Thermal cycling induced alteration of the stacking order and spin-flip in the room temperature van der Waals magnet Fe$_5$GeTe$_2$

The magnetic properties of the quasi-two-dimensional van der Waals magnet Fe$_{5-\delta}$GeTe$_2$ (F5GT), which has a high ferromagnetic ordering temperature $T_{\text{C}}$ $\sim$ 315 K, remains to be better understood. It has been demonstrated that the magnetization of F5GT is sensitive to both the Fe deficiency ${\delta}$ and the thermal cycling history. Here, we investigate the structural and magnetic properties of F5GT with a minimal Fe deficiency ($|{\delta}|$ $\le$ 0.1), utilizing combined x-ray and neutron scattering techniques. Our study reveals that the quenched F5GT single crystals experience an irreversible, first-order transition at $T_{\text{S}}$ $\sim$ 110 K upon first cooling, where the stacking order partly or entirely converts from ABC-stacking to AA-stacking order. Importantly, the magnetic properties, including the magnetic moment direction and the enhanced $T_{\text{C}}$ after the thermal cycling, are intimately related to the alteration of the stacking order. Our work highlights the significant influence of the lattice symmetry to the magnetism in F5GT.