High-Spin Orbital Interactions Across van der Waals Gaps Controlling the Interlayer Ferromagnetism in van der Waals Ferromagnets.

We examined what interactions control the sign and strength of the interlayer coupling in van der Waals ferromagnets such as Fe 3- x GeTe 2 , Cr 2 Ge 2 Te 6 , CrI 3 , and VI 3 to find that high-spin orbital interactions across the van der Waals gaps are a key to understanding their ferromagnetism. Interlayer ferromagnetic coupling in Fe 3- x GeTe 2 , Cr 2 Ge 2 Te 6 , and CrI 3 is governed by the high-spin two-orbital two-electron destabilization, but that in VI 3 by the high-spin four-orbital two-electron stabilization. These interactions explain a number of seemingly puzzling observations in van der Waals ferromagnets.