4D-STEM磁性测量Python程序包： 功能介绍与应用

4D-STEM磁性测量Python程序包： 功能介绍与应用

程 涛#，贾英泽#，汪陆洋，刘杨瑞，裴旭东，刘 畅，杜海峰， 葛炳辉*，宋东升* (信息材料与智能感知安徽省实验室，安徽大学杂化材料结构与功能调控教育部重点实验室，安徽大学物质科学与信息技术研究院，安徽 合肥 230601)

摘 要 了解磁结构对于深入探究磁性材料中的磁行为及其相关现象具有至关重要的意义。四维扫描透射电子显微镜（4D-STEM）技术的出现，为定量分析磁场提供了一种全新的技术手段，特别是通过精确定位衍射盘的位置，来解析磁场在纳米尺度上的分布情况。本文介绍了一款集成了多种衍射盘定位算法的Python程序包，并通过对实验数据的分析，探讨了该程序包中核心算法的性能及其适用场景。

关键词 4D-STEM；衍射盘定位；算法分析

中图分类号：TP317.4；TP302.7；TN16 文献标识码：B Doi:10.3969/j.issn.1000-6281.2025.02.010

4D-STEM magnetic measurement python package: Functional introduction and application

CHENG Tao#，JIA Yingzei#，WANG Luyang，LIU Yangrui，PEI Xudong，LIU Chang，DU Haifeng， GE Binghui*，SONG Dongsheng*

(Information Materials and Intelligent Sensing Laboratory of Anhui Province, Key Laboratory of Structure and Functional Regulation of Hybrid Materials of Ministry of Education, Institutes of Physical Science and Information Technology, Anhui University, Hefei Anhui 230601, China)

Abstract A comprehensive understanding of the magnetic structure is crucial for investigating the magnetic behavior and associated phenomena in magnetic materials. Four-dimensional scanning transmission electron microscopy (4D-STEM) technology offers a novel technical avenue for the quantitative analysis of magnetic fields, particularly through the precise positioning of the diffraction disk, the distribution of the magnetic field can be determined at the nanoscale. This work presents a Python package that incorporates various diffraction disk positioning algorithms and, through an analysis of experimental data, evaluates the performance of the core algorithm within the package and explores its potential applications.

Keywords 4D-STEM; diffraction disk positioning; algorithm analysis

[1] PETFORD-LONG A K, CHAPMAN J N. Lorentz microscopy[M]. Magnetic Microscopy of Nanostructures. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005: 67-86.

[2] PHATAK C, PETFORD-LONG A K, De GRAEF M. Recent advances in Lorentz microscopy[J]. Current Opinion in Solid State and Materials Science, 2016, 20(2): 107-114.

[3] GRUNDY P J, TEBBLE R S. Lorentz electron microscopy[J]. Advances in Physics, 1968, 17(66): 153-242.

[4] TONOMURA A. Applications of electron holography[J]. Reviews of Modern Physics, 1987, 59(3): 639-669.

[5] MIDGLEY P A, DUNIN-BORKOWSKI R E. Electron tomography and holography in materials science[J]. Nature Materials, 2009, 8(4): 271-280.

[6] CHAPMAN J N, McFADYEN I R, McVITIE S. Modified differential phase contrast Lorentz microscopy for improved imaging of magnetic structures[J]. IEEE Transactions on Magnetics, 1990, 26(5): 1506-1511.

[7] CAMPANINI M, NASI L, ALBERTINI F, et al. Disentangling nanoscale electric and magnetic fields by time-reversal operation in differential phase-contrast STEM[J]. Applied Physics Letters, 2020, 117(15): 154102.

[8] LIU Y, FERRIER R P. Quantitative evaluation of a thin film recording head field using the DPC mode of Lorentz electron microscopy[J]. IEEE Transactions on Magnetics, 1995, 31(6): 3373-3375.

[9] SEKI T, IKUHARA Y, SHIBATA N. Toward quantitative electromagnetic field imaging by differential-phase-contrast scanning transmission electron microscopy[J]. Microscopy, 2021, 70(1): 148-160.

