Interlayer ferromagnetic order revealed through pressure-enhanced interlayer exchange coupling in Fe${}_3$GaTe${}_2$

Van der Waals ferromagnets possess finite interlayer magnetic coupling despite their layered crystal structures, and this coupling plays an important role in determining their magnetic properties. In this study, we performed magnetization measurements on high-quality Fe${}_3$GaTe${}_2$ single crystals while selectively tuning the interlayer coupling using hydrostatic pressure. We identified two characteristic temperatures, $T_{\mathrm{i}\mathrm{n}\mathrm{f}1}$ and $T_{\mathrm{i}\mathrm{n}\mathrm{f}2}$, below the Curie temperature with opposite pressure dependences: $T_{\mathrm{i}\mathrm{n}\mathrm{f}1}$ is associated with thermally activated domain-wall depinning, whereas $T_{\mathrm{i}\mathrm{n}\mathrm{f}2}$ reflects the formation of interlayer ferromagnetic order. Both temperatures exhibit pronounced pressure dependences, in sharp contrast to the nearly pressure-independent Curie temperature associated with intralayer ferromagnetic order. First-principles calculations revealed a substantial pressure-induced enhancement of the interlayer exchange interaction and reasonably reproduced $T_{\mathrm{i}\mathrm{n}\mathrm{f}2}$ and its pressure dependence. These results demonstrate that the emergence of interlayer magnetic ordering can be predicted from the microscopic interlayer exchange coupling, establishing a predictive framework for understanding and designing interlayer coupling phenomena in layered magnetic materials.