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We report differential phase contrast scanning transmission electronmicroscopy (TEM) of nanoscale magnetic objects in Kagome ferromagnetFe$_3$Sn$_2$ nanostructures. This technique can directly detect the deflectionangle of a focused electron beam, thus allowing clear identification of thereal magnetic structures of two magnetic objects including three-ring andcomplex arch-shaped vortices in Fe$_3$Sn$_2$ by Lorentz transmission electronmicroscopy imaging. Numerical calculations based on real material-specificparameters well reproduced the experimental results, showing that the magneticobjects can be attributed to integral magnetizations of two types of complexthree-dimensional (3D) magnetic skyrmion bubbles with depth-modulated spintwisting. Magnetic configurations obtained using the high-resolution TEM aregenerally considered as two-dimensional (2D) magnetic objects previously. Ourresults imply the importance of the integral magnetizations of underestimated3D magnetic structures in 2D TEM magnetic characterizations.

Two-dimensional characterization of three-dimensional magnetic bubbles in Fe$_3$Sn$_2$ nanostructures