[10] MURAKAMI Y O, SEKI T, KINOSHITA A, et al. Magnetic-structure imaging in polycrystalline materials by specimen-tilt series averaged DPC STEM[J]. Microscopy, 2020, 69(5): 312-320.

[11] KOHNO Y, SEKI T, FINDLAY S D, et al. Real-space visualization of intrinsic magnetic fields of an antiferromagnet[J]. Nature, 2022, 602(7896): 234-239.

[12] SCHATTSCHNEIDER P, RUBINO S, HÉBERT C, et al. Detection of magnetic circular dichroism using a transmission electron microscope[J]. Nature, 2006, 441(7092): 486-488.

[13] SONG D, WANG Z, ZHU J. Magnetic measurement by electron magnetic circular dichroism in the transmission electron microscope[J]. Ultramicroscopy, 2019, 201: 1-17.

[14] CHEN Z, TURGUT E, JIANG Y, et al. Lorentz electron ptychography for imaging magnetic textures beyond the diffraction limit[J]. Nature Nanotechnology, 2022, 17(11): 1165-1170.

[15] JEONG J, CAUTAERTS N, DEHM G, et al. Automated crystal orientation mapping by precession electron diffraction-assisted four-dimensional scanning transmission electron microscopy using a scintillator-based CMOS detector[J]. Microscopy and Microanalysis, 2021, 27(5): 1102-1112.

[16] OZDOL V B, GAMMER C, JIN X G, et al. Strain mapping at nanometer resolution using advanced nano-beam electron diffraction[J]. Applied Physics Letters, 2015, 106(25) : 253107.

[17] COOPER D, DENNEULIN T, BERNIER N, et al. Strain mapping of semiconductor specimens with nm-scale resolution in a transmission electron microscope[J]. Micron, 2016, 80: 145-165.

[18] HAN Y, NGUYEN K, CAO M, et al. Strain mapping of two-dimensional heterostructures with subpicometer precision[J]. Nano Letters, 2018, 18(6): 3746-3751.

[19] WU L, HAN M G, ZHU Y. Toward accurate measurement of electromagnetic field by retrieving and refining the center position of non-uniform diffraction disks in Lorentz 4D-STEM[J]. Ultramicroscopy, 2023, 250: 113745.

[20] YUEN H K, PRINCEN J, ILLINGWORTH J, et al. Comparative study of Hough transform methods for circle finding[J]. Image and Vision Computing, 1990, 8(1): 71-77.

[21] HASTAWAN A F, SOESANTI I, SETIAWAN N A. Effective method for circle detection based on transformation of chain code direction[C]. AIP Conference Proceedings[J]. AIP Publishing, 2016, 1755(1) : 070004.

[22] LIU Y, DENG H, ZHANG Z, et al. A fast circle detector with efficient arc extraction[J]. Symmetry, 2022, 14(4): 734.

[23] CUEVAS E, SENCIÓN-ECHAURI F, ZALDIVAR D, et al. Multi-circle detection on images using artificial bee colony (ABC) optimization[J]. Soft Computing, 2012, 16: 281-296.

[24] FOURIE J. Robust circle detection using harmony search[J]. Journal of Optimization, 2017, 2017(1): 9710719.

[25] GRIEB T, KRAUSE F F, MÜLLER-CASPARY K, et al. 4D-STEM at interfaces to GaN: Centre-of-mass approach & NBED-disc detection[J]. Ultramicroscopy, 2021, 228: 113321.

[26] MAHR C, MÜLLER-CASPARY K, GRIEB T, et al. Accurate measurement of strain at interfaces in 4D-STEM: A comparison of various methods[J]. Ultramicroscopy, 2021, 221: 113196.

[27] PEKIN T C, GAMMER C, CISTON J, et al. Optimizing disk registration algorithms for nanobeam electron diffraction strain mapping[J]. Ultramicroscopy, 2017, 176: 170-176.

[28] MAHR C, MÜLLER-CASPARY K, GRIEB T, et al. Theoretical study of precision and accuracy of strain analysis by nano-beam electron diffraction[J]. Ultramicroscopy, 2015, 158: 38-48.

[29] SAVITZKY B H, ZELTMANN S E, HUGHES L A, et al. py4DSTEM: A software package for four-dimensional scanning transmission electron microscopy data analysis[J]. Microscopy and Microanalysis, 2021, 27(4): 712-743.

[30] PIEROBON L, SCHÄUBLIN R E, LÖFFLER J F. Comparison of conventional and Lorentz transmission electron microscopy in magnetic imaging of permanent magnets[J]. Applied Physics Letters, 2021, 119 (2): 022401.

[31] PADGETT E, HOLTZ M E, CUEVA P, et al. The exit-wave power-cepstrum transform for scanning nanobeam electron diffraction: robust strain mapping at subnanometer resolution and subpicometer precision[J]. Ultramicroscopy, 2020, 214: 112994.

[32] MÜLLER K, ROSENAUER A, SCHOWALTER M, et al. Strain measurement in semiconductor heterostructures by scanning transmission electron microscopy[J]. Microscopy and Microanalysis, 2012, 18(5): 995-1009.

[33] YUAN R, ZHANG J, ZUO J M. Lattice strain mapping using circular Hough transform for electron diffraction disk detection[J]. Ultramicroscopy, 2019, 207: 112837.

[34] ZELTMANN S E, MÜLLER A, BUSTILLO K C, et al. Patterned probes for high precision 4D-STEM bragg measurements[J]. Ultramicroscopy, 2020, 209: 112890.

[35] NGUYEN K X, ZHANG X S, TURGUT E, et al. Disentangling magnetic and grain contrast in polycrystalline FeGe thin films using four-dimensional Lorentz scanning transmission electron microscopy[J]. Physical Review Applied, 2022, 17(3): 034066.

[36] WANG B, BAGUÉS N, LIU T, et al. Extracting weak magnetic contrast from complex background contrast in plan-view FeGe thin films[J]. Ultramicroscopy, 2022, 232: 113395.

[37] BOUREAU V, STAŇO M, ROUVIERE J L, et al. High-sensitivity mapping of magnetic induction fields with nanometer-scale resolution: Comparison of off-axis electron holography and pixelated differential phase contrast[J]. Journal of Physics D: Applied Physics, 2020, 54(8): 085001.

[38] NGUYEN K X, HUANG J, KARIGERASI M H, et al. Angstrom-scale imaging of magnetization in antiferromagnetic Fe2As via 4D-STEM[J]. Ultramicroscopy, 2023, 247: 113696.

[39] KRAJNAK M, McGROUTHER D, MANEUSKI D, et al. Pixelated detectors and improved efficiency for magnetic imaging in STEM differential phase contrast[J]. Ultramicroscopy, 2016, 165: 42-50.

[40] OPHUS C. Four-dimensional scanning transmission electron microscopy (4D-STEM): From scanning nanodiffraction to ptychography and beyond[J]. Microscopy and Microanalysis, 2019, 25(3): 563-582.

[41] GOH T Y, BASAH S N, YAZID H, et al. Performance analysis of image thresholding: Otsu technique[J]. Measurement, 2018, 114: 298-307. [42] ZHU C, BYRD R H, LU P, et al. Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization[J]. ACM Transactions on Mathematical Software (TOMS), 1997, 23(4): 550-560.

[43] ZHENG F, RYBAKOV F N, BORISOV A B, et al. Experimental observation of chiral magnetic bobbers in B20-type FeGe[J]. Nature Nanotechnology, 2018, 13(6): 451-455.

[44] KOVÁCS A, CARON J, SAVCHENKO A S, et al. Mapping the magnetization fine structure of a lattice of Bloch-type skyrmions in an FeGe thin film[J]. Applied Physics Letters, 2017, 111(19): 192410.