine-Learning Recognition of Dzyaloshinskii-Moriya Interaction from Magnetometry

TL;DR

It is shown that a convolutional neural network can extract the DMI magnitude from minor hysteresis loops, or magnetic "fingerprints" of a material, which are readily available by conventional magnetometry measurements.

Abstract

The Dzyaloshinskii-Moriya interaction (DMI), which is the antisymmetric part of the exchange interaction between neighboring local spins, winds the spin manifold and can stabilize non-trivial topological spin textures. Since topology is a robust information carrier, characterization techniques that can extract the DMI magnitude are important for the discovery and optimization of spintronic materials. Existing experimental techniques for quantitative determination of DMI, such as high-resolution magnetic imaging of spin textures and measurement of magnon or transport properties, are time consuming and require specialized instrumentation. Here we show that a convolutional neural network can extract the DMI magnitude from minor hysteresis loops, or magnetic "fingerprints" of a material. These hysteresis loops are readily available by conventional magnetometry measurements. This provides a convenient tool to investigate topological spin textures for next-generation information processing.

Figures (6)

• Figure 1: Setup of the machine-learning problem. (a) A typical family of FORCs in our dataset. One minor loop is shown by the red dashed line, whereas the full hysteresis loop is denoted by the solid blue line. Other minor loops are illustrated by the gray dotted curves. (b) The input image corresponding to the FORCs shown in (a), with each pixel denoting one discrete point during the field scan. The magnetization during the field scan is normalized to a 1-byte integer between $0$ and $255$, corresponding to the brightness of each pixel. (c) The structure of the CNN. The top path (red) denotes the distribution matching method, whereas the lower path (blue) represents a conventional regression. (d) The convergence of the training. The distribution-matching and conventional regression results are denoted by the red and blue curves, respectively. The inset illustrates the scheme of the loss function in the distribution-matching method.
• Figure 2: Performance of the CNN. (a-b) The statistics of the training outcome among the training set (a) and the testing set (b). The dashed green lines denote a prediction error of 20% marking our threshold for good guesses. The red arrows in (b) denote four representative cases (i-iv) among the faint band of wrong predictions.
• Figure 3: The statistics of the predictions. The distributions of $A_{\textrm{ex}}$ and $d_{0}$ among the testing data are shown in (a) and (b), respectively. The red histogram denotes the predictions with errors greater than $20\%$, whereas the blue ones illustrate the entire test set. (c) The distribution of $M_{s}$ and $K_{u}$ among the wrong predictions. (d) The distribution of $\frac{K_{\textrm{shape}}}{K_{u}}$ among the wrong predictions (red) and the entire test set (blue).
• Figure 4: Example inputs corresponding to uncertain predictions. (a-d) The hysteresis loops for Cases (i-iv) highlighted in Fig. \ref{['fig:TrainningAndTestingResults']}(b). The inset in each case illustrates the corresponding input image fed to the CNN.
• Figure 5: Evolution of CNN performance. (a-c) The evolution of the CNN performance during training. The three panels (a-c) correspond to Epochs 3, 50 and 385, respectively.