Real-space visualization of atomic displacements in a long-wavelength charge density wave using cryogenic 4D-STEM

EuAl4, a known skyrmion magnet, represents a class of materials that show complex electronic behaviors involving long-wavelength charge density wave (CDW). Here we realize direct real-space imaging of the concomitant periodic lattice distortion (PLD) with picometer precision in EuAl4. Simultaneous imaging of microstructure, polarization, and interatomic distance is made possible using cryogenic four-dimensional scanning transmitting electron microscopy (cryo-4DSTEM). With this approach, we determined that the PLD in EuAl4 incorporates two out-of-phase atomic displacement modes on the Eu and Al sublattices. The PLD introduces periodic local symmetry fluctuations from the average symmetry of the bulk EuAl4 crystal. This critical local structural insight helps understanding of charge-spin-lattice couplings behind the intertwined quantum order in EuAl4. Our results also demonstrate cryo-4DSTEM as an indispensable approach for probing CDW and related quantum materials at low temperatures.