Space Group Symmetry of Chiral Fe-deficient van der Waals Magnet ${\text{Fe}}_{\text{3-x}}{\text{GeTe}}_{\text{2}}$ Probed by Convergent Beam Electron Diffraction

The crystal symmetry of Fe-deficient ${\text{Fe}}_{\text{3-x}}{\text{GeTe}}_{\text{2}}$ at room temperature has been investigated by a combination of selected-area electron diffraction (SAED) and convergent-beam electron diffraction (CBED). By symmetry analysis of CBED patterns along different zone axis, the space group of ${\text{Fe}}_{\text{3-x}}{\text{GeTe}}_{\text{2}}$ at room-temperature has been identified as $P{6}_{3}mc$ (No.186), which derives from the high-symmetry parent system ${\text{Fe}}_{\text{3}}{\text{GeTe}}_{\text{2}}$ ($P{6}_3\mathrm{/}mmc$) by breaking the mirror symmetry along the 6-fold rotation axis. The $P3m1$ (No.156) space group previously reported for ${\text{Fe}}_{\text{3-x}}{\text{GeTe}}_{\text{2}}$ is a subgroup of $P{6}_{3}mc$ suggesting further possible symmetry breaks in this non-stoichiometric system.