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Fluctuations and stochastic transitions are ubiquitous in nanometre-scale systems, especially in the presence of disorder. However, their direct observation has so far been impeded by a seemingly fundamental, signal-limited compromise between spatial and temporal resolution. Here we develop coherent correlation imaging (CCI) to overcome this dilemma. Our method begins by classifying recorded camera frames in Fourier space. Contrast and spatial resolution emerge by averaging selectively over same-state frames. Temporal resolution down to the acquisition time of a single frame arises independently from an exceptionally low misclassification rate, which we achieve by combining a correlation-based similarity metric1,2 with a modified, iterative hierarchical clustering algorithm3,4. We apply CCI to study previously inaccessible magnetic fluctuations in a highly degenerate magnetic stripe domain state with nanometre-scale resolution. We uncover an intricate network of transitions between more than 30 discrete states. Our spatiotemporal data enable us to reconstruct the pinning energy landscape and to thereby explain the dynamics observed on a microscopic level. CCI massively expands the potential of emerging high-coherence X-ray sources and paves the way for addressing large fundamental questions such as the contribution of pinning5–8 and topology9–12 in phase transitions and the role of spin and charge order fluctuations in high-temperature superconductivity13,14.

Magnetic domains play a fundamental role in physics of magnetism and its technological applications. Dynamics of antiferromagnetic domains is poorly understood, although antiferromagnets are expected to be extensively used in future electronic devices wherein it determines the stability and operational speed. Dynamics of antiferromagnets also features prominently in the studies of topological quantum matter. Real-space imaging of fluctuating antiferromagnetic domains is therefore highly desired but has never been demonstrated. We use coherent x-ray diffraction to obtain videos of fluctuating micrometer-scale antiferromagnetic domains in Ni 2 MnTeO 6 on time scales from 10 −1 to 10 3 s. In the collinear phase, thermally activated domain wall motion is observed in the vicinity of the Néel temperature. Unexpectedly, the fluctuations persist through the full range of the higher-temperature helical phase. These observations illustrate the high potential significance of the dynamic domain imaging in phase transition studies and in magnetic device research.

Charge density waves (CDWs) in the cuprate high-temperature superconductors have evoked much interest, yet their typical short-range nature has raised questions regarding the role of disorder. Here we report a resonant X-ray diffraction study of ZrTe\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{3}$$\end{document}3, a model CDW system, with focus on the influence of disorder. Near the CDW transition temperature, we observe two independent signals that arise concomitantly, only to become clearly separated in momentum while developing very different correlation lengths in the well-ordered state that is reached at a distinctly lower temperature. Anomalously slow dynamics of mesoscopic charge domains are further found near the transition temperature, in spite of the expected strong thermal fluctuations. Our observations signify the presence of distinct experimental fingerprints of pristine and disorder-perturbed CDWs. We discuss the latter also in the context of Friedel oscillations, which we argue might promote CDW formation via a self-amplifying process., The role of disorder in the formation of charge density waves (CDWs) remains elusive in typical CDW materials. Here, the authors report coexisting diffraction signals and anomalous slow dynamics of charge domains near the CDW transition temperature in ZrTe\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{3}$$\end{document}3, suggesting as fingerprints of pristine and disorder-perturbed CDWs.