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The first-order reversal curve (FORC) method is a macroscopic measurement technique that can be used to extract quantitative and microscopic properties of hysteretic systems. Using magnetic transmission x-ray microscopy (MTXM), local element-specific FORC measurements are performed on a 20 nm thick film of CoTb. The FORCs measured with microscopy reveal a step-by-step domain evolution under the magnetic field cycling protocol and provide a direct visualization of the mechanistic interpretation of FORC diagrams. They are compared with magnetometry FORCs and show good quantitative agreement. Furthermore, the high spatial resolution and element-specific sensitivity of MTXM provide new capabilities to measure FORCs in small regions or specific phases within multicomponent systems, including buried layers in heterostructures. The ability to perform FORCs on very small features is demonstrated with the MTXM-FORC measurement of a rectangular microstructure with vortex-like Landau structures. This work demonstrates the confluence of two uniquely powerful techniques to achieve quantitative insight into nanoscale magnetic behavior. 

Abstract Magnetic skyrmions exhibit unique, technologically relevant pseudo‐particle behaviors which arise from their topological protection, including well‐defined, 3D dynamic modes that occur at microwave frequencies. During dynamic excitation, spin waves are ejected into the interstitial regions between skyrmions, creating the magnetic equivalent of a turbulent sea. However, since the spin waves in these systems have a well‐defined length scale, and the skyrmions are on an ordered lattice, ordered structures from spin‐wave interference can precipitate from the chaos. This work uses small‐angle neutron scattering (SANS) to capture the dynamics in hybrid skyrmions and investigate the spin‐wave structure. Performing simultaneous ferromagnetic resonance and SANS, the diffraction pattern shows a large increase in low‐angle scattering intensity, which is present only in the resonance condition. This scattering pattern is best fit using a mass fractal model, which suggests the spin waves form a long‐range fractal network. The fractal structure is constructed of fundamental units with a size that encodes the spin‐wave emissions and are constrained by the skyrmion lattice. These results offer critical insights into the nanoscale dynamics of skyrmions, identify a new dynamic spin‐wave fractal structure, and demonstrate SANS as a unique tool to probe high‐speed dynamics. 

Abstract Integration of a quantum anomalous Hall insulator with a magnetically ordered material provides an additional degree of freedom through which the resulting exotic quantum states can be controlled. Here, an experimental observation is reported of the quantum anomalous Hall effect in a magnetically‐doped topological insulator grown on the antiferromagnetic insulator Cr₂O₃. The exchange coupling between the two materials is investigated using field‐cooling‐dependent magnetometry and polarized neutron reflectometry. Both techniques reveal strong interfacial interaction between the antiferromagnetic order of the Cr₂O₃and the magnetic topological insulator, manifested as an exchange bias when the sample is field‐cooled under an out‐of‐plane magnetic field, and an exchange spring‐like magnetic depth profile when the system is magnetized within the film plane. These results identify antiferromagnetic insulators as suitable candidates for the manipulation of magnetic and topological order in topological insulator films